| Title: | Case-Cohort Cox Survival Inference |
|---|---|
| Description: | Cox model inference for relative hazard and covariate-specific pure risk estimated from stratified and unstratified case-cohort data as described in Etievant, L., Gail, M.H. (Lifetime Data Analysis, 2024) <doi:10.1007/s10985-024-09621-2>. |
| Authors: | Lola Etievant [cre, aut], Mitchell H. Gail [aut], Bill Wheeler [aut] |
| Maintainer: | Lola Etievant <[email protected]> |
| License: | GPL-2 |
| Version: | 0.0.36 |
| Built: | 2024-11-23 05:33:48 UTC |
| Source: | https://github.com/cran/CaseCohortCoxSurvival |
This package uses case-cohort data to estimate log-relative hazard, baseline hazards at each unique event time, cumulative baseline hazard in a given time interval and pure risk on the time interval and for a given covariate profile, under the Cox model. For the corresponding variance estimation, it relies on influence functions and follows the complete variance decomposition, to enable correct analysis of case-cohort data with and without stratification, weight calibration or missing phase-two covariate data.
The package provides functions implementing the methods described in Etievant and Gail (2024). More precisely, it includes
a main driver function, caseCohortCoxSurvival.
one function, estimatePureRisk, to estimate pure risks and the corresponding variances with additional covariate profiles.
three functions, estimation, estimation.CumBH and
estimation.PR, for parameters estimation.
four functions, influences, influences.RH,
influences.CumBH and influences.PR, for influence functions
derivation when estimation is with design or calibrated weights and from a
case-cohort consisting of the subcohort and cases not in the subcohort
(i.e., case-cohort obtained from two phases of sampling).
four functions, influences.missingdata, influences.RH.missingdata,
influences.CumBH.missingdata and influences.PR.missingdata,
for influence functions derivation when estimation is with design
weights and from a case-cohort when covariate information was missing for
certain individuals in the phase-two data
(i.e., case-cohort obtained from three phases of sampling).
two functions, variance and variance.missingdata,
for variance estimation following complete variance
decomposition (with design or calibrated weights and without missing
phase-two data, or with design weights and missing phase-two covariate data).
one function, robustvariance, for robust variance estimation.
one function, auxiliary.construction, to compute the auxiliary
variables proposed by Breslow et al. (Stat. Biosci., 2009), Breslow and Lumley (IMS, 2013), and Shin et al. (Biometrics, 2020),.
one function, calibration, for weight calibration.
one function, estimation.weights.phase3, for estimating the phase-three weights.
Lola Etievant, Mitchell H. Gail
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
Etievant, L., Gail, M. H. (2024). Software Application Profile: CaseCohortCoxSurvival: an R package for case-cohort inference for relative hazard and pure risk under the Cox model. Submitted.
Creates the auxiliary variables proposed by Breslow et al. (Stat. Biosci., 2009), Breslow and Lumley (IMS, 2013), and proposed by Shin et al. (Biometrics, 2020).
auxiliary.construction(mod, Tau1 = NULL, Tau2 = NULL, method = "Breslow", time.on.study = NULL, casecohort = NULL)auxiliary.construction(mod, Tau1 = NULL, Tau2 = NULL, method = "Breslow", time.on.study = NULL, casecohort = NULL)
mod |
A cox model object, result of function coxph run on the cohort data with imputed covariate values. |
Tau1 |
Left bound of the time interval considered for the cumulative baseline hazard. Default is the first event time. |
Tau2 |
Right bound of the time interval considered for the cumulative baseline hazard. Default is the last event time. |
method |
"Breslow", "Breslow2013" or "Shin" to specify the algorithm to construct the auxiliary variables. The default is "Breslow". |
time.on.study |
Total folow-up time in |
casecohort |
Data frame containing the casecohort data.
It must include columns "weights" containing
the design weights and "id" as an id variable.
Required for |
Construction of the auxiliary variables can follow Breslow et al. (2009), Breslow and Lumley (2013), or Shin et al. (2020) (method). It relies on predictions of the phase-two covariates for all members of the cohort. The auxiliary variables are given by (i) the influences for the log-relative hazard parameters estimated from the Cox model with imputed cohort data; (ii) the influences for the cumulative baseline parameter estimated from the Cox model with imputed cohort data; (iii) the products of total follow-up time (on the time interval for which pure risk is to be estimated) with the estimated relative hazard for the imputed cohort data, where the log-relative hazard parameters are estimated from the Cox model with case-cohort data and weights calibrated with (i). When method = Breslow, calibration of the design weights is against (i), as proposed by Breslow et al. (2009) to improve efficiency of case-cohort estimates of relative hazard. When method = Breslow2013, calibration of the design weights is against (i) and (ii), as proposed by Breslow and Lumley (2013) to also improve efficiency of case-cohort estimates of cumulative baseline hazard. When method = Shin, calibration is against (i) and (iii), as proposed by Shin et al. (2020) to improve efficiency of relative hazard and pure risk estimates under the nested case-control design. See Etievant and Gail (2024).
Following Etievant and Gail (2024), in function caseCohortCoxSurvival
we only provide calibration
of the design weight as proposed by Breslow et al. (2009) or Shin et al. (2020).
A.RH.Breslow: matrix with the influences on the log-relative hazard,
estimated from the cohort with imputed phase-two covariate
values for method = "Breslow" and
method = "Breslow2013".
A.CumBH.Breslow: matrix with the influences on the cumulative baseline
hazard in [Tau1, Tau2],
estimated from the cohort with imputed phase-two
covariate values for method = "Breslow2013".
A.RH.Shin: matrix with the influences on the log-relative hazard,
estimated from the cohort with imputed phase-two covariate
values for method = "Shin".
A.PR.Shin: matrix with the products of total follow-up times in
[Tau1, Tau2] and estimated relative hazards,
estimated from the cohort with imputed phase-two
covariate values for method = "Shin".
Breslow, N.E. and Lumley, T. (2013). Semiparametric models and two-phase samples: Applications to Cox regression. From Probability to Statistics and Back: High-Dimensional Models and Processes, 9, 65-78.
Breslow, N.E., Lumley, T., Ballantyne, C.M., Chambless, L.E. and Kulich, M. (2009). Improved Horvitz-Thompson Estimation of Model Parameters from Two-phase Stratified Samples: Applications in Epidemiology. Statistics in Biosciences, 1, 32-49.
Shin Y.E., Pfeiffer R.M., Graubard B.I., Gail M.H. (2020) Weight calibration to improve the efficiency of pure risk estimates from case-control samples nested in a cohort. Biometrics, 76, 1087-1097.
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
calibration, influences, influences.RH,
influences.CumBH and influences.PR.
data(dataexample.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.stratified$cohort Tau1 <- 0 Tau2 <- 8 # Running the coxph model on the imputed cohort data mod.imputedcohort <- coxph(Surv(event.time, status) ~ X1.pred + X2 + X3.pred, data = cohort, robust = TRUE) # method = Breslow ret <- auxiliary.construction(mod.imputedcohort) # print auxiliary variables based on the log-relative hazard influences ret$A.RH.Breslow[1:5,] # Example for method = Shin, variables names must match with fitted model casecohort <- cohort[which(cohort$status == 1 | cohort$subcohort == 1),] # the stratified case-cohort casecohort$weights <- casecohort$strata.n / casecohort$strata.m casecohort$weights[which(casecohort$status == 1)] <- 1 casecohort[, "X1.pred"] <- casecohort[, "X1"] casecohort[, "X3.pred"] <- casecohort[, "X3"] time.on.study <- pmax(pmin(Tau2, cohort$event.time) - Tau1, 0) ret <- auxiliary.construction(mod.imputedcohort, method = "Shin", time.on.study = time.on.study, casecohort = casecohort) ret$A.PR.Shin[1:5]data(dataexample.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.stratified$cohort Tau1 <- 0 Tau2 <- 8 # Running the coxph model on the imputed cohort data mod.imputedcohort <- coxph(Surv(event.time, status) ~ X1.pred + X2 + X3.pred, data = cohort, robust = TRUE) # method = Breslow ret <- auxiliary.construction(mod.imputedcohort) # print auxiliary variables based on the log-relative hazard influences ret$A.RH.Breslow[1:5,] # Example for method = Shin, variables names must match with fitted model casecohort <- cohort[which(cohort$status == 1 | cohort$subcohort == 1),] # the stratified case-cohort casecohort$weights <- casecohort$strata.n / casecohort$strata.m casecohort$weights[which(casecohort$status == 1)] <- 1 casecohort[, "X1.pred"] <- casecohort[, "X1"] casecohort[, "X3.pred"] <- casecohort[, "X3"] time.on.study <- pmax(pmin(Tau2, cohort$event.time) - Tau1, 0) ret <- auxiliary.construction(mod.imputedcohort, method = "Shin", time.on.study = time.on.study, casecohort = casecohort) ret$A.PR.Shin[1:5]
Calibrates the design weights using the raking procedure.
calibration(A.phase2, design.weights, total, eta0 = NULL, niter.max = NULL, epsilon.stop = NULL)calibration(A.phase2, design.weights, total, eta0 = NULL, niter.max = NULL, epsilon.stop = NULL)
A.phase2 |
matrix with the values of the q auxiliary variables to be used for the calibration of the weights in the case-cohort (phase-two data). |
design.weights |
design weights to be calibrated. |
total |
vector of length q with un-weighted auxiliary variable totals in the whole cohort. |
eta0 |
vector of length q with initial values for |
niter.max |
maximum number of iterations for the iterative optimization algorithm. Default is 10^4 iterations. |
epsilon.stop |
threshold for the difference between the estimated weighted total and the total in the whole cohort. If this difference is less than the value of epsilon.stop, no more iterations will be performed. Default is 10^(-10). |
Calibration matches the weighted total of the auxiliary variables in the case-cohort
(with calibrated weights), to the un-weighted auxiliary variables total in the whole cohort.
In other words, it solves in
,
with the sampling indicator and the design weight of
individual in stratum , and with
the total in the whole cohort. See Etievant and Gail (2024). The Newton Raphson method is used to solve the optimization problem.
In the end, the calibrated weights of the case-cohort individuals are given by
, and
gives the estimated total.
eta.hat: vector of length q with final eta values.
calibrated.weights: vector with the calibrated weights for the individuals
in the case-cohort (phase-two data), computed from design.weights,
A.phase2 and eta.hat.
estimated.total: vector with the estimated totals, computed from the
calibrated.weights and A.phase2.
Deville, J.C. and Sarndal, C.E. (1992). Calibration Estimators in Survey Sampling. Journal of the American Statistical Association, 87, 376-382.
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
auxiliary.construction, influences, influences.RH, influences.CumBH and influences.PR.
data(dataexample.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.stratified$cohort casecohort <- cohort[which(cohort$status == 1 | cohort$subcohort == 1),] # the stratified case-cohort casecohort$weight <- casecohort$strata.n / casecohort$strata.m casecohort$weight[which(casecohort$status == 1)] <- 1 A <- dataexample.stratified$A # auxiliary variables values in the cohort indiv.phase2 <- casecohort$id q <- ncol(A) total <- colSums(A) A.phase2 <- A[indiv.phase2,] calib <- calibration(A.phase2 = A[indiv.phase2,], design.weights = casecohort$weight, total = total, eta0 = rep(0, q), niter.max = 10^3, epsilon.stop = 10^(-10)) #calib$calibrated.weights # print calibrated weightsdata(dataexample.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.stratified$cohort casecohort <- cohort[which(cohort$status == 1 | cohort$subcohort == 1),] # the stratified case-cohort casecohort$weight <- casecohort$strata.n / casecohort$strata.m casecohort$weight[which(casecohort$status == 1)] <- 1 A <- dataexample.stratified$A # auxiliary variables values in the cohort indiv.phase2 <- casecohort$id q <- ncol(A) total <- colSums(A) A.phase2 <- A[indiv.phase2,] calib <- calibration(A.phase2 = A[indiv.phase2,], design.weights = casecohort$weight, total = total, eta0 = rep(0, q), niter.max = 10^3, epsilon.stop = 10^(-10)) #calib$calibrated.weights # print calibrated weights
Function for estimating parameters (log-relative hazard, baseline hazards, cumulative baseline hazard, pure risks) and their variance (robust or the one accounting for sampling features) from cohort or case-cohort data, under the Cox model.
caseCohortCoxSurvival(data, status, time, cox.phase1 = NULL, cox.phase2 = NULL, other.covars = NULL, strata = NULL, weights.phase2 = NULL, calibrated = FALSE, subcohort = NULL, subcohort.strata.counts = NULL, predict = TRUE, predicted.cox.phase2 = NULL, predictors.cox.phase2 = NULL, aux.vars = NULL, aux.method = "Shin", phase3 = NULL, strata.phase3 = NULL, weights.phase3 = NULL, weights.phase3.type = "both", Tau1 = NULL, Tau2 = NULL, x = NULL, weights.op = NULL, print = 1)caseCohortCoxSurvival(data, status, time, cox.phase1 = NULL, cox.phase2 = NULL, other.covars = NULL, strata = NULL, weights.phase2 = NULL, calibrated = FALSE, subcohort = NULL, subcohort.strata.counts = NULL, predict = TRUE, predicted.cox.phase2 = NULL, predictors.cox.phase2 = NULL, aux.vars = NULL, aux.method = "Shin", phase3 = NULL, strata.phase3 = NULL, weights.phase3 = NULL, weights.phase3.type = "both", Tau1 = NULL, Tau2 = NULL, x = NULL, weights.op = NULL, print = 1)
data |
Data frame containing the cohort and all variables needed for the analysis. |
status |
Column name in |
time |
Column name(s) in |
cox.phase1 |
Column name(s) in |
cox.phase2 |
Column name(s) in |
other.covars |
Column name(s) in data giving other covariates
measured on the entire cohort that might be useful,
alone or in combination with |
strata |
NULL or column name in data with the stratum value for each individual in the cohort. The number of strata used for the sampling of the subcohort equals the number of different stratum values. For example, a stratum variable might take values 0,1,2,3 or 4. The default is NULL. |
weights.phase2 |
NULL or column name in data giving the phase-two design
weights for each individual in the cohort.
For a whole cohort analysis (see |
calibrated |
TRUE or FALSE to calibrate the |
subcohort |
NULL or column name in |
subcohort.strata.counts |
NULL or a list of the number of individuals sampled into the subcohort from each stratum of strata. The names in the list must be the strata values and the length of the list must be equal to the number of strata. If NULL, then the count for each stratum is estimated by the number of subcohort individuals in each stratum. The default is NULL. |
predict |
TRUE or FALSE to predict the phase-two covariates using
|
predicted.cox.phase2 |
NULL or a named list giving the predicted values of the
phase-two covariates ( |
predictors.cox.phase2 |
NULL, a vector, or a list specifying the columns in data
to use as predictor variables for obtaining the predicted values
on the whole cohort for the phase-two covariates ( |
aux.vars |
NULL or column name(s) in data giving the auxiliary variables for
each individual in the cohort. This option is only used when
|
aux.method |
"Breslow", or "Shin" to specify the algorithm to construct the
auxiliary variables. This option is only used if |
phase3 |
NULL or column name in data giving the indicators of membership in the in
the phase-three sample. The indicators are 1 if the individual belongs to the
phase-three sample and 0 otherwise. All individuals in the phase-three sample
must also belong to the phase-two sample.
This option is not used if |
strata.phase3 |
NULL or column name in |
weights.phase3 |
NULL or column name in |
weights.phase3.type |
One of NULL, "design", "estimated", or "both" to specify whether the phase-three weights are design weights (known), or to be estimated. The variance estimation differs for estimated and design weights. If set to "both", then both variance estimates will be computed. If not NULL, then only the first letter is matched for this option. The default is "both". |
Tau1 |
NULL or left bound of the time interval considered for the cumulative baseline hazard and the pure risk. If NULL, then the first event time is used. |
Tau2 |
NULL or right bound of the time interval considered for the cumulative baseline hazard and the pure risk. If NULL, then the last event time is used. |
x |
Data frame containing |
weights.op |
NULL or a list of options for calibration of phase-two design weights
or estimating phase-three design weights.
The available options are |
print |
0-3 to print information as the analysis is performed.
The larger the value, the more information will be printed. To not
print any information, set |
The different scenarios covered by the function are:
1) Whole cohort (subcohort = NULL)
2) (stratified) case-cohort (= stratified phase-two sample with no missing covariate data)
a. With design weights (subcohort, strata, calibrated = FALSE)
b. With calibrated weights and proxies to predict phase-two covariates and the
auxiliary variables (subcohort, strata, calibrated=TRUE,
predict=TRUE, predictors.cox.phase2, aux.method)
c. With calibrated weights and externally supplied predicted values of phase-two covariates
(calibrated=TRUE, strata, predict=FALSE, predicted.cox.phase2)
3) (unstratified) case-cohort (= unstratified phase-two sample with no missing covariate data)
a. With design weights (subcohort, strata=NULL, calibrated=FALSE)
b. With calibrated weights and proxies to predict phase-two covariates and obtain the
auxiliary variables (subcohort, strata=NULL, calibrated=TRUE,
predict=TRUE, predictors.cox.phase2, aux.method)
c. With calibrated weights and externally supplied predicted values of phase-two covariates
(calibrated=TRUE, strata=NULL, predict=FALSE, predicted.cox.phase2)
4) Case-cohort (= phase-three sample, because of missing covariate information in phase-two
data, with stratified or unstratified phase-two sampling)
a. With known phase-three design weights (subcohort, strata, phase3,
strata.phase3, weights.phase3.type="design")
b. With estimated phase-three design weights (subcohort, strata, phase3,
strata.phase3, weights.phase3.type="estimated")
covariates and prediction
Prediction of phase-two covariates is performed when calibrated = TRUE, predict = TRUE,
aux.vars = NULL and predicted.cox.phase2 = NULL. If predictors.cox.phase2 = NULL,
all the covariates measured on the entire cohort will be used for the prediction
(see cox.phase1 and other.covars).
Prediction of phase-two covariates is performed by linear regression for a continuous variable,
logistic regression for a binary variable and the function multinom for a
categorical variable. Dummy variables should not be used for categorical covariates,
because independent logistic (or linear) regressions will be performed using the dummy variables.
Alternatively, predicted values of phase-two covariates on the whole cohort can be specified with
predicted.cox.phase2.
calibration
Calibrating the design weights against some informative auxiliary variables,
measured on all cohort members, can increase efficiency.
When calibrated = TRUE, the user can either provide the auxiliary variables
(aux.vars), or let the driver function build the auxiliary variables (aux.method).
Construction of the auxiliary variables follows Breslow et al. (2009) or Shin et al. (2020)
(see aux.method), and relies on predictions of the phase-two covariates for all members
of the cohort (see covariates and prediction above).
The auxiliary variables are given by (i) the influences for the log-relative hazard parameters
estimated from the Cox model with imputed cohort data; and (ii) the products of total
follow-up time (on the time interval for which pure risk is to be estimated) with the estimated
relative hazard for the imputed cohort data, where the log-relative hazard parameters are
estimated from the Cox model with case-cohort data and weights calibrated with (i).
When aux.method = Breslow, calibration of the design weights is against (i),
as proposed by Breslow et al. (2009) to improve efficiency of case-cohort estimates
of relative hazard. When aux.method = Shin, calibration is against (i) and (ii),
as proposed by Shin et al. (2020) to improve efficiency of relative hazard and pure risk
estimates under the nested case-control design.
Note
If subcohort = NULL, then a whole cohort analysis will be run and only robust variance estimates
will be computed.
A list with class casecohortcoxsurv containing:
beta Estimated log-relative hazard estimates
Lambda0 Cumulative baseline hazard estimate in [Tau1, Tau2]
beta.var Influence-based variance estimate for beta
Lambda0.var Influence-based variance estimate for Lambda0
beta.var.estimated Influence-based variance estimate for beta with estimated
phase-three weights
Lambda0.var.estimated Influence-based variance estimate for Lambda0 with estimated
phase-three weights
beta.var.design Influence-based variance estimate for beta with design
phase-three weights
Lambda0.var.design Influence-based variance estimate for Lambda0 with design
phase-three weights
beta.robustvar Robust variance estimate for beta
Lambda0.robustvar Robust variance estimate for Lambda0
beta.robustvar.estimated Robust variance estimate for beta with estimated
phase-three weights
Lambda0.robustvar.estimated Robust variance estimate for Lambda0 with estimated
phase-three weights
beta.robustvar.design Robust variance estimate for beta with design
phase-three weights
Lambda0.robustvar.design Robust variance estimate for Lambda0 with design
phase-three weights
Pi.var Matrix of pure risk estimates in [Tau1, Tau2] and variance estimates
Pi.var.estimated Matrix of pure risk estimates in [Tau1, Tau2] and variance estimates
with estimated phase-three weights
Pi.var.design Matrix of pure risk estimates in [Tau1, Tau2] and variance estimates
with design phase-three weights
coxph.fit Return object from coxph of the model fit
changed.times Matrix of original and new event times for individuals who had their event times
changed due to ties. Will be NULL if event times were not changed.
args List containing the values of the input arguments (except data)
risk.obj List containing objects needed to compute pure risk estimates and variances
for a different set of data
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
Etievant, L., Gail, M. H. (2024). Software Application Profile: CaseCohortCoxSurvival: an R package for case-cohort inference for relative hazard and pure risk under the Cox model. Submitted.
Shin Y.E., Pfeiffer R.M., Graubard B.I., Gail M.H. (2020) Weight calibration to improve the efficiency of pure risk estimates from case-control samples nested in a cohort. Biometrics, 76, 1087-1097.
Breslow, N.E., Lumley, T., Ballantyne, C.M., Chambless, L.E. and Kulich, M. (2009). Improved Horvitz-Thompson Estimation of Model Parameters from Two-phase Stratified Samples: Applications in Epidemiology. Statistics in Biosciences, 1, 32-49.
data(dataexample.missingdata.stratified, package="CaseCohortCoxSurvival") data <- dataexample.missingdata.stratified$cohort cov1 <- "X2" cov2 <- c("X1", "X3") # Whole cohort, get pure risk estimate for every individual's profile in the # cohort. Only robust variance estimates are computed for a whole cohort analysis caseCohortCoxSurvival(data = data, status = "status", time = "event.time", cox.phase1 = cov1, x = data) # Stratified case-cohort analysis with missing covariate information in the # phase-two data, and with phase-three strata based on W3 caseCohortCoxSurvival(data = data, status = "status", time = "event.time", cox.phase1 = cov1, cox.phase2 = cov2, strata = "W", subcohort = "subcohort", phase3 = "phase3", strata.phase3 = "W3") # Stratified case-cohort (phase-two) analysis with weight calibration specifying # a different set of proxy variables to predict each phase-two covariate data(dataexample.stratified, package="CaseCohortCoxSurvival") data <- dataexample.stratified$cohort cov1 <- "X2" cov2 <- c("X1", "X3") caseCohortCoxSurvival(data = data, status = "status", time = "event.time", cox.phase1 = cov1, cox.phase2 = cov2, strata = "W", subcohort = "subcohort", calibrated = TRUE, predictors.cox.phase2 = list(X1 = c("X1.proxy", "W"), X3 = c("X1.proxy", "X3.proxy", "X2"))) # Stratified case-cohort (phase-two) analysis with weight calibration, get pure # risk estimate for one given covariate profile est <- caseCohortCoxSurvival(data = data, status = "status", time = "event.time", cox.phase1 = cov1, cox.phase2 = cov2, strata = "W", subcohort = "subcohort", calibrated = TRUE, predictors.cox.phase2 = list(X1 = c("X1.proxy", "W"), X3 = c("X1.proxy", "X3.proxy", "X2")), x = list(X1 = 1, X2 = -1, X3 = 0.6), Tau1 = 0, Tau2 = 8) est$Pi.var # Stratified case-cohort (phase-two) analysis with weight calibration, get pure # risk estimate for two given covariate profiles pr1 <- as.data.frame(cbind(X1 = -1, X2 = 1, X3 = -0.6)) pr2 <- as.data.frame(cbind(X1 = 1, X2 = -1, X3 = 0.6)) est <- caseCohortCoxSurvival(data = data, status = "status", time = "event.time", cox.phase1 = cov1, cox.phase2 = cov2, strata = "W", subcohort = "subcohort", calibrated = TRUE, predictors.cox.phase2 = list(X1 = c("X1.proxy", "W"), X3 = c("X1.proxy", "X3.proxy", "X2")), x = rbind(pr1, pr2), Tau1 = 0, Tau2 = 8) est$Pi.var # Stratified case-cohort (phase-two) analysis with design weights, get pure # risk estimate for one given covariate profile est <- caseCohortCoxSurvival(data = data, status = "status", time = "event.time", cox.phase1 = cov1, cox.phase2 = cov2, strata = "W", subcohort = "subcohort", x = list(X1 = 1, X2 = -1, X3 = 0.6), Tau1 = 0, Tau2 = 8) est$beta est$Pi.var # Set the correct sampling counts in phase-two for each level of strata. # The strata variable W has levels 0-3. est <- caseCohortCoxSurvival(data = data, status = "status", time = "event.time", cox.phase1 = cov1, cox.phase2 = cov2, strata = "W", subcohort = "subcohort", subcohort.strata.counts = list("0" = 97, "1" = 294, "2" = 300, "3" = 380)) est$betadata(dataexample.missingdata.stratified, package="CaseCohortCoxSurvival") data <- dataexample.missingdata.stratified$cohort cov1 <- "X2" cov2 <- c("X1", "X3") # Whole cohort, get pure risk estimate for every individual's profile in the # cohort. Only robust variance estimates are computed for a whole cohort analysis caseCohortCoxSurvival(data = data, status = "status", time = "event.time", cox.phase1 = cov1, x = data) # Stratified case-cohort analysis with missing covariate information in the # phase-two data, and with phase-three strata based on W3 caseCohortCoxSurvival(data = data, status = "status", time = "event.time", cox.phase1 = cov1, cox.phase2 = cov2, strata = "W", subcohort = "subcohort", phase3 = "phase3", strata.phase3 = "W3") # Stratified case-cohort (phase-two) analysis with weight calibration specifying # a different set of proxy variables to predict each phase-two covariate data(dataexample.stratified, package="CaseCohortCoxSurvival") data <- dataexample.stratified$cohort cov1 <- "X2" cov2 <- c("X1", "X3") caseCohortCoxSurvival(data = data, status = "status", time = "event.time", cox.phase1 = cov1, cox.phase2 = cov2, strata = "W", subcohort = "subcohort", calibrated = TRUE, predictors.cox.phase2 = list(X1 = c("X1.proxy", "W"), X3 = c("X1.proxy", "X3.proxy", "X2"))) # Stratified case-cohort (phase-two) analysis with weight calibration, get pure # risk estimate for one given covariate profile est <- caseCohortCoxSurvival(data = data, status = "status", time = "event.time", cox.phase1 = cov1, cox.phase2 = cov2, strata = "W", subcohort = "subcohort", calibrated = TRUE, predictors.cox.phase2 = list(X1 = c("X1.proxy", "W"), X3 = c("X1.proxy", "X3.proxy", "X2")), x = list(X1 = 1, X2 = -1, X3 = 0.6), Tau1 = 0, Tau2 = 8) est$Pi.var # Stratified case-cohort (phase-two) analysis with weight calibration, get pure # risk estimate for two given covariate profiles pr1 <- as.data.frame(cbind(X1 = -1, X2 = 1, X3 = -0.6)) pr2 <- as.data.frame(cbind(X1 = 1, X2 = -1, X3 = 0.6)) est <- caseCohortCoxSurvival(data = data, status = "status", time = "event.time", cox.phase1 = cov1, cox.phase2 = cov2, strata = "W", subcohort = "subcohort", calibrated = TRUE, predictors.cox.phase2 = list(X1 = c("X1.proxy", "W"), X3 = c("X1.proxy", "X3.proxy", "X2")), x = rbind(pr1, pr2), Tau1 = 0, Tau2 = 8) est$Pi.var # Stratified case-cohort (phase-two) analysis with design weights, get pure # risk estimate for one given covariate profile est <- caseCohortCoxSurvival(data = data, status = "status", time = "event.time", cox.phase1 = cov1, cox.phase2 = cov2, strata = "W", subcohort = "subcohort", x = list(X1 = 1, X2 = -1, X3 = 0.6), Tau1 = 0, Tau2 = 8) est$beta est$Pi.var # Set the correct sampling counts in phase-two for each level of strata. # The strata variable W has levels 0-3. est <- caseCohortCoxSurvival(data = data, status = "status", time = "event.time", cox.phase1 = cov1, cox.phase2 = cov2, strata = "W", subcohort = "subcohort", subcohort.strata.counts = list("0" = 97, "1" = 294, "2" = 300, "3" = 380)) est$beta
[dataexample is deprecated and will be removed in the next version of the package].
Simulated cohort, case-cohort and set of auxiliary variables for examples. The case-cohort is a stratified phase-two sample with no missing covariate data.
dataexample.stratified, dataexample.unstratified
data(dataexample, package="CaseCohortCoxSurvival") # Display some of the data dataexample$cohort[1:5, ] dataexample$A[1:5, ] # auxiliary variable values in the cohortdata(dataexample, package="CaseCohortCoxSurvival") # Display some of the data dataexample$cohort[1:5, ] dataexample$A[1:5, ] # auxiliary variable values in the cohort
[dataexample.missingdata is deprecated and will be removed in the next version of the package].
Simulated cohort and case-cohort for examples. The case-cohort is a stratified phase-three sample, because of missing covariate information in the stratified phase-two data.
dataexample.missingdata.stratified, dataexample.missingdata.unstratified
data(dataexample.missingdata, package="CaseCohortCoxSurvival") # Display some of the data dataexample.missingdata$cohort[1:5, ]data(dataexample.missingdata, package="CaseCohortCoxSurvival") # Display some of the data dataexample.missingdata$cohort[1:5, ]
List with cohort.
cohort is a simulated cohort with 20 000 subjects. It contains:
id is the subject identifier.
X1 is a continuous baseline covariate. Its measurements are only available for subjects in the case-cohort, i.e., with phase3 = 1.
X2 is a categorical baseline covariate, with categories 0, 1, and 2. It is measured on all cohort subjects.
X3 is a continuous baseline covariate. Its measurements are only available for subjects in the case-cohort.
W is a baseline categorical variable, with categories 0, 1, 2, and 3. It depends on predictors of X1 and X2. It is measured on all cohort subjects.
status indicates case status.
event.time gives the event or censoring time. status indicates whether the subject experienced the event of interest or was censored.
The stratified sampling of the subcohort was based on the 4 strata defined by W. 97, 294, 300, and 380 subjects were sampled (independently of case status) from the 4 strata, respectively. subcohort indicates all these subjects included in the subcohort.
The phase-two sample consisted of the subcohort and any other cases not in the subcohort. phase2 indicates all these subjects included in the phase-two sample.
W3 is a baseline binary variable, based on case status. It is measured on all cohort subjects.
The third phase of sampling was stratified based on the 2 strata defined by W3. Subjects were sampled from the 2 strata with sampling probabilities 0.9 and 0.8. phase3 indicates all these subjects included in the case-cohort (phase-three sample).
strata.n gives the number of subjects in the stratum in the cohort.
strata.m gives the number of subjects sampled from each of the 4 phase-two strata to be included in the subcohort (i.e., 97, 294, 300, or 380).
strata.m and strata.n would be used to compute the phase-two design weights of non-cases. Because all the cases were included in the phase-two sample, they would be assigned a phase-two design weight of 1.
strata.n.cases gives the number of cases in each of the 4 phase-two strata in the cohort.
n.cases gives the number of cases in the entire cohort.
strata.proba.missing gives the the sampling probablity for the 2 phase-three strata based on W3 and that were used for the third phase of sampling.
weight.true gives the true design weight (i.e., product of the phase-two and true phase-three design weight).
weight.p2.true gives true phase-two design weight. They are stratum-specific based on W.
weight.p3.true gives the true phase-three design weight. They are stratum-specific based on W3. weight.p3.true can be used with argument weights.phase3 of function caseCohortCoxSurvival, along with argument weights.phase3.type = "design".
weight.p3.est gives the estimated phase-three design weight. They were obtained from W3, phase2 and phase3. weight.p3.est can be used with argument weights.phase3 of function caseCohortCoxSurvival, along with argument weights.phase3.type = "estimated". If in function caseCohortCoxSurvival weights.phase3 = NULL but weights.phase3.type = "estimated", the phase-three design weights will be estimated from W3, phase2 and phase3 and should be identical.
weight.est gives the estimated design weight (i.e., product of the phase-two and estimated phase-three design weight).
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
Etievant, L., Gail, M. H. (2024). Software Application Profile: CaseCohortCoxSurvival: an R package for case-cohort inference for relative hazard and pure risk under the Cox model. Submitted.
data(dataexample.missingdata.stratified, package="CaseCohortCoxSurvival") # Display some of the data dataexample.missingdata.stratified$cohort[1:5, ]data(dataexample.missingdata.stratified, package="CaseCohortCoxSurvival") # Display some of the data dataexample.missingdata.stratified$cohort[1:5, ]
List with cohort.
cohort is a simulated cohort with 20 000 subjects. It contains:
id is the subject identifier.
X1 is a continuous baseline covariate. Its measurements are only available for subjects in the case-cohort, i.e., with phase3 = 1.
X2 is a categorical baseline covariate, with categories 0, 1, and 2. It is measured on all cohort subjects.
X3 is a continuous baseline covariate. Its measurements are only available for subjects in the case-cohort.
status indicates case status.
event.time gives the event or censoring time. status indicates whether the subject experienced the event of interest or was censored.
The sampling of the subcohort was not stratified. 1053 subjects were sampled (independently of case status) from the cohort. subcohort indicates all these subjects included in the subcohort.
The phase-two sample consisted of the subcohort and any other cases not in the subcohort. phase2 indicates all these subjects included in the phase-two sample.
W3 is a baseline binary variable, based on case status. It is measured on all cohort subjects.
The third phase of sampling was stratified based on the 2 strata defined by W3. Subjects were sampled from the 2 strata with sampling probabilities 0.9 and 0.8. phase3 indicates all these subjects included in the case-cohort (phase-three sample).
n gives the number of subjects in the cohort.
m gives the number of subjects sampled from the cohort (i.e., 1053).
m and n would be used to compute the design weights of non-cases. Because all the cases were included in the case-cohort, they would be assigned a design weight of 1.
n.cases gives the number of cases in the entire cohort.
W3 is a baseline binary variable, based on case status. It is measured on all cohort subjects.
strata.proba.missing gives the the sampling probablity for the 2 phase-three strata based on W3 and that were used for the third phase of sampling.
weight.true gives the true design weight (i.e., product of the phase-two and true phase-three design weight).
weight.p2.true gives true phase-two design weight. They are stratum-specific based on W.
weight.p3.true gives the true phase-three design weight. They are stratum-specific based on W3. weight.p3.true can be used with argument weights.phase3 of function caseCohortCoxSurvival, along with argument weights.phase3.type = "design".
weight.p3.est gives the estimated phase-three design weight. They were obtained from W3, phase2 and phase3. weight.p3.est can be used with argument weights.phase3 of function caseCohortCoxSurvival, along with argument weights.phase3.type = "estimated". If in function caseCohortCoxSurvival weights.phase3 = NULL but weights.phase3.type = "estimated", the phase-three design weights will be estimated from W3, phase2 and phase3 and should be identical.
weight.est gives the estimated design weight (i.e., product of the phase-two and estimated phase-three design weight).
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
Etievant, L., Gail, M. H. (2024). Software Application Profile: CaseCohortCoxSurvival: an R package for case-cohort inference for relative hazard and pure risk under the Cox model. Submitted.
data(dataexample.missingdata.unstratified, package="CaseCohortCoxSurvival") # Display some of the data dataexample.missingdata.unstratified$cohort[1:5, ]data(dataexample.missingdata.unstratified, package="CaseCohortCoxSurvival") # Display some of the data dataexample.missingdata.unstratified$cohort[1:5, ]
List with cohort and A.
cohort is a simulated cohort with 20 000 subjects. It contains:
id is the subject identifier.
X1 is a continuous baseline covariate. Its measurements are only available for subjects in the case-cohort, i.e., on subjects with subcohort = 1 and/or status = 1.
X2 is a categorical baseline covariate, with categories 0, 1, and 2. It is measured on all cohort subjects.
X3 is a continuous baseline covariate. Its measurements are only available for subjects in the case-cohort.
W is a baseline categorical variable, with categories 0, 1, 2, and 3. It depends on predictors of X1 and X2. It is measured on all cohort subjects. The stratified sampling of the subcohort was based on the 4 strata defined by W.
status indicates case status.
event.time gives the event or censoring time. status indicates whether the subject experienced the event of interest or was censored.
97, 294, 300, and 380 subjects were sampled (independently of case status) from the 4 strata, respectively. subcohort indicates all these subjects included in the subcohort. The stratified case-cohort (phase-two sample) consists of the subcohort and any other cases not in the subcohort.
strata.n gives the number of subjects in the stratum in the cohort.
strata.m gives the number of subjects sampled from each of the 4 strata (i.e., 97, 294, 300, or 380).
strata.m and strata.n would be used to compute the stratum-specific design weights of non-cases. Because all the cases were included in the case-cohort, they would be assigned a design weight of 1.
strata.n.cases gives the number of cases in each of the 4 strata.
n.cases gives the number of cases in the entire cohort.
X1.proxy is a continuous baseline covariate. It is a proxy of X1, with 0.8 correlation. It is measured on all cohort subjects. It can be used for design weights calibration in the argument predictors.cox.phase2 of function caseCohortCoxSurvival, as one would need to predict X1 on the entire cohort.
X3.proxy is a continuous baseline covariate. It is a proxy of X3, with 0.8 correlation. It is measured on all cohort subjects. It can be used for design weights calibration in the argument predictors.cox.phase2 of function caseCohortCoxSurvival, as one would need to predict X3 on the entire cohort.
X1.pred is a prediction of X1, available for all cohort subjects. The predictions were obtained by weighted linear regression on X1.proxy and W, with the design weights.
X3.pred is a prediction of X3, available for all cohort subjects. The predictions were obtained by weighted linear regression on X1.proxy, X2, and X3.proxy, with the design weights.
A contains auxiliary variables, obtained as proposed by Breslow et al. (2009) and Shin et al. (2020). A can be used with argument aux.var of function caseCohortCoxSurvival.
Predictions of X1 were obtained by weighted linear regression on X1.proxy and W, with the design weights. Predictions of X3 were obtained by weighted linear regression on X1.proxy, X2, and X3.proxy, with the design weights. Then the Cox model with X2 and the predicted values of X1 and X3 (available for all cohort subjects) was run. A.X1, A.X2, and A.X3 contain the influences on the estimated log-RHs (available for all cohort subjects).
Second, design weights were then calibrated based on A.1, A.X1, A.X2, and A.X3, with A.1 that is identically equal to 1. The log-RH parameter was then estimated from the case-cohort data with these calibrated weights. Finally, the log-RH estimate was used with X2 and the predicted values of X1 and X3 (available for all cohort subjects), and exponentiated. A.Shin contains the product of this quantity with the total follow-up time on interval (0,8].
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
Etievant, L., Gail, M. H. (2024). Software Application Profile: CaseCohortCoxSurvival: an R package for case-cohort inference for relative hazard and pure risk under the Cox model. Submitted.
Shin Y.E., Pfeiffer R.M., Graubard B.I., Gail M.H. (2020) Weight calibration to improve the efficiency of pure risk estimates from case-control samples nested in a cohort. Biometrics, 76, 1087-1097
Breslow, N.E., Lumley, T., Ballantyne, C.M., Chambless, L.E. and Kulich, M. (2009). Improved Horvitz-Thompson Estimation of Model Parameters from Two-phase Stratified Samples: Applications in Epidemiology. Statistics in Biosciences, 1, 32-49.
data(dataexample.stratified, package="CaseCohortCoxSurvival") # Display some of the data dataexample.stratified$cohort[1:5, ] dataexample.stratified$A[1:5, ] # auxiliary variable values in the cohortdata(dataexample.stratified, package="CaseCohortCoxSurvival") # Display some of the data dataexample.stratified$cohort[1:5, ] dataexample.stratified$A[1:5, ] # auxiliary variable values in the cohort
List with cohort and A.
cohort is a simulated cohort with 20 000 subjects. It contains:
id is the subject identifier.
X1 is a continuous baseline covariate. Its measurements are only available for subjects in the case-cohort, i.e., on subjects with subcohort = 1 and/or status = 1.
X2 is a categorical baseline covariate, with categories 0, 1, and 2. It is measured on all cohort subjects.
X3 is a continuous baseline covariate. Its measurements are only available for subjects in the case-cohort.
status indicates case status.
event.time gives the event or censoring time. status indicates whether the subject experienced the event of interest or was censored.
1053 subjects were sampled (independently of case status) from the cohort. subcohort indicates all these subjects included in the subcohort. The case-cohort (phase-two sample) consists of the subcohort and any other cases not in the subcohort.
n gives the number of subjects in the cohort.
m gives the number of subjects sampled from the cohort (i.e., 1053).
m and n would be used to compute the design weights of non-cases. Because all the cases were included in the case-cohort, they would be assigned a design weight of 1.
n.cases gives the number of cases in the entire cohort.
X1.proxy is a continuous baseline covariate. It is a proxy of X1, with 0.8 correlation. It is measured on all cohort subjects. It can be used for design weights calibration in the argument predictors.cox.phase2 of function caseCohortCoxSurvival, as one would need to predict X1 on the entire cohort.
X3.proxy is a continuous baseline covariate. It is a proxy of X3, with 0.8 correlation. It is measured on all cohort subjects. It can be used for design weights calibration in the argument predictors.cox.phase2 of function caseCohortCoxSurvival, as one would need to predict X3 on the entire cohort.
X1.pred is a prediction of X1, available for all cohort subjects. The predictions were obtained by weighted linear regression on X1.proxy, with the design weights.
X3.pred is a prediction of X3, available for all cohort subjects. The predictions were obtained by weighted linear regression on X1.proxy, X2, and X3.proxy, with the design weights.
A contains auxiliary variables, obtained as proposed by Breslow et al. (2009) and Shin et al. (2020). A can be used with argument aux.var of function caseCohortCoxSurvival.
Predictions of X1 were obtained by weighted linear regression on X1.proxy and X2, with the design weights. Predictions of X3 were obtained by weighted linear regression on X1.proxy, X2, and X3.proxy, with the design weights. Then the Cox model with X2 and the predicted values of X1 and X3 (available for all cohort subjects) was run. A.X1, A.X2, and A.X3 contain the influences on the estimated log-RHs (available for all cohort subjects).
Second, design weights were then calibrated based on A.1, A.X1, A.X2, and A.X3, with A.1 that is identically equal to 1. The log-RH parameter was then estimated from the case-cohort data with these calibrated weights. Finally, the log-RH estimate was used with X2 and the predicted values of X1 and X3 (available for all cohort subjects), and exponentiated. A.Shin contains the product of this quantity with the total follow-up time on interval (0,8].
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
Etievant, L., Gail, M. H. (2024). Software Application Profile: CaseCohortCoxSurvival: an R package for case-cohort inference for relative hazard and pure risk under the Cox model. Submitted.
Shin Y.E., Pfeiffer R.M., Graubard B.I., Gail M.H. (2020) Weight calibration to improve the efficiency of pure risk estimates from case-control samples nested in a cohort. Biometrics, 76, 1087-1097
Breslow, N.E., Lumley, T., Ballantyne, C.M., Chambless, L.E. and Kulich, M. (2009). Improved Horvitz-Thompson Estimation of Model Parameters from Two-phase Stratified Samples: Applications in Epidemiology. Statistics in Biosciences, 1, 32-49.
data(dataexample.unstratified, package="CaseCohortCoxSurvival") # Display some of the data dataexample.unstratified$cohort[1:5, ] dataexample.unstratified$A[1:5, ] # auxiliary variable values in the cohortdata(dataexample.unstratified, package="CaseCohortCoxSurvival") # Display some of the data dataexample.unstratified$cohort[1:5, ] dataexample.unstratified$A[1:5, ] # auxiliary variable values in the cohort
These data sets still work but will be removed (defuncted) in the next version of the package.
dataexample is deprecated and will be removed in the next version of the package.
dataexample.missingdata is deprecated and will be removed in the next version of the package.
dataexample.stratified, dataexample.unstratified, dataexample.missingdata.stratified, dataexample.missingdata.unstratified
Computes pure risk estimates and variances for new covariate values.
estimatePureRisk(obj, x)estimatePureRisk(obj, x)
obj |
Return object from |
x |
Data frame or a list containing values of the covariates that were used
when |
A list containing:
var Matrix of pure risk estimates in [Tau1, Tau2] and variance estimates
var.estimated Matrix of pure risk estimates in [Tau1, Tau2] and variance estimates
when the phase-three weights are estimated
var.design Matrix of pure risk estimates in [Tau1, Tau2] and variance estimates
when the phase-three weights are known
Depending on the analysis run, some of the above objects will be NULL.
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
data(dataexample.stratified, package="CaseCohortCoxSurvival") data <- dataexample.stratified$cohort cov1 <- "X2" cov2 <- c("X1", "X3") obj <- caseCohortCoxSurvival(data = data, status = "status", time = "event.time", cox.phase1 = cov1, cox.phase2 = cov2, strata = "W", subcohort = "subcohort", Tau1 = 0, Tau2 = 8) # get pure risk estimate for every individual's profile in the cohort ret <- estimatePureRisk(obj, data) # get pure risk estimate for one given covariate profile ret <- estimatePureRisk(obj, list(X1 = 1, X2 = -1, X3 = 0.6)) # get pure risk estimates for two given covariate profiles pr1 <- as.data.frame(cbind(X1 = -1, X2 = 1, X3 = -0.6)) pr2 <- as.data.frame(cbind(X1 = 1, X2 = -1, X3 = 0.6)) ret <- estimatePureRisk(obj, rbind(pr1, pr2)) ret$vardata(dataexample.stratified, package="CaseCohortCoxSurvival") data <- dataexample.stratified$cohort cov1 <- "X2" cov2 <- c("X1", "X3") obj <- caseCohortCoxSurvival(data = data, status = "status", time = "event.time", cox.phase1 = cov1, cox.phase2 = cov2, strata = "W", subcohort = "subcohort", Tau1 = 0, Tau2 = 8) # get pure risk estimate for every individual's profile in the cohort ret <- estimatePureRisk(obj, data) # get pure risk estimate for one given covariate profile ret <- estimatePureRisk(obj, list(X1 = 1, X2 = -1, X3 = 0.6)) # get pure risk estimates for two given covariate profiles pr1 <- as.data.frame(cbind(X1 = -1, X2 = 1, X3 = -0.6)) pr2 <- as.data.frame(cbind(X1 = 1, X2 = -1, X3 = 0.6)) ret <- estimatePureRisk(obj, rbind(pr1, pr2)) ret$var
Estimates the log-relative hazard, baseline hazards at each unique event time, cumulative baseline hazard in a given time interval [Tau1, Tau2] and pure risk in [Tau1, Tau2] and for a given covariate profile x.
estimation(mod, Tau1 = NULL, Tau2 = NULL, x = NULL, missing.data = NULL, riskmat.phase2 = NULL, dNt.phase2 = NULL, status.phase2 = NULL)estimation(mod, Tau1 = NULL, Tau2 = NULL, x = NULL, missing.data = NULL, riskmat.phase2 = NULL, dNt.phase2 = NULL, status.phase2 = NULL)
mod |
a Cox model object, result of function |
Tau1 |
left bound of the time interval considered for the cumulative baseline hazard and pure risk. Default is the first event time. |
Tau2 |
right bound of the time interval considered for the cumulative baseline hazard and pure risk. Default is the last event time. |
x |
vector of length |
missing.data |
was data on the |
riskmat.phase2 |
at risk matrix for the phase-two data at all of the case
event times, even those with missing covariate data. Needs to be provided if
|
dNt.phase2 |
counting process matrix for failures in the phase-two data.
Needs to be provided if |
status.phase2 |
vector indicating the case status in the phase-two data.
Needs to be provided if |
estimation returns the log-relative hazard estimates provided by
mod, and estimates the baseline hazard point mass at any event time
non-parametrically.
estimation works for estimation from a case-cohort with design weights
or calibrated weights, when the case-cohort consists of the subcohort and cases
not in the subcohort (i.e., case-cohort obtained from two phases of sampling),
as well as with design weights when covariate data was missing for certain
individuals in the phase-two data (i.e., case-cohort obtained from three phases
of sampling).
beta.hat: vector of length with log-relative hazard estimates.
lambda0.t.hat: vector with baseline hazards estimates at each unique event time.
Lambda0.Tau1Tau2.hat: cumulative baseline hazard estimate in [Tau1, Tau2].
Pi.x.Tau1Tau2.hat: pure risk estimate in [Tau1, Tau2] and for covariate profile x.
Breslow, N. (1974). Covariance Analysis of Censored Survival Data. Biometrics, 30, 89-99.
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
estimation.CumBH, estimation.PR, influences, influences.RH,
influences.CumBH, influences.PR,
influences.missingdata, influences.RH.missingdata, influences.CumBH.missingdata,
and influences.PR.missingdata.
data(dataexample.missingdata.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.missingdata.stratified$cohort phase2 <- cohort[which(cohort$phase2 == 1),] # the phase-two sample casecohort <- cohort[which(cohort$phase3 == 1),] # the stratified case-cohort B.phase2 <- cbind(1 * (phase2$W3 == 0), 1 * (phase2$W3 == 1)) rownames(B.phase2) <- cohort[cohort$phase2 == 1, "id"] B.phase3 <- cbind(1 * (casecohort$W3 == 0), 1 * (casecohort$W3 == 1)) rownames(B.phase3) <- cohort[cohort$phase3 == 1, "id"] total.B.phase2 <- colSums(B.phase2) J3 <- ncol(B.phase3) n <- nrow(cohort) # Quantities needed for estimation of the cumulative baseline hazard when # covariate data is missing mod.cohort <- coxph(Surv(event.time, status) ~ X2, data = cohort, robust = TRUE) # X2 is available on all cohort members mod.cohort.detail <- coxph.detail(mod.cohort, riskmat = TRUE) riskmat.phase2 <- with(cohort, mod.cohort.detail$riskmat[phase2 == 1,]) rownames(riskmat.phase2) <- cohort[cohort$phase2 == 1, "id"] observed.times.phase2 <- apply(riskmat.phase2, 1, function(v) {which.max(cumsum(v))}) dNt.phase2 <- matrix(0, nrow(riskmat.phase2), ncol(riskmat.phase2)) dNt.phase2[cbind(1:nrow(riskmat.phase2), observed.times.phase2)] <- 1 dNt.phase2 <- sweep(dNt.phase2, 1, phase2$status, "*") colnames(dNt.phase2) <- colnames(riskmat.phase2) rownames(dNt.phase2) <- rownames(riskmat.phase2) Tau1 <- 0 # given time interval for the pure risk Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with true known design weights mod.true <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.true, id = id, robust = TRUE) est.true <- estimation(mod.true, Tau1 = Tau1, Tau2 = Tau2, x = x, missing.data = TRUE, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2) # print the vector with log-relative hazard estimates est.true$beta.hat # print the cumulative baseline hazard estimate est.true$Lambda0.Tau1Tau2.hat # print the pure risk estimate est.true$Pi.x.Tau1Tau2.hatdata(dataexample.missingdata.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.missingdata.stratified$cohort phase2 <- cohort[which(cohort$phase2 == 1),] # the phase-two sample casecohort <- cohort[which(cohort$phase3 == 1),] # the stratified case-cohort B.phase2 <- cbind(1 * (phase2$W3 == 0), 1 * (phase2$W3 == 1)) rownames(B.phase2) <- cohort[cohort$phase2 == 1, "id"] B.phase3 <- cbind(1 * (casecohort$W3 == 0), 1 * (casecohort$W3 == 1)) rownames(B.phase3) <- cohort[cohort$phase3 == 1, "id"] total.B.phase2 <- colSums(B.phase2) J3 <- ncol(B.phase3) n <- nrow(cohort) # Quantities needed for estimation of the cumulative baseline hazard when # covariate data is missing mod.cohort <- coxph(Surv(event.time, status) ~ X2, data = cohort, robust = TRUE) # X2 is available on all cohort members mod.cohort.detail <- coxph.detail(mod.cohort, riskmat = TRUE) riskmat.phase2 <- with(cohort, mod.cohort.detail$riskmat[phase2 == 1,]) rownames(riskmat.phase2) <- cohort[cohort$phase2 == 1, "id"] observed.times.phase2 <- apply(riskmat.phase2, 1, function(v) {which.max(cumsum(v))}) dNt.phase2 <- matrix(0, nrow(riskmat.phase2), ncol(riskmat.phase2)) dNt.phase2[cbind(1:nrow(riskmat.phase2), observed.times.phase2)] <- 1 dNt.phase2 <- sweep(dNt.phase2, 1, phase2$status, "*") colnames(dNt.phase2) <- colnames(riskmat.phase2) rownames(dNt.phase2) <- rownames(riskmat.phase2) Tau1 <- 0 # given time interval for the pure risk Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with true known design weights mod.true <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.true, id = id, robust = TRUE) est.true <- estimation(mod.true, Tau1 = Tau1, Tau2 = Tau2, x = x, missing.data = TRUE, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2) # print the vector with log-relative hazard estimates est.true$beta.hat # print the cumulative baseline hazard estimate est.true$Lambda0.Tau1Tau2.hat # print the pure risk estimate est.true$Pi.x.Tau1Tau2.hat
Estimates the log-relative hazard, baseline hazards at each unique event time and cumulative baseline hazard in a given time interval [Tau1, Tau2].
estimation.CumBH(mod, Tau1 = NULL, Tau2 = NULL, missing.data = FALSE, riskmat.phase2 = NULL, dNt.phase2 = NULL, status.phase2 = NULL)estimation.CumBH(mod, Tau1 = NULL, Tau2 = NULL, missing.data = FALSE, riskmat.phase2 = NULL, dNt.phase2 = NULL, status.phase2 = NULL)
mod |
a Cox model object, result of function coxph. |
Tau1 |
left bound of the time interval considered for the cumulative baseline hazard. Default is the first event time. |
Tau2 |
right bound of the time interval considered for the cumulative baseline hazard. Default is the last event time. |
missing.data |
was data on the |
riskmat.phase2 |
at risk matrix for the phase-two data at all of the case
event times, even those with missing covariate data. Needs to be provided if
|
dNt.phase2 |
counting process matrix for failures in the phase-two data.
Needs to be provided if |
status.phase2 |
vector indicating the case status in the phase-two data.
Needs to be provided if |
estimation.CumBH returns the log-relative hazard estimates provided by
mod, and estimates the baseline hazard point mass at any event time
non-parametrically.
estimation.CumBH works for estimation from a case-cohort with design weights
or calibrated weights, when the case-cohort consists of the subcohort and cases
not in the subcohort (i.e., case-cohort obtained from two phases of sampling),
as well as with design weights when covariate data was missing for certain
individuals in the phase-two data (i.e., case-cohort obtained from three phases
of sampling).
beta.hat: vector of length with log-relative hazard estimates.
lambda0.t.hat: vector with baseline hazards estimates at each unique event time.
Lambda0.Tau1Tau2.hat: cumulative baseline hazard estimate in [Tau1, Tau2].
Breslow, N. (1974). Covariance Analysis of Censored Survival Data. Biometrics, 30, 89-99.
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
estimation, estimation.PR, influences, influences.RH,
influences.CumBH, influences.PR,
influences.missingdata, influences.RH.missingdata, influences.CumBH.missingdata,
and influences.PR.missingdata
data(dataexample.missingdata.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.missingdata.stratified$cohort phase2 <- cohort[which(cohort$phase2 == 1),] # the phase-two sample casecohort <- cohort[which(cohort$phase3 == 1),] # the stratified case-cohort B.phase2 <- cbind(1 * (phase2$W3 == 0), 1 * (phase2$W3 == 1)) rownames(B.phase2) <- cohort[cohort$phase2 == 1, "id"] B.phase3 <- cbind(1 * (casecohort$W3 == 0), 1 * (casecohort$W3 == 1)) rownames(B.phase3) <- cohort[cohort$phase3 == 1, "id"] total.B.phase2 <- colSums(B.phase2) J3 <- ncol(B.phase3) n <- nrow(cohort) # Quantities needed for estimation of the cumulative baseline hazard when # covariate data is missing mod.cohort <- coxph(Surv(event.time, status) ~ X2, data = cohort, robust = TRUE) # X2 is available on all cohort members mod.cohort.detail <- coxph.detail(mod.cohort, riskmat = TRUE) riskmat.phase2 <- with(cohort, mod.cohort.detail$riskmat[phase2 == 1,]) rownames(riskmat.phase2) <- cohort[cohort$phase2 == 1, "id"] observed.times.phase2 <- apply(riskmat.phase2, 1, function(v) {which.max(cumsum(v))}) dNt.phase2 <- matrix(0, nrow(riskmat.phase2), ncol(riskmat.phase2)) dNt.phase2[cbind(1:nrow(riskmat.phase2), observed.times.phase2)] <- 1 dNt.phase2 <- sweep(dNt.phase2, 1, phase2$status, "*") colnames(dNt.phase2) <- colnames(riskmat.phase2) rownames(dNt.phase2) <- rownames(riskmat.phase2) Tau1 <- 0 # given time interval for the pure risk Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with true known design weights mod.true <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.true, id = id, robust = TRUE) est.true <- estimation(mod.true, Tau1 = Tau1, Tau2 = Tau2, x = x, missing.data = TRUE, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2) est.true <- estimation.CumBH(mod.true, Tau1 = Tau1, Tau2 = Tau2, missing.data = TRUE, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2) # print the cumulative baseline hazard estimate est.true$Lambda0.Tau1Tau2.hatdata(dataexample.missingdata.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.missingdata.stratified$cohort phase2 <- cohort[which(cohort$phase2 == 1),] # the phase-two sample casecohort <- cohort[which(cohort$phase3 == 1),] # the stratified case-cohort B.phase2 <- cbind(1 * (phase2$W3 == 0), 1 * (phase2$W3 == 1)) rownames(B.phase2) <- cohort[cohort$phase2 == 1, "id"] B.phase3 <- cbind(1 * (casecohort$W3 == 0), 1 * (casecohort$W3 == 1)) rownames(B.phase3) <- cohort[cohort$phase3 == 1, "id"] total.B.phase2 <- colSums(B.phase2) J3 <- ncol(B.phase3) n <- nrow(cohort) # Quantities needed for estimation of the cumulative baseline hazard when # covariate data is missing mod.cohort <- coxph(Surv(event.time, status) ~ X2, data = cohort, robust = TRUE) # X2 is available on all cohort members mod.cohort.detail <- coxph.detail(mod.cohort, riskmat = TRUE) riskmat.phase2 <- with(cohort, mod.cohort.detail$riskmat[phase2 == 1,]) rownames(riskmat.phase2) <- cohort[cohort$phase2 == 1, "id"] observed.times.phase2 <- apply(riskmat.phase2, 1, function(v) {which.max(cumsum(v))}) dNt.phase2 <- matrix(0, nrow(riskmat.phase2), ncol(riskmat.phase2)) dNt.phase2[cbind(1:nrow(riskmat.phase2), observed.times.phase2)] <- 1 dNt.phase2 <- sweep(dNt.phase2, 1, phase2$status, "*") colnames(dNt.phase2) <- colnames(riskmat.phase2) rownames(dNt.phase2) <- rownames(riskmat.phase2) Tau1 <- 0 # given time interval for the pure risk Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with true known design weights mod.true <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.true, id = id, robust = TRUE) est.true <- estimation(mod.true, Tau1 = Tau1, Tau2 = Tau2, x = x, missing.data = TRUE, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2) est.true <- estimation.CumBH(mod.true, Tau1 = Tau1, Tau2 = Tau2, missing.data = TRUE, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2) # print the cumulative baseline hazard estimate est.true$Lambda0.Tau1Tau2.hat
Estimates the pure risk in the time interval [Tau1, Tau2] and for a covariate profile x, from the log-relative hazard and cumulative baseline hazard values.
estimation.PR(beta, Lambda0.Tau1Tau2, x = NULL)estimation.PR(beta, Lambda0.Tau1Tau2, x = NULL)
beta |
vector of length |
Lambda0.Tau1Tau2 |
cumulative baseline hazard in [Tau1, Tau2]. |
x |
vector of length |
Pi.x.Tau1Tau2.hat: pure risk estimate in [Tau1, Tau2] and for covariate profile .
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
estimation, estimation.CumBH, influences, influences.RH,
influences.CumBH, influences.PR,
influences.missingdata, influences.RH.missingdata, influences.CumBH.missingdata,
and influences.PR.missingdata.
estimation.PR(beta = c(-0.2, 0.25, -0.3), Lambda0.Tau1Tau2 = 0.03, x = c(-1, 1, -0.6))estimation.PR(beta = c(-0.2, 0.25, -0.3), Lambda0.Tau1Tau2 = 0.03, x = c(-1, 1, -0.6))
Estimates the weights for the third phase of sampling (due to missingness in phase two).
estimation.weights.phase3(B.phase3, total.phase2, gamma0 = NULL, niter.max = NULL, epsilon.stop = NULL)estimation.weights.phase3(B.phase3, total.phase2, gamma0 = NULL, niter.max = NULL, epsilon.stop = NULL)
B.phase3 |
matrix for the case-cohort (phase-three data), with phase-three
sampling strata indicators. It should have as many columns as phase-three strata
( |
total.phase2 |
vector of length |
gamma0 |
vector of length |
niter.max |
maximum number of iterations for the iterative optimization
algorithm. Default is |
epsilon.stop |
threshold for the difference between the estimated weighted
total and the total in the whole cohort. If this difference is less than the
value of |
estimation.weights.phase3 estimates the phase-three sampling weights by solving in
with the phase-two sampling indicator and the phase-three
sampling indicator of individual in stratum , and with
the total in the
phase-two data. See Etievant and Gail (2024).
The Newton Raphson method is used to solve the optimization problem.
In the end, the estimated weights are given by ,
and
gives the estimated total.
gamma.hat: vector of length with final gamma values.
estimated.weights: vector with the estimated phase-three weights for the
individuals in the case-cohort (phase-three data), computed from B.phase3
and gamma.hat.
estimated.total: vector with the estimated totals, computed from the
estimated.weights and B.phase3.
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
influences.missingdata, influences.RH.missingdata,influences.CumBH.missingdata and influences.PR.missingdata.
data(dataexample.missingdata.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.missingdata.stratified$cohort phase2 <- cohort[which(cohort$phase2 == 1),] # the phase-two sample casecohort <- cohort[which(cohort$phase3 == 1),] # the stratified case-cohort B.phase2 <- cbind(1 * (phase2$W3 == 0), 1 * (phase2$W3 == 1)) rownames(B.phase2) <- cohort[cohort$phase2 == 1, "id"] B.phase3 <- cbind(1 * (casecohort$W3 == 0), 1 * (casecohort$W3 == 1)) rownames(B.phase3) <- cohort[cohort$phase3 == 1, "id"] total.B.phase2 <- colSums(B.phase2) J3 <- ncol(B.phase3) estimation.weights.p3 <- estimation.weights.phase3(B.phase3 = B.phase3, total.phase2 = total.B.phase2, gamma0 = rep(0, J3), niter.max = 10^(4), epsilon.stop = 10^(-10))data(dataexample.missingdata.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.missingdata.stratified$cohort phase2 <- cohort[which(cohort$phase2 == 1),] # the phase-two sample casecohort <- cohort[which(cohort$phase3 == 1),] # the stratified case-cohort B.phase2 <- cbind(1 * (phase2$W3 == 0), 1 * (phase2$W3 == 1)) rownames(B.phase2) <- cohort[cohort$phase2 == 1, "id"] B.phase3 <- cbind(1 * (casecohort$W3 == 0), 1 * (casecohort$W3 == 1)) rownames(B.phase3) <- cohort[cohort$phase3 == 1, "id"] total.B.phase2 <- colSums(B.phase2) J3 <- ncol(B.phase3) estimation.weights.p3 <- estimation.weights.phase3(B.phase3 = B.phase3, total.phase2 = total.B.phase2, gamma0 = rep(0, J3), niter.max = 10^(4), epsilon.stop = 10^(-10))
Computes the influences on the log-relative hazard, baseline hazards at each unique event time, cumulative baseline hazard in a given time interval [Tau1, Tau2] and on the pure risk in [Tau1, Tau2] and for a given covariate profile x. Can take calibration of the design weights into account.
influences(mod, Tau1 = NULL, Tau2 = NULL, x = NULL, calibrated = NULL, A = NULL)influences(mod, Tau1 = NULL, Tau2 = NULL, x = NULL, calibrated = NULL, A = NULL)
mod |
a cox model object, result of function coxph. |
Tau1 |
left bound of the time interval considered for the cumulative baseline hazard and pure risk. Default is the first event time. |
Tau2 |
right bound of the time interval considered for the cumulative baseline hazard and pure risk. Default is the last event time. |
x |
vector of length |
calibrated |
are calibrated weights used for the estimation of the
parameters? If |
A |
|
influences works for estimation from a case-cohort with design weights
or calibrated weights (case-cohort consisting of the subcohort and cases not in
the subcohort, i.e., case-cohort obtained from two phases of sampling).
If covariate information is missing for certain individuals in the phase-two data
(i.e., case-cohort obtained from three phases of sampling), use influences.missingdata.
influences uses the influence formulas provided in Etievant and Gail
(2024).
If calibrated = FALSE, the infuences are only provided for the individuals
in the case-cohort. If calibrated = TRUE, the influences are provided for
all the individuals in the cohort.
infl.beta: matrix with the overall influences on the log-relative hazard estimates.
infl.lambda0.t: matrix with the overall influences on the baseline hazards estimates at each unique event time.
infl.Lambda0.Tau1Tau2.hat: vector with the overall influences on the cumulative baseline hazard estimate in [Tau1, Tau2].
infl.Pi.x.Tau1Tau2.hat: vector with the overall influences on the pure risk estimate in [Tau1, Tau2] and for covariate profile x.
infl2.beta: matrix with the phase-two influences on the log-relative hazard estimates. Returned if calibrated = TRUE.
infl2.lambda0.t: matrix with the phase-two influences on the baseline hazards estimates at each unique event time. Returned if calibrated = TRUE.
infl2.Lambda0.Tau1Tau2.hat: vector with the phase-two influences on the cumulative baseline hazard estimate in [Tau1, Tau2]. Returned if calibrated = TRUE.
infl2.Pi.x.Tau1Tau2.hat: vector with the phase-two influences on the pure risk estimate in [Tau1, Tau2] and for covariate profile x. Returned if calibrated = TRUE.
beta.hat: vector of length with log-relative hazard estimates.
lambda0.t.hat: vector with baseline hazards estimates at each unique event time.
Lambda0.Tau1Tau2.hat: cumulative baseline hazard estimate in [Tau1, Tau2].
Pi.x.Tau1Tau2.hat: pure risk estimate in [Tau1, Tau2] and for covariate profile x.
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
estimation, estimation.CumBH, estimation.PR,
influences.RH, influences.CumBH, influences.PR,
influences.missingdata, influences.RH.missingdata,
influences.CumBH.missingdata,
influences.PR.missingdata, robustvariance and variance.
data(dataexample.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.stratified$cohort casecohort <- cohort[which(cohort$status == 1 | cohort$subcohort == 1),] # the stratified case-cohort casecohort$weights <- casecohort$strata.n / casecohort$strata.m casecohort$weights[which(casecohort$status == 1)] <- 1 Tau1 <- 0 Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with design weights mod <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weights, id = id, robust = TRUE) est <- influences(mod, Tau1 = Tau1, Tau2 = Tau2, x = x) # print the vector with log-relative hazard estimates est$beta.hat # print the cumulative baseline hazard estimate est$Lambda0.Tau1Tau2.hat # print the pure risk estimate est$Pi.x.Tau1Tau2.hat # print the influences on the log-relative hazard estimates # est$infl.beta # print the influences on the cumulative baseline hazard estimate # est$infl.Lambda0.Tau1Tau2 # print the influences on the pure risk estimate # est$infl.Pi.x.Tau1Tau2data(dataexample.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.stratified$cohort casecohort <- cohort[which(cohort$status == 1 | cohort$subcohort == 1),] # the stratified case-cohort casecohort$weights <- casecohort$strata.n / casecohort$strata.m casecohort$weights[which(casecohort$status == 1)] <- 1 Tau1 <- 0 Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with design weights mod <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weights, id = id, robust = TRUE) est <- influences(mod, Tau1 = Tau1, Tau2 = Tau2, x = x) # print the vector with log-relative hazard estimates est$beta.hat # print the cumulative baseline hazard estimate est$Lambda0.Tau1Tau2.hat # print the pure risk estimate est$Pi.x.Tau1Tau2.hat # print the influences on the log-relative hazard estimates # est$infl.beta # print the influences on the cumulative baseline hazard estimate # est$infl.Lambda0.Tau1Tau2 # print the influences on the pure risk estimate # est$infl.Pi.x.Tau1Tau2
Computes the influences on the log-relative hazard, baseline hazards at each unique event time, and on the cumulative baseline hazard in a given time interval [Tau1, Tau2]. Can take calibration of the design weights into account.
influences.CumBH(mod, Tau1 = NULL, Tau2 = NULL, A=NULL, calibrated = NULL)influences.CumBH(mod, Tau1 = NULL, Tau2 = NULL, A=NULL, calibrated = NULL)
mod |
a cox model object, result of function coxph. |
Tau1 |
left bound of the time interval considered for the cumulative baseline hazard and pure risk. Default is the first event time. |
Tau2 |
right bound of the time interval considered for the cumulative baseline hazard and pure risk. Default is the last event time. |
A |
|
calibrated |
are calibrated weights used for the estimation of the
parameters? If |
influences.CumBH works for estimation from a case-cohort with design weights
or calibrated weights (case-cohort consisting of the subcohort and cases not in
the subcohort, i.e., case-cohort obtained from two phases of sampling).
If covariate information is missing for certain individuals in the phase-two data
(i.e., case-cohort obtained from three phases of sampling), use influences.CumBH.missingdata.
influences.CumBH uses the influence formulas provided in Etievant and Gail
(2024).
If calibrated = FALSE, the infuences are only provided for the individuals
in the case-cohort. If calibrated = TRUE, the influences are provided for
all the individuals in the cohort.
infl.beta: matrix with the overall influences on the log-relative hazard
estimates.
infl.lambda0.t: matrix with the overall influences on the baseline hazards
estimates at each unique event time.
infl.Lambda0.Tau1Tau2.hat: vector with the overall influences on the
cumulative baseline hazard estimate in [Tau1, Tau2].
infl2.beta: matrix with the phase-two influences on the log-relative
hazard estimates. Returned if calibrated = TRUE.
infl2.lambda0.t: matrix with the phase-two influences on the baseline
hazards estimates at each unique event time. Returned if calibrated = TRUE.
infl2.Lambda0.Tau1Tau2.hat: vector with the phase-two influences on the
cumulative baseline hazard estimate in [Tau1, Tau2]. Returned if
calibrated = TRUE.
beta.hat: vector of length with log-relative hazard estimates.
lambda0.t.hat: vector with baseline hazards estimates at each unique event
time.
Lambda0.Tau1Tau2.hat: cumulative baseline hazard estimate in [Tau1, Tau2].
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
estimation, estimation.CumBH, estimation.PR,
influences, influences.RH, influences.PR,
influences.missingdata, influences.RH.missingdata,
influences.CumBH.missingdata,influences.PR.missingdata, robustvariance and variance.
data(dataexample.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.stratified$cohort casecohort <- cohort[which(cohort$status == 1 | cohort$subcohort == 1),] # the stratified case-cohort casecohort$weights <- casecohort$strata.n / casecohort$strata.m casecohort$weights[which(casecohort$status == 1)] <- 1 Tau1 <- 0 Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with design weights mod <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weights, id = id, robust = TRUE) est <- influences(mod, Tau1 = Tau1, Tau2 = Tau2, x = x) # print the influences on the cumulative baseline hazard estimate # est$infl.Lambda0.Tau1Tau2data(dataexample.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.stratified$cohort casecohort <- cohort[which(cohort$status == 1 | cohort$subcohort == 1),] # the stratified case-cohort casecohort$weights <- casecohort$strata.n / casecohort$strata.m casecohort$weights[which(casecohort$status == 1)] <- 1 Tau1 <- 0 Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with design weights mod <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weights, id = id, robust = TRUE) est <- influences(mod, Tau1 = Tau1, Tau2 = Tau2, x = x) # print the influences on the cumulative baseline hazard estimate # est$infl.Lambda0.Tau1Tau2
Computes the influences on the log-relative hazard, baseline hazards at each unique event time, and on the cumulative baseline hazard in a given time interval [Tau1, Tau2], when covariate data is missing for certain individuals in the phase-two data.
influences.CumBH.missingdata(mod, riskmat.phase2, dNt.phase2 = NULL, status.phase2 = NULL, Tau1 = NULL, Tau2 = NULL, estimated.weights = FALSE, B.phase2 = NULL)influences.CumBH.missingdata(mod, riskmat.phase2, dNt.phase2 = NULL, status.phase2 = NULL, Tau1 = NULL, Tau2 = NULL, estimated.weights = FALSE, B.phase2 = NULL)
mod |
a cox model object, result of function coxph. |
riskmat.phase2 |
at risk matrix for the phase-two data at all of the cases event times, even those with missing covariate data. |
dNt.phase2 |
counting process matrix for failures in the phase-two data.
Needs to be provided if |
status.phase2 |
vector indicating the case status in the phase-two data.
Needs to be provided if |
Tau1 |
left bound of the time interval considered for the cumulative baseline hazard and pure risk. Default is the first event time. |
Tau2 |
right bound of the time interval considered for the cumulative baseline hazard and pure risk. Default is the last event time. |
estimated.weights |
are the weights for the third phase of sampling (due to
missingness) estimated? If |
B.phase2 |
matrix for the phase-two data, with phase-three sampling strata
indicators. It should have as many columns as phase-three strata ( |
influences.CumBH.missingdata works for estimation from a case-cohort with design
weights and when covariate data was missing for certain individuals in the
phase-two data (i.e., case-cohort obtained from three phases of sampling).
If there are no missing covariates in the phase-two sample, use influences.CumBH
with either design weights or calibrated weights.
influences.CumBH.missingdata uses the influence formulas provided in Etievant
and Gail (2024).
infl.beta: matrix with the overall influences on the log-relative hazard estimates.
infl.lambda0.t: matrix with the overall influences on the baseline hazards estimates at each unique event time.
infl.Lambda0.Tau1Tau2.hat: vector with the overall influences on the cumulative baseline hazard estimate in [Tau1, Tau2].
infl2.beta: matrix with the phase-two influences on the log-relative hazard estimates.
infl2.lambda0.t: matrix with the phase-two influences on the baseline hazards estimates at each unique event time.
infl2.Lambda0.Tau1Tau2.hat: vector with the phase-two influences on the cumulative baseline hazard estimate in [Tau1, Tau2].
infl3.beta: matrix with the phase-three influences on the log-relative hazard estimates.
infl3.lambda0.t: matrix with the phase-three influences on the baseline hazards estimates at each unique event time.
infl3.Lambda0.Tau1Tau2.hat: vector with the phase-three influences on the cumulative baseline hazard estimate in [Tau1, Tau2].
beta.hat: vector of length with log-relative hazard estimates.
lambda0.t.hat: vector with baseline hazards estimates at each unique event time.
Lambda0.Tau1Tau2.hat: cumulative baseline hazard estimate in [Tau1, Tau2].
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
estimation, estimation.CumBH, estimation.PR,
influences.missingdata, influences.RH.missingdata,
influences.PR.missingdata, influences, influences.RH, influences.CumBH,
influences.PR, robustvariance and variance.
data(dataexample.missingdata.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.missingdata.stratified$cohort phase2 <- cohort[which(cohort$phase2 == 1),] # the phase-two sample casecohort <- cohort[which(cohort$phase3 == 1),] # the stratified case-cohort B.phase2 <- cbind(1 * (phase2$W3 == 0), 1 * (phase2$W3 == 1)) rownames(B.phase2) <- cohort[cohort$phase2 == 1, "id"] B.phase3 <- cbind(1 * (casecohort$W3 == 0), 1 * (casecohort$W3 == 1)) rownames(B.phase3) <- cohort[cohort$phase3 == 1, "id"] total.B.phase2 <- colSums(B.phase2) J3 <- ncol(B.phase3) n <- nrow(cohort) # Quantities needed for estimation of the cumulative baseline hazard when # covariate data is missing mod.cohort <- coxph(Surv(event.time, status) ~ X2, data = cohort, robust = TRUE) # X2 is available on all cohort members mod.cohort.detail <- coxph.detail(mod.cohort, riskmat = TRUE) riskmat.phase2 <- with(cohort, mod.cohort.detail$riskmat[phase2 == 1,]) rownames(riskmat.phase2) <- cohort[cohort$phase2 == 1, "id"] observed.times.phase2 <- apply(riskmat.phase2, 1, function(v) {which.max(cumsum(v))}) dNt.phase2 <- matrix(0, nrow(riskmat.phase2), ncol(riskmat.phase2)) dNt.phase2[cbind(1:nrow(riskmat.phase2), observed.times.phase2)] <- 1 dNt.phase2 <- sweep(dNt.phase2, 1, phase2$status, "*") colnames(dNt.phase2) <- colnames(riskmat.phase2) rownames(dNt.phase2) <- rownames(riskmat.phase2) Tau1 <- 0 # given time interval for the pure risk Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with true known design weights mod.true <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.true, id = id, robust = TRUE) est.true <- influences.missingdata(mod = mod.true, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2, Tau1 = Tau1, Tau2 = Tau2, x = x) # print the influences on the cumulative baseline hazard estimate # est.true$infl.Lambda0.Tau1Tau2 # print the phase-two influences on the cumulative baseline hazard estimate # est.true$infl2.Lambda0.Tau1Tau2 # print the phase-three influences on the cumulative baseline hazard estimate # est.true$infl3.Lambda0.Tau1Tau2 # Estimation using the stratified case cohort with estimated weights, and # accounting for the estimation through the influences mod.estimated <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.est, id = id, robust = TRUE) est.estimated <- influences.missingdata(mod.estimated, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2, estimated.weights = TRUE, B.phase2 = B.phase2, Tau1 = Tau1, Tau2 = Tau2, x = x) # print the influences on the cumulative baseline hazard estimate # est.estimated$infl.Lambda0.Tau1Tau2 # print the phase-two influences on the cumulative baseline hazard estimate # est.estimated$infl2.Lambda0.Tau1Tau2 # print the phase-three influences on the cumulative baseline hazard estimate # est.estimated$infl3.Lambda0.Tau1Tau2data(dataexample.missingdata.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.missingdata.stratified$cohort phase2 <- cohort[which(cohort$phase2 == 1),] # the phase-two sample casecohort <- cohort[which(cohort$phase3 == 1),] # the stratified case-cohort B.phase2 <- cbind(1 * (phase2$W3 == 0), 1 * (phase2$W3 == 1)) rownames(B.phase2) <- cohort[cohort$phase2 == 1, "id"] B.phase3 <- cbind(1 * (casecohort$W3 == 0), 1 * (casecohort$W3 == 1)) rownames(B.phase3) <- cohort[cohort$phase3 == 1, "id"] total.B.phase2 <- colSums(B.phase2) J3 <- ncol(B.phase3) n <- nrow(cohort) # Quantities needed for estimation of the cumulative baseline hazard when # covariate data is missing mod.cohort <- coxph(Surv(event.time, status) ~ X2, data = cohort, robust = TRUE) # X2 is available on all cohort members mod.cohort.detail <- coxph.detail(mod.cohort, riskmat = TRUE) riskmat.phase2 <- with(cohort, mod.cohort.detail$riskmat[phase2 == 1,]) rownames(riskmat.phase2) <- cohort[cohort$phase2 == 1, "id"] observed.times.phase2 <- apply(riskmat.phase2, 1, function(v) {which.max(cumsum(v))}) dNt.phase2 <- matrix(0, nrow(riskmat.phase2), ncol(riskmat.phase2)) dNt.phase2[cbind(1:nrow(riskmat.phase2), observed.times.phase2)] <- 1 dNt.phase2 <- sweep(dNt.phase2, 1, phase2$status, "*") colnames(dNt.phase2) <- colnames(riskmat.phase2) rownames(dNt.phase2) <- rownames(riskmat.phase2) Tau1 <- 0 # given time interval for the pure risk Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with true known design weights mod.true <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.true, id = id, robust = TRUE) est.true <- influences.missingdata(mod = mod.true, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2, Tau1 = Tau1, Tau2 = Tau2, x = x) # print the influences on the cumulative baseline hazard estimate # est.true$infl.Lambda0.Tau1Tau2 # print the phase-two influences on the cumulative baseline hazard estimate # est.true$infl2.Lambda0.Tau1Tau2 # print the phase-three influences on the cumulative baseline hazard estimate # est.true$infl3.Lambda0.Tau1Tau2 # Estimation using the stratified case cohort with estimated weights, and # accounting for the estimation through the influences mod.estimated <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.est, id = id, robust = TRUE) est.estimated <- influences.missingdata(mod.estimated, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2, estimated.weights = TRUE, B.phase2 = B.phase2, Tau1 = Tau1, Tau2 = Tau2, x = x) # print the influences on the cumulative baseline hazard estimate # est.estimated$infl.Lambda0.Tau1Tau2 # print the phase-two influences on the cumulative baseline hazard estimate # est.estimated$infl2.Lambda0.Tau1Tau2 # print the phase-three influences on the cumulative baseline hazard estimate # est.estimated$infl3.Lambda0.Tau1Tau2
Computes the influences on the log-relative hazard, baseline hazards at each unique event time, cumulative baseline hazard in a given time interval [Tau1, Tau2] and on the pure risk in [Tau1, Tau2] and for a given covariate profile x, when covariate data is missing for certain individuals in the phase-two data.
influences.missingdata(mod, riskmat.phase2, dNt.phase2 = NULL, status.phase2 = NULL, Tau1 = NULL, Tau2 = NULL, x = NULL, estimated.weights = FALSE, B.phase2 = NULL)influences.missingdata(mod, riskmat.phase2, dNt.phase2 = NULL, status.phase2 = NULL, Tau1 = NULL, Tau2 = NULL, x = NULL, estimated.weights = FALSE, B.phase2 = NULL)
mod |
a cox model object, result of function coxph. |
riskmat.phase2 |
at risk matrix for the phase-two data at all of the cases event times, even those with missing covariate data. |
dNt.phase2 |
counting process matrix for failures in the phase-two data.
Needs to be provided if |
status.phase2 |
vector indicating the case status in the phase-two data.
Needs to be provided if |
Tau1 |
left bound of the time interval considered for the cumulative baseline hazard and pure risk. Default is the first event time. |
Tau2 |
right bound of the time interval considered for the cumulative baseline hazard and pure risk. Default is the last event time. |
x |
vector of length |
estimated.weights |
are the weights for the third phase of sampling (due to
missingness) estimated? If |
B.phase2 |
matrix for the phase-two data, with phase-three sampling strata
indicators. It should have as many columns as phase-three strata ( |
influences.missingdata works for estimation from a case-cohort with design
weights and when covariate data was missing for certain individuals in the
phase-two data (i.e., case-cohort obtained from three phases of sampling).
If there are no missing covariates in the phase- two sample, use influences
with either design weights or calibrated weights.
When covariate information was missing for certain individuals in the phase-two data
(i.e., case-cohort obtained from three phases of sampling), use influences.missingdata.
influences.missingdata uses the influence formulas provided in Etievant
and Gail (2024).
infl.beta: matrix with the overall influences on the log-relative hazard estimates.
infl.lambda0.t: matrix with the overall influences on the baseline hazards estimates at each unique event time.
infl.Lambda0.Tau1Tau2.hat: vector with the overall influences on the cumulative baseline hazard estimate in [Tau1, Tau2].
infl.Pi.x.Tau1Tau2.hat: vector with the overall influences on the pure risk estimate in
[Tau1, Tau2] and for covariate profile x.
infl2.beta: matrix with the phase-two influences on the log-relative hazard estimates.
infl2.lambda0.t: matrix with the phase-two influences on the baseline hazards estimates at each unique event time.
infl2.Lambda0.Tau1Tau2.hat: vector with the phase-two influences on the cumulative baseline hazard estimate in [Tau1, Tau2].
infl2.Pi.x.Tau1Tau2.hat: vector with the phase-two influences on the pure risk estimate in
[Tau1, Tau2] and for covariate profile x.
infl3.beta: matrix with the phase-three influences on the log-relative hazard estimates.
infl3.lambda0.t: matrix with the phase-three influences on the baseline hazards estimates at each unique event time.
infl3.Lambda0.Tau1Tau2.hat: vector with the phase-three influences on the cumulative baseline hazard estimate in [Tau1, Tau2].
infl3.Pi.x.Tau1Tau2.hat: vector with the phase-three influences on the pure risk estimate in
[Tau1, Tau2] and for covariate profile x.
beta.hat: vector of length with log-relative hazard estimates.
lambda0.t.hat: vector with baseline hazards estimates at each unique event time.
Lambda0.Tau1Tau2.hat: cumulative baseline hazard estimate in [Tau1, Tau2].
Pi.x.Tau1Tau2.hat: pure risk estimate in [Tau1, Tau2] and for covariate profile x.
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
estimation, estimation.CumBH, estimation.PR,
influences.RH.missingdata, influences.CumBH.missingdata,
influences.PR.missingdata, influences, influences.RH, influences.CumBH,
influences.PR, robustvariance and variance.
data(dataexample.missingdata.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.missingdata.stratified$cohort phase2 <- cohort[which(cohort$phase2 == 1),] # the phase-two sample casecohort <- cohort[which(cohort$phase3 == 1),] # the stratified case-cohort B.phase2 <- cbind(1 * (phase2$W3 == 0), 1 * (phase2$W3 == 1)) rownames(B.phase2) <- cohort[cohort$phase2 == 1, "id"] B.phase3 <- cbind(1 * (casecohort$W3 == 0), 1 * (casecohort$W3 == 1)) rownames(B.phase3) <- cohort[cohort$phase3 == 1, "id"] total.B.phase2 <- colSums(B.phase2) J3 <- ncol(B.phase3) n <- nrow(cohort) # Quantities needed for estimation of the cumulative baseline hazard when # covariate data is missing mod.cohort <- coxph(Surv(event.time, status) ~ X2, data = cohort, robust = TRUE) # X2 is available on all cohort members mod.cohort.detail <- coxph.detail(mod.cohort, riskmat = TRUE) riskmat.phase2 <- with(cohort, mod.cohort.detail$riskmat[phase2 == 1,]) rownames(riskmat.phase2) <- cohort[cohort$phase2 == 1, "id"] observed.times.phase2 <- apply(riskmat.phase2, 1, function(v) {which.max(cumsum(v))}) dNt.phase2 <- matrix(0, nrow(riskmat.phase2), ncol(riskmat.phase2)) dNt.phase2[cbind(1:nrow(riskmat.phase2), observed.times.phase2)] <- 1 dNt.phase2 <- sweep(dNt.phase2, 1, phase2$status, "*") colnames(dNt.phase2) <- colnames(riskmat.phase2) rownames(dNt.phase2) <- rownames(riskmat.phase2) Tau1 <- 0 # given time interval for the pure risk Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with true known design weights mod.true <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.true, id = id, robust = TRUE) est.true <- influences.missingdata(mod = mod.true, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2, Tau1 = Tau1, Tau2 = Tau2, x = x) # print the influences on the log-relative hazard estimates # est.true$infl.beta # print the phase-two influences on the log-relative hazard estimates # est.true$infl2.beta # print the phase-three influences on the log-relative hazard estimates # est.true$infl3.beta # print the influences on the cumulative baseline hazard estimate # est.true$infl.Lambda0.Tau1Tau2 # print the phase-two influences on the cumulative baseline hazard estimate # est.true$infl2.Lambda0.Tau1Tau2 # print the phase-three influences on the cumulative baseline hazard estimate # est.true$infl3.Lambda0.Tau1Tau2 # print the influences on the pure risk estimate # est.true$infl.Pi.x.Tau1Tau2 # print the phase-two influences on the pure risk estimate # est.true$infl2.Pi.x.Tau1Tau2 # print the phase-three influences on the pure risk estimate # est.true$infl3.Pi.x.Tau1Tau2 # Estimation using the stratified case cohort with estimated weights, and # accounting for the estimation through the influences mod.estimated <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.est, id = id, robust = TRUE) est.estimated <- influences.missingdata(mod.estimated, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2, estimated.weights = TRUE, B.phase2 = B.phase2, Tau1 = Tau1, Tau2 = Tau2, x = x) # print the influences on the log-relative hazard estimates # est.estimated$infl.beta # print the phase-two influences on the log-relative hazard estimates # est.estimated$infl2.beta # print the phase-three influences on the log-relative hazard estimates # est.estimated$infl3.beta # print the influences on the cumulative baseline hazard estimate # est.estimated$infl.Lambda0.Tau1Tau2 # print the phase-two influences on the cumulative baseline hazard estimate # est.estimated$infl2.Lambda0.Tau1Tau2 # print the phase-three influences on the cumulative baseline hazard estimate # est.estimated$infl3.Lambda0.Tau1Tau2 # print the influences on the pure risk estimate # est.estimated$infl.Pi.x.Tau1Tau2 # print the phase-two influences on the pure risk estimate # est.estimated$infl2.Pi.x.Tau1Tau2 # print the phase-three influences on the pure risk estimate # est.estimated$infl3.Pi.x.Tau1Tau2data(dataexample.missingdata.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.missingdata.stratified$cohort phase2 <- cohort[which(cohort$phase2 == 1),] # the phase-two sample casecohort <- cohort[which(cohort$phase3 == 1),] # the stratified case-cohort B.phase2 <- cbind(1 * (phase2$W3 == 0), 1 * (phase2$W3 == 1)) rownames(B.phase2) <- cohort[cohort$phase2 == 1, "id"] B.phase3 <- cbind(1 * (casecohort$W3 == 0), 1 * (casecohort$W3 == 1)) rownames(B.phase3) <- cohort[cohort$phase3 == 1, "id"] total.B.phase2 <- colSums(B.phase2) J3 <- ncol(B.phase3) n <- nrow(cohort) # Quantities needed for estimation of the cumulative baseline hazard when # covariate data is missing mod.cohort <- coxph(Surv(event.time, status) ~ X2, data = cohort, robust = TRUE) # X2 is available on all cohort members mod.cohort.detail <- coxph.detail(mod.cohort, riskmat = TRUE) riskmat.phase2 <- with(cohort, mod.cohort.detail$riskmat[phase2 == 1,]) rownames(riskmat.phase2) <- cohort[cohort$phase2 == 1, "id"] observed.times.phase2 <- apply(riskmat.phase2, 1, function(v) {which.max(cumsum(v))}) dNt.phase2 <- matrix(0, nrow(riskmat.phase2), ncol(riskmat.phase2)) dNt.phase2[cbind(1:nrow(riskmat.phase2), observed.times.phase2)] <- 1 dNt.phase2 <- sweep(dNt.phase2, 1, phase2$status, "*") colnames(dNt.phase2) <- colnames(riskmat.phase2) rownames(dNt.phase2) <- rownames(riskmat.phase2) Tau1 <- 0 # given time interval for the pure risk Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with true known design weights mod.true <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.true, id = id, robust = TRUE) est.true <- influences.missingdata(mod = mod.true, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2, Tau1 = Tau1, Tau2 = Tau2, x = x) # print the influences on the log-relative hazard estimates # est.true$infl.beta # print the phase-two influences on the log-relative hazard estimates # est.true$infl2.beta # print the phase-three influences on the log-relative hazard estimates # est.true$infl3.beta # print the influences on the cumulative baseline hazard estimate # est.true$infl.Lambda0.Tau1Tau2 # print the phase-two influences on the cumulative baseline hazard estimate # est.true$infl2.Lambda0.Tau1Tau2 # print the phase-three influences on the cumulative baseline hazard estimate # est.true$infl3.Lambda0.Tau1Tau2 # print the influences on the pure risk estimate # est.true$infl.Pi.x.Tau1Tau2 # print the phase-two influences on the pure risk estimate # est.true$infl2.Pi.x.Tau1Tau2 # print the phase-three influences on the pure risk estimate # est.true$infl3.Pi.x.Tau1Tau2 # Estimation using the stratified case cohort with estimated weights, and # accounting for the estimation through the influences mod.estimated <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.est, id = id, robust = TRUE) est.estimated <- influences.missingdata(mod.estimated, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2, estimated.weights = TRUE, B.phase2 = B.phase2, Tau1 = Tau1, Tau2 = Tau2, x = x) # print the influences on the log-relative hazard estimates # est.estimated$infl.beta # print the phase-two influences on the log-relative hazard estimates # est.estimated$infl2.beta # print the phase-three influences on the log-relative hazard estimates # est.estimated$infl3.beta # print the influences on the cumulative baseline hazard estimate # est.estimated$infl.Lambda0.Tau1Tau2 # print the phase-two influences on the cumulative baseline hazard estimate # est.estimated$infl2.Lambda0.Tau1Tau2 # print the phase-three influences on the cumulative baseline hazard estimate # est.estimated$infl3.Lambda0.Tau1Tau2 # print the influences on the pure risk estimate # est.estimated$infl.Pi.x.Tau1Tau2 # print the phase-two influences on the pure risk estimate # est.estimated$infl2.Pi.x.Tau1Tau2 # print the phase-three influences on the pure risk estimate # est.estimated$infl3.Pi.x.Tau1Tau2
Computes the influences on the pure risk in the time interval [Tau1, Tau2] and for a given covariate profile x, from that on the log-relative hazard and cumulative baseline hazard. Can take calibration of the design weights into account.
influences.PR(beta, Lambda0.Tau1Tau2, x = NULL, infl.beta, infl.Lambda0.Tau1Tau2, calibrated = NULL, infl2.beta = NULL, infl2.Lambda0.Tau1Tau2 = NULL)influences.PR(beta, Lambda0.Tau1Tau2, x = NULL, infl.beta, infl.Lambda0.Tau1Tau2, calibrated = NULL, infl2.beta = NULL, infl2.Lambda0.Tau1Tau2 = NULL)
beta |
vector of length |
Lambda0.Tau1Tau2 |
cumulative baseline hazard in [Tau1, Tau2]. |
x |
vector of length |
infl.beta |
matrix with the overall influences on the log-relative hazard estimates. |
infl.Lambda0.Tau1Tau2 |
vector with the overall influences on the cumulative baseline hazard estimate in [Tau1, Tau2]. |
calibrated |
are calibrated weights used for the estimation of the
parameters? If |
infl2.beta |
matrix with the phase-two influences on the log-relative
hazard estimates. Needs to be provided if |
infl2.Lambda0.Tau1Tau2 |
vector with the phase-two influences on the
cumulative baseline hazard estimate in [Tau1, Tau2]. Needs to be provided
if |
influences.PR works for estimation from a case-cohort with design weights
or calibrated weights (case-cohort consisting of the subcohort and cases not in
the subcohort, i.e., case-cohort obtained from two phases of sampling).
If covariate information is missing for certain individuals in the phase-two data
(i.e., case-cohort obtained from three phases of sampling), use influences.PR.missingdata.
influences uses the influence formulas provided in Etievant and Gail
(2024).
If calibrated = FALSE, the infuences are only provided for the individuals
in the case-cohort. If calibrated = TRUE, the influences are provided for
all the individuals in the cohort.
infl.Pi.x.Tau1Tau2.hat: vector with the overall influences on the pure risk estimate in [Tau1, Tau2] and for covariate profile x.
infl2.Pi.x.Tau1Tau2.hat: vector with the phase-two influences on the pure risk estimate in [Tau1, Tau2] and for covariate profile x.
Returned if calibrated = TRUE.
Pi.x.Tau1Tau2.hat: pure risk estimate in [Tau1, Tau2] and for covariate profile x.
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
estimation, estimation.CumBH, estimation.PR,
influences, influences.RH, influences.CumBH,
influences.missingdata, influences.RH.missingdata,
influences.CumBH.missingdata, influences.PR.missingdata,
robustvariance and variance.
data(dataexample.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.stratified$cohort casecohort <- cohort[which(cohort$status == 1 | cohort$subcohort == 1),] # the stratified case-cohort casecohort$weights <- casecohort$strata.n / casecohort$strata.m casecohort$weights[which(casecohort$status == 1)] <- 1 Tau1 <- 0 Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with design weights mod <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weights, id = id, robust = TRUE) est <- influences(mod, Tau1 = Tau1, Tau2 = Tau2, x = x) # print the influences on the pure risk estimate # est$infl.Pi.x.Tau1Tau2data(dataexample.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.stratified$cohort casecohort <- cohort[which(cohort$status == 1 | cohort$subcohort == 1),] # the stratified case-cohort casecohort$weights <- casecohort$strata.n / casecohort$strata.m casecohort$weights[which(casecohort$status == 1)] <- 1 Tau1 <- 0 Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with design weights mod <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weights, id = id, robust = TRUE) est <- influences(mod, Tau1 = Tau1, Tau2 = Tau2, x = x) # print the influences on the pure risk estimate # est$infl.Pi.x.Tau1Tau2
Computes the influences on the pure risk in the time interval [Tau1, Tau2] and for a given covariate profile x, from that on the log-relative hazard and cumulative baseline hazard, when covariate data is missing for certain individuals in the phase-two data.
influences.PR.missingdata(beta, Lambda0.Tau1Tau2, x = NULL, infl2.beta, infl2.Lambda0.Tau1Tau2, infl3.beta, infl3.Lambda0.Tau1Tau2)influences.PR.missingdata(beta, Lambda0.Tau1Tau2, x = NULL, infl2.beta, infl2.Lambda0.Tau1Tau2, infl3.beta, infl3.Lambda0.Tau1Tau2)
beta |
vector of length |
Lambda0.Tau1Tau2 |
cumulative baseline hazard in [Tau1, Tau2]. |
x |
vector of length |
infl2.beta |
matrix with the overall influences on the log-relative hazard estimates. |
infl2.Lambda0.Tau1Tau2 |
vector with the overall influences on the cumulative baseline hazard estimate in [Tau1, Tau2]. |
infl3.beta |
matrix with the phase-three influences on the log-relative hazard estimates. |
infl3.Lambda0.Tau1Tau2 |
vector with the phase-three influences on the cumulative baseline hazard estimate in [Tau1, Tau2]. |
influences.PR.missingdata works for estimation from a case-cohort with design
weights and when covariate data was missing for certain individuals in the
phase-two data (i.e., case-cohort obtained from three phases of sampling).
If there are no missing covariates in the phase- two sample, use influences.PR
with either design weights or calibrated weights.
influences.PR.missingdata uses the influence formulas provided in Etievant
and Gail (2024).
infl.Pi.x.Tau1Tau2.hat: vector with the overall influences on the pure risk estimate
in [Tau1, Tau2] and for covariate profile x.
infl2.Pi.x.Tau1Tau2.hat: vector with the phase-two influences on the pure risk estimate
in [Tau1, Tau2] and for covariate profile x.
infl3.Pi.x.Tau1Tau2.hat: vector with the phase-three influences on the pure risk estimate
in [Tau1, Tau2] and for covariate profile x.
Pi.x.Tau1Tau2.hat: pure risk estimate in [Tau1, Tau2] and for covariate profile x.
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
estimation, estimation.CumBH, estimation.PR,
influences.missingdata, influences.RH.missingdata,
influences.CumBH.missingdata, influences, influences.RH, influences.CumBH,
influences.PR, robustvariance and variance.
data(dataexample.missingdata.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.missingdata.stratified$cohort phase2 <- cohort[which(cohort$phase2 == 1),] # the phase-two sample casecohort <- cohort[which(cohort$phase3 == 1),] # the stratified case-cohort B.phase2 <- cbind(1 * (phase2$W3 == 0), 1 * (phase2$W3 == 1)) rownames(B.phase2) <- cohort[cohort$phase2 == 1, "id"] B.phase3 <- cbind(1 * (casecohort$W3 == 0), 1 * (casecohort$W3 == 1)) rownames(B.phase3) <- cohort[cohort$phase3 == 1, "id"] total.B.phase2 <- colSums(B.phase2) J3 <- ncol(B.phase3) n <- nrow(cohort) # Quantities needed for estimation of the cumulative baseline hazard when # covariate data is missing mod.cohort <- coxph(Surv(event.time, status) ~ X2, data = cohort, robust = TRUE) # X2 is available on all cohort members mod.cohort.detail <- coxph.detail(mod.cohort, riskmat = TRUE) riskmat.phase2 <- with(cohort, mod.cohort.detail$riskmat[phase2 == 1,]) rownames(riskmat.phase2) <- cohort[cohort$phase2 == 1, "id"] observed.times.phase2 <- apply(riskmat.phase2, 1, function(v) {which.max(cumsum(v))}) dNt.phase2 <- matrix(0, nrow(riskmat.phase2), ncol(riskmat.phase2)) dNt.phase2[cbind(1:nrow(riskmat.phase2), observed.times.phase2)] <- 1 dNt.phase2 <- sweep(dNt.phase2, 1, phase2$status, "*") colnames(dNt.phase2) <- colnames(riskmat.phase2) rownames(dNt.phase2) <- rownames(riskmat.phase2) Tau1 <- 0 # given time interval for the pure risk Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk v <- c(1, -1, 0.6) # over covariate profile # Estimation using the stratified case cohort with true known design weights mod.true <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.true, id = id, robust = TRUE) est.true <- influences.missingdata(mod = mod.true, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2, Tau1 = Tau1, Tau2 = Tau2, x = x) beta.true <- est.true$beta.hat Lambda0.true <- est.true$Lambda0.Tau1Tau2.hat infl2.beta.true <- est.true$infl2.beta infl2.Lambda0.true <- est.true$infl2.Lambda0.Tau1Tau2 infl3.beta.true <- est.true$infl3.beta infl3.Lambda0.true <- est.true$infl3.Lambda0.Tau1Tau2 est.PR2.true <- influences.PR.missingdata(beta = beta.true, Lambda0.Tau1Tau2 = Lambda0.true, x = v, infl2.beta = infl2.beta.true, infl2.Lambda0.Tau1Tau2 = infl2.Lambda0.true, infl3.beta = infl3.beta.true, infl3.Lambda0.Tau1Tau2 = infl3.Lambda0.true) # print the influences on the pure risk estimate # est.PR2.true$infl.Pi.x.Tau1Tau2 # print the phase-two influences on the pure risk estimate # est.PR2.true$infl2.Pi.x.Tau1Tau2 # print the phase-three influences on the pure risk estimate # est.PR2.true$infl3.Pi.x.Tau1Tau2 # Estimation using the stratified case cohort with estimated weights, and # accounting for the estimation through the influences mod.estimated <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.est, id = id, robust = TRUE) est.estimated <- influences.missingdata(mod.estimated, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2, estimated.weights = TRUE, B.phase2 = B.phase2, Tau1 = Tau1, Tau2 = Tau2, x = x) beta.estimated <- est.estimated$beta.hat Lambda0.estimated <- est.estimated$Lambda0.Tau1Tau2.hat infl2.beta.estimated <- est.estimated$infl2.beta infl2.Lambda0.estimated <- est.estimated$infl2.Lambda0.Tau1Tau2 infl3.beta.estimated <- est.estimated$infl3.beta infl3.Lambda0.estimated <- est.estimated$infl3.Lambda0.Tau1Tau2 est.PR2.estimated <- influences.PR.missingdata(beta = beta.estimated, Lambda0.Tau1Tau2 = Lambda0.estimated, x = v, infl2.beta = infl2.beta.estimated, infl2.Lambda0.Tau1Tau2 = infl2.Lambda0.estimated, infl3.beta = infl3.beta.estimated, infl3.Lambda0.Tau1Tau2 = infl3.Lambda0.estimated) # print the influences on the pure risk estimate # est.PR2.estimated$infl.Pi.x.Tau1Tau2 # print the phase-two influences on the pure risk estimate # est.PR2.estimated$infl2.Pi.x.Tau1Tau2 # print the phase-three influences on the pure risk estimate # est.PR2.estimated$infl3.Pi.x.Tau1Tau2data(dataexample.missingdata.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.missingdata.stratified$cohort phase2 <- cohort[which(cohort$phase2 == 1),] # the phase-two sample casecohort <- cohort[which(cohort$phase3 == 1),] # the stratified case-cohort B.phase2 <- cbind(1 * (phase2$W3 == 0), 1 * (phase2$W3 == 1)) rownames(B.phase2) <- cohort[cohort$phase2 == 1, "id"] B.phase3 <- cbind(1 * (casecohort$W3 == 0), 1 * (casecohort$W3 == 1)) rownames(B.phase3) <- cohort[cohort$phase3 == 1, "id"] total.B.phase2 <- colSums(B.phase2) J3 <- ncol(B.phase3) n <- nrow(cohort) # Quantities needed for estimation of the cumulative baseline hazard when # covariate data is missing mod.cohort <- coxph(Surv(event.time, status) ~ X2, data = cohort, robust = TRUE) # X2 is available on all cohort members mod.cohort.detail <- coxph.detail(mod.cohort, riskmat = TRUE) riskmat.phase2 <- with(cohort, mod.cohort.detail$riskmat[phase2 == 1,]) rownames(riskmat.phase2) <- cohort[cohort$phase2 == 1, "id"] observed.times.phase2 <- apply(riskmat.phase2, 1, function(v) {which.max(cumsum(v))}) dNt.phase2 <- matrix(0, nrow(riskmat.phase2), ncol(riskmat.phase2)) dNt.phase2[cbind(1:nrow(riskmat.phase2), observed.times.phase2)] <- 1 dNt.phase2 <- sweep(dNt.phase2, 1, phase2$status, "*") colnames(dNt.phase2) <- colnames(riskmat.phase2) rownames(dNt.phase2) <- rownames(riskmat.phase2) Tau1 <- 0 # given time interval for the pure risk Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk v <- c(1, -1, 0.6) # over covariate profile # Estimation using the stratified case cohort with true known design weights mod.true <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.true, id = id, robust = TRUE) est.true <- influences.missingdata(mod = mod.true, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2, Tau1 = Tau1, Tau2 = Tau2, x = x) beta.true <- est.true$beta.hat Lambda0.true <- est.true$Lambda0.Tau1Tau2.hat infl2.beta.true <- est.true$infl2.beta infl2.Lambda0.true <- est.true$infl2.Lambda0.Tau1Tau2 infl3.beta.true <- est.true$infl3.beta infl3.Lambda0.true <- est.true$infl3.Lambda0.Tau1Tau2 est.PR2.true <- influences.PR.missingdata(beta = beta.true, Lambda0.Tau1Tau2 = Lambda0.true, x = v, infl2.beta = infl2.beta.true, infl2.Lambda0.Tau1Tau2 = infl2.Lambda0.true, infl3.beta = infl3.beta.true, infl3.Lambda0.Tau1Tau2 = infl3.Lambda0.true) # print the influences on the pure risk estimate # est.PR2.true$infl.Pi.x.Tau1Tau2 # print the phase-two influences on the pure risk estimate # est.PR2.true$infl2.Pi.x.Tau1Tau2 # print the phase-three influences on the pure risk estimate # est.PR2.true$infl3.Pi.x.Tau1Tau2 # Estimation using the stratified case cohort with estimated weights, and # accounting for the estimation through the influences mod.estimated <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.est, id = id, robust = TRUE) est.estimated <- influences.missingdata(mod.estimated, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2, estimated.weights = TRUE, B.phase2 = B.phase2, Tau1 = Tau1, Tau2 = Tau2, x = x) beta.estimated <- est.estimated$beta.hat Lambda0.estimated <- est.estimated$Lambda0.Tau1Tau2.hat infl2.beta.estimated <- est.estimated$infl2.beta infl2.Lambda0.estimated <- est.estimated$infl2.Lambda0.Tau1Tau2 infl3.beta.estimated <- est.estimated$infl3.beta infl3.Lambda0.estimated <- est.estimated$infl3.Lambda0.Tau1Tau2 est.PR2.estimated <- influences.PR.missingdata(beta = beta.estimated, Lambda0.Tau1Tau2 = Lambda0.estimated, x = v, infl2.beta = infl2.beta.estimated, infl2.Lambda0.Tau1Tau2 = infl2.Lambda0.estimated, infl3.beta = infl3.beta.estimated, infl3.Lambda0.Tau1Tau2 = infl3.Lambda0.estimated) # print the influences on the pure risk estimate # est.PR2.estimated$infl.Pi.x.Tau1Tau2 # print the phase-two influences on the pure risk estimate # est.PR2.estimated$infl2.Pi.x.Tau1Tau2 # print the phase-three influences on the pure risk estimate # est.PR2.estimated$infl3.Pi.x.Tau1Tau2
Computes the influences on the log-relative hazard. Can take calibration of the design weights into account.
influences.RH(mod, calibrated = NULL, A = NULL)influences.RH(mod, calibrated = NULL, A = NULL)
mod |
a cox model object, result of function coxph. |
calibrated |
are calibrated weights used for the estimation of the
parameters? If |
A |
|
influences.RH works for estimation from a case-cohort with design weights
or calibrated weights (case-cohort consisting of the subcohort and cases not in
the subcohort, i.e., case-cohort obtained from two phases of sampling).
If covariate information is missing for certain individuals in the phase-two data
(i.e., case-cohort obtained from three phases of sampling), use influences.RH.missingdata.
influence.RH uses the influence formulas provided in Etievant and Gail
(2024).
If calibrated = FALSE, the infuences are only provided for the individuals
in the case-cohort. If calibrated = TRUE, the influences are provided for
all the individuals in the cohort.
infl.beta: matrix with the overall influences on the log-relative hazard estimates.
infl2.beta: matrix with the phase-two influences on the log-relative hazard estimates. Returned if calibrated = TRUE.
beta.hat: vector of length with log-relative hazard estimates.
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
estimation, estimation.CumBH, estimation.PR,
influences, influences.CumBH, influences.PR,
influences.missingdata, influences.RH.missingdata,
influences.CumBH.missingdata,influences.PR.missingdata, robustvariance and variance.
data(dataexample.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.stratified$cohort casecohort <- cohort[which(cohort$status == 1 | cohort$subcohort == 1),] # the stratified case-cohort casecohort$weights <- casecohort$strata.n / casecohort$strata.m casecohort$weights[which(casecohort$status == 1)] <- 1 Tau1 <- 0 Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with design weights mod <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weights, id = id, robust = TRUE) est <- influences(mod, Tau1 = Tau1, Tau2 = Tau2, x = x) # print the influences on the log-relative hazard estimates # est$infl.betadata(dataexample.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.stratified$cohort casecohort <- cohort[which(cohort$status == 1 | cohort$subcohort == 1),] # the stratified case-cohort casecohort$weights <- casecohort$strata.n / casecohort$strata.m casecohort$weights[which(casecohort$status == 1)] <- 1 Tau1 <- 0 Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with design weights mod <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weights, id = id, robust = TRUE) est <- influences(mod, Tau1 = Tau1, Tau2 = Tau2, x = x) # print the influences on the log-relative hazard estimates # est$infl.beta
Computes the influences on the log-relative hazard, when covariate data is missing for certain individuals in the phase-two data.
influences.RH.missingdata(mod, riskmat.phase2, dNt.phase2 = NULL, status.phase2 = NULL, estimated.weights = FALSE, B.phase2 = NULL)influences.RH.missingdata(mod, riskmat.phase2, dNt.phase2 = NULL, status.phase2 = NULL, estimated.weights = FALSE, B.phase2 = NULL)
mod |
a cox model object, result of function coxph. |
riskmat.phase2 |
at risk matrix for the phase-two data at all of the cases event times, even those with missing covariate data. |
dNt.phase2 |
counting process matrix for failures in the phase-two data.
Needs to be provided if |
status.phase2 |
vector indicating the case status in the phase-two data.
Needs to be provided if |
estimated.weights |
are the weights for the third phase of sampling (due to
missingness) estimated? If |
B.phase2 |
matrix for the phase-two data, with phase-three sampling strata
indicators. It should have as many columns as phase-three strata ( |
influences.RH.missingdata works for estimation from a case-cohort with design
weights and when covariate data was missing for certain individuals in the
phase-two data (i.e., case-cohort obtained from three phases of sampling and
consisting of individuals in the phase-two data without missing covariate information).
If there are no missing covariates in the phase- two sample, use influences.RH
with either design weights or calibrated weights.
influences.RH.missingdata uses the influence formulas provided in Etievant
and Gail (2024).
infl.beta: matrix with the overall influences on the log-relative hazard estimates.
infl2.beta: matrix with the phase-two influences on the log-relative hazard estimates.
infl3.beta: matrix with the phase-three influences on the log-relative hazard estimates.
beta.hat: vector of length with log-relative hazard estimates.
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
estimation, estimation.CumBH, estimation.PR,
influences.missingdata, influences.CumBH.missingdata,
influences.PR.missingdata, influences, influences.RH, influences.CumBH,
influences.PR, robustvariance and variance.
data(dataexample.missingdata.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.missingdata.stratified$cohort phase2 <- cohort[which(cohort$phase2 == 1),] # the phase-two sample casecohort <- cohort[which(cohort$phase3 == 1),] # the stratified case-cohort B.phase2 <- cbind(1 * (phase2$W3 == 0), 1 * (phase2$W3 == 1)) rownames(B.phase2) <- cohort[cohort$phase2 == 1, "id"] B.phase3 <- cbind(1 * (casecohort$W3 == 0), 1 * (casecohort$W3 == 1)) rownames(B.phase3) <- cohort[cohort$phase3 == 1, "id"] total.B.phase2 <- colSums(B.phase2) J3 <- ncol(B.phase3) n <- nrow(cohort) # Quantities needed for estimation of the cumulative baseline hazard when # covariate data is missing mod.cohort <- coxph(Surv(event.time, status) ~ X2, data = cohort, robust = TRUE) # X2 is available on all cohort members mod.cohort.detail <- coxph.detail(mod.cohort, riskmat = TRUE) riskmat.phase2 <- with(cohort, mod.cohort.detail$riskmat[phase2 == 1,]) rownames(riskmat.phase2) <- cohort[cohort$phase2 == 1, "id"] observed.times.phase2 <- apply(riskmat.phase2, 1, function(v) {which.max(cumsum(v))}) dNt.phase2 <- matrix(0, nrow(riskmat.phase2), ncol(riskmat.phase2)) dNt.phase2[cbind(1:nrow(riskmat.phase2), observed.times.phase2)] <- 1 dNt.phase2 <- sweep(dNt.phase2, 1, phase2$status, "*") colnames(dNt.phase2) <- colnames(riskmat.phase2) rownames(dNt.phase2) <- rownames(riskmat.phase2) Tau1 <- 0 # given time interval for the pure risk Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with true known design weights mod.true <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.true, id = id, robust = TRUE) est.true <- influences.missingdata(mod = mod.true, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2, Tau1 = Tau1, Tau2 = Tau2, x = x) # print the influences on the log-relative hazard estimates # est.true$infl.beta # print the phase-two influences on the log-relative hazard estimates # est.true$infl2.beta # print the phase-three influences on the log-relative hazard estimates # est.true$infl3.beta # Estimation using the stratified case cohort with estimated weights, and # accounting for the estimation through the influences mod.estimated <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.est, id = id, robust = TRUE) est.estimated <- influences.missingdata(mod.estimated, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2, estimated.weights = TRUE, B.phase2 = B.phase2, Tau1 = Tau1, Tau2 = Tau2, x = x) # print the influences on the log-relative hazard estimates # est.estimated$infl.beta # print the phase-two influences on the log-relative hazard estimates # est.estimated$infl2.beta # print the phase-three influences on the log-relative hazard estimates # est.estimated$infl3.betadata(dataexample.missingdata.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.missingdata.stratified$cohort phase2 <- cohort[which(cohort$phase2 == 1),] # the phase-two sample casecohort <- cohort[which(cohort$phase3 == 1),] # the stratified case-cohort B.phase2 <- cbind(1 * (phase2$W3 == 0), 1 * (phase2$W3 == 1)) rownames(B.phase2) <- cohort[cohort$phase2 == 1, "id"] B.phase3 <- cbind(1 * (casecohort$W3 == 0), 1 * (casecohort$W3 == 1)) rownames(B.phase3) <- cohort[cohort$phase3 == 1, "id"] total.B.phase2 <- colSums(B.phase2) J3 <- ncol(B.phase3) n <- nrow(cohort) # Quantities needed for estimation of the cumulative baseline hazard when # covariate data is missing mod.cohort <- coxph(Surv(event.time, status) ~ X2, data = cohort, robust = TRUE) # X2 is available on all cohort members mod.cohort.detail <- coxph.detail(mod.cohort, riskmat = TRUE) riskmat.phase2 <- with(cohort, mod.cohort.detail$riskmat[phase2 == 1,]) rownames(riskmat.phase2) <- cohort[cohort$phase2 == 1, "id"] observed.times.phase2 <- apply(riskmat.phase2, 1, function(v) {which.max(cumsum(v))}) dNt.phase2 <- matrix(0, nrow(riskmat.phase2), ncol(riskmat.phase2)) dNt.phase2[cbind(1:nrow(riskmat.phase2), observed.times.phase2)] <- 1 dNt.phase2 <- sweep(dNt.phase2, 1, phase2$status, "*") colnames(dNt.phase2) <- colnames(riskmat.phase2) rownames(dNt.phase2) <- rownames(riskmat.phase2) Tau1 <- 0 # given time interval for the pure risk Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with true known design weights mod.true <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.true, id = id, robust = TRUE) est.true <- influences.missingdata(mod = mod.true, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2, Tau1 = Tau1, Tau2 = Tau2, x = x) # print the influences on the log-relative hazard estimates # est.true$infl.beta # print the phase-two influences on the log-relative hazard estimates # est.true$infl2.beta # print the phase-three influences on the log-relative hazard estimates # est.true$infl3.beta # Estimation using the stratified case cohort with estimated weights, and # accounting for the estimation through the influences mod.estimated <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.est, id = id, robust = TRUE) est.estimated <- influences.missingdata(mod.estimated, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2, estimated.weights = TRUE, B.phase2 = B.phase2, Tau1 = Tau1, Tau2 = Tau2, x = x) # print the influences on the log-relative hazard estimates # est.estimated$infl.beta # print the phase-two influences on the log-relative hazard estimates # est.estimated$infl2.beta # print the phase-three influences on the log-relative hazard estimates # est.estimated$infl3.beta
Computes the product of joint design weights and joint sampling indicators covariances, needed for the phase-two component of the variance (with design or calibrated weights).
product.covar.weight(casecohort, stratified = NULL)product.covar.weight(casecohort, stratified = NULL)
casecohort |
if |
stratified |
was the sampling of the case-cohort stratified on |
product.covar.weight creates the matrix with the products of joint design
weights and joint sampling indicator covariances, for the non-cases in the case
cohort. In other words, it has as many rows and columns as non-cases in the case
cohort, and contains the , with
if individuals
and in stratum are both non-cases, and
otherwise,
,
.
if individuals in stratum
is a non-case, ,
.
if individuals and
in stratum are both non-cases,
,
.
if individuals in stratum is a non-case,
,
.
See Etievant and Gail (2024).
product.covar.weight: matrix with the products of joint design weights and
joint sampling indicator covariances, for the non-cases in the case-cohort.
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
variance, that uses product.covar.weight to compute the variance
estimate that follows the complete variance decomposition (superpopulation and
phase-two variance components).
data(dataexample.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.stratified$cohort casecohort <- cohort[which(cohort$status == 1 | cohort$subcohort == 1),] # the stratified case-cohort prod.covar.weight <- product.covar.weight(casecohort, stratified = TRUE) sum(casecohort$status == 0) # number of non-cases in the case-cohortdata(dataexample.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.stratified$cohort casecohort <- cohort[which(cohort$status == 1 | cohort$subcohort == 1),] # the stratified case-cohort prod.covar.weight <- product.covar.weight(casecohort, stratified = TRUE) sum(casecohort$status == 0) # number of non-cases in the case-cohort
Computes the robust variance estimate, i.e., the sum of the squared influence functions, for a parameter such as log-relative hazard, cumulative baseline hazard or covariate specific pure-risk.
robustvariance(infl)robustvariance(infl)
infl |
overall influences on a parameter such as log-relative hazard, cumulative baseline hazard or covariate specific pure-risk. |
robustvariance works for estimation with design or calibrated weights from
a case cohort obtained from two phases of sampling (i.e., case cohort consisting
of the subcohort and cases not in the subcohort), or when covariate information
was missing for certain individuals in the phase-two data (i.e., case cohort
obtained from three phases of sampling and consisting of individuals in the
phase-two data without missing covariate information).
robust.var: robust variance estimate.
Barlow W. (1994). Robust Variance Estimation for the Case-Cohort Design. Biometrics, 50, 1064-1072.
Langholz B., Jiao J. (2007). Computational methods for case-cohort studies. Computational Statistics & Data Analysis, 51, 3737-37.
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
influences.RH, influences.CumBH, influences.PR,
influences.missingdata, influences.RH.missingdata,
influences.CumBH.missingdata, influences.PR.missingdata and variance.
data(dataexample.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.stratified$cohort casecohort <- cohort[which(cohort$status == 1 | cohort$subcohort == 1),] # the stratified case-cohort casecohort$weights <- casecohort$strata.n / casecohort$strata.m casecohort$weights[which(casecohort$status == 1)] <- 1 Tau1 <- 0 Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with design weights mod <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weights, id = id, robust = TRUE) est <- influences(mod, Tau1 = Tau1, Tau2 = Tau2, x = x) # robust variance estimate for the log-relative hazard robustvariance(est$infl.beta) # robust variance estimate for the cumulative baseline hazard estimate robustvariance(est$infl.Lambda0.Tau1Tau2) # robust variance estimate for the pure risk estimate robustvariance(est$infl.Pi.x.Tau1Tau2)data(dataexample.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.stratified$cohort casecohort <- cohort[which(cohort$status == 1 | cohort$subcohort == 1),] # the stratified case-cohort casecohort$weights <- casecohort$strata.n / casecohort$strata.m casecohort$weights[which(casecohort$status == 1)] <- 1 Tau1 <- 0 Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with design weights mod <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weights, id = id, robust = TRUE) est <- influences(mod, Tau1 = Tau1, Tau2 = Tau2, x = x) # robust variance estimate for the log-relative hazard robustvariance(est$infl.beta) # robust variance estimate for the cumulative baseline hazard estimate robustvariance(est$infl.Lambda0.Tau1Tau2) # robust variance estimate for the pure risk estimate robustvariance(est$infl.Pi.x.Tau1Tau2)
Computes the variance estimate that follows the complete variance decomposition, for a parameter such as log-relative hazard, cumulative baseline hazard or covariate specific pure-risk.
variance(n, casecohort, weights = NULL, infl, calibrated = NULL, infl2 = NULL, cohort = NULL, stratified = NULL, variance.phase2 = NULL)variance(n, casecohort, weights = NULL, infl, calibrated = NULL, infl2 = NULL, cohort = NULL, stratified = NULL, variance.phase2 = NULL)
n |
number of individuals in the whole cohort. |
casecohort |
If |
weights |
vector with design weights for the individuals in the case-cohort data. |
infl |
matrix with the overall influences on the parameter. |
calibrated |
are calibrated weights used for the estimation of the
parameters? If |
infl2 |
matrix with the phase-two influences on the parameter. Needs to be
provided if |
cohort |
If |
stratified |
was the sampling of the case-cohort stratified on |
variance.phase2 |
should the phase-two variance component also be returned?
Default is |
variance works for estimation from a case-cohort with design weights
or calibrated weights (case-cohort consisting of the subcohort and cases not in
the subcohort, i.e., case-cohort obtained from two phases of sampling).
If covariate information is missing for certain individuals in the phase-two data
(i.e., case-cohort obtained from three phases of sampling), use variance.missingdata.
variance uses the variance formulas provided in Etievant and Gail
(2024).
variance: variance estimate.
variance.phase2: phase-two variance component.
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
influences, influences.RH, influences.CumBH,
influences.PR, robustvariance and variance.missingdata.
data(dataexample.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.stratified$cohort casecohort <- cohort[which(cohort$status == 1 | cohort$subcohort == 1),] # the stratified case-cohort casecohort$weights <- casecohort$strata.n / casecohort$strata.m casecohort$weights[which(casecohort$status == 1)] <- 1 Tau1 <- 0 Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk n <- nrow(cohort) # Estimation using the stratified case-cohort with design weights mod <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weights, id = id, robust = TRUE) # parameters and influences estimation est <- influences(mod, Tau1 = Tau1, Tau2 = Tau2, x = x) beta.hat <- est$beta.hat Lambda0.hat <- est$Lambda0.Tau1Tau2.hat Pi.x.hat <- est$Pi.x.Tau1Tau2.hat infl.beta <- est$infl.beta infl.Lambda0 <- est$infl.Lambda0.Tau1Tau2 infl.Pi.x <- est$infl.Pi.x.Tau1Tau2 # variance estimate for the log-relative hazard estimate variance(n = n, casecohort = casecohort, infl = infl.beta, stratified = TRUE) # variance estimate for the cumulative baseline hazard estimate variance(n = n, casecohort = casecohort, infl = infl.Lambda0, stratified = TRUE) # variance estimate for the pure risk estimate variance(n = n, casecohort = casecohort, infl = infl.Pi.x, stratified = TRUE)data(dataexample.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.stratified$cohort casecohort <- cohort[which(cohort$status == 1 | cohort$subcohort == 1),] # the stratified case-cohort casecohort$weights <- casecohort$strata.n / casecohort$strata.m casecohort$weights[which(casecohort$status == 1)] <- 1 Tau1 <- 0 Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk n <- nrow(cohort) # Estimation using the stratified case-cohort with design weights mod <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weights, id = id, robust = TRUE) # parameters and influences estimation est <- influences(mod, Tau1 = Tau1, Tau2 = Tau2, x = x) beta.hat <- est$beta.hat Lambda0.hat <- est$Lambda0.Tau1Tau2.hat Pi.x.hat <- est$Pi.x.Tau1Tau2.hat infl.beta <- est$infl.beta infl.Lambda0 <- est$infl.Lambda0.Tau1Tau2 infl.Pi.x <- est$infl.Pi.x.Tau1Tau2 # variance estimate for the log-relative hazard estimate variance(n = n, casecohort = casecohort, infl = infl.beta, stratified = TRUE) # variance estimate for the cumulative baseline hazard estimate variance(n = n, casecohort = casecohort, infl = infl.Lambda0, stratified = TRUE) # variance estimate for the pure risk estimate variance(n = n, casecohort = casecohort, infl = infl.Pi.x, stratified = TRUE)
Computes the variance estimate that follows the complete variance decomposition, for a parameter such as log-relative hazard, cumulative baseline hazard or covariate specific pure-risk, when covariate information is missing for individuals in the phase-two sample.
variance.missingdata(n, casecohort, casecohort.phase2, weights, weights.phase2, weights.p2.phase2, infl2, infl3, stratified.p2 = NULL, estimated.weights = NULL)variance.missingdata(n, casecohort, casecohort.phase2, weights, weights.phase2, weights.p2.phase2, infl2, infl3, stratified.p2 = NULL, estimated.weights = NULL)
n |
number of individuals in the whole cohort. |
casecohort |
If |
casecohort.phase2 |
If |
weights |
vector with design weights for the individuals in the case cohort data. |
weights.phase2 |
vector with design weights for the individuals in the phase-two sample. |
weights.p2.phase2 |
vector with phase-two design weights for the individuals in the phase-two sample. |
infl2 |
matrix with the phase-two influences on the parameter. |
infl3 |
matrix with the phase-three influences on the parameter. |
stratified.p2 |
was the second phase of sampling stratified on |
estimated.weights |
were the phase-three weights estimated? Default is |
variance.missingdata works for estimation from a case cohort with design
weights and when covariate information was missing for certain individuals in the
phase-two data (i.e., case cohort obtained from three phases of sampling and
consisting of individuals in the phase-two data without missing covariate
information).
If there are no missing covariates in the phase- two sample, use variance
with either design weights or calibrated weights.
variance.missingdata uses the variance formulas provided in Etievant and
Gail (2024).
variance: variance estimate.
Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.
influences.missingdata, influences.RH.missingdata, influences.CumBH.missingdata,
influences.PR.missingdata, robustvariance and variance.
data(dataexample.missingdata.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.missingdata.stratified$cohort phase2 <- cohort[which(cohort$phase2 == 1),] # the phase-two sample casecohort <- cohort[which(cohort$phase3 == 1),] # the stratified case-cohort B.phase2 <- cbind(1 * (phase2$W3 == 0), 1 * (phase2$W3 == 1)) rownames(B.phase2) <- cohort[cohort$phase2 == 1, "id"] B.phase3 <- cbind(1 * (casecohort$W3 == 0), 1 * (casecohort$W3 == 1)) rownames(B.phase3) <- cohort[cohort$phase3 == 1, "id"] total.B.phase2 <- colSums(B.phase2) J3 <- ncol(B.phase3) n <- nrow(cohort) # Quantities needed for estimation of the cumulative baseline hazard when # covariate data is missing mod.cohort <- coxph(Surv(event.time, status) ~ X2, data = cohort, robust = TRUE) # X2 is available on all cohort members mod.cohort.detail <- coxph.detail(mod.cohort, riskmat = TRUE) riskmat.phase2 <- with(cohort, mod.cohort.detail$riskmat[phase2 == 1,]) rownames(riskmat.phase2) <- cohort[cohort$phase2 == 1, "id"] observed.times.phase2 <- apply(riskmat.phase2, 1, function(v) {which.max(cumsum(v))}) dNt.phase2 <- matrix(0, nrow(riskmat.phase2), ncol(riskmat.phase2)) dNt.phase2[cbind(1:nrow(riskmat.phase2), observed.times.phase2)] <- 1 dNt.phase2 <- sweep(dNt.phase2, 1, phase2$status, "*") colnames(dNt.phase2) <- colnames(riskmat.phase2) rownames(dNt.phase2) <- rownames(riskmat.phase2) Tau1 <- 0 # given time interval for the pure risk Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with true known design weights mod.true <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.true, id = id, robust = TRUE) est.true <- influences.missingdata(mod = mod.true, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2, Tau1 = Tau1, Tau2 = Tau2, x = x) infl.beta.true <- est.true$infl.beta infl.Lambda0.true <- est.true$infl.Lambda0.Tau1Tau2 infl.Pi.x.true <- est.true$infl.Pi.x.Tau1Tau2 infl2.beta.true <- est.true$infl2.beta infl2.Lambda0.true <- est.true$infl2.Lambda0.Tau1Tau2 infl2.Pi.x.true <- est.true$infl2.Pi.x.Tau1Tau2 infl3.beta.true <- est.true$infl3.beta infl3.Lambda0.true <- est.true$infl3.Lambda0.Tau1Tau2 infl3.Pi.x.true <- est.true$infl3.Pi.x.Tau1Tau2 # variance estimate for the log-relative hazard estimate variance.missingdata(n = n, casecohort = casecohort, casecohort.phase2 = phase2, weights = casecohort$weight.true, weights.phase2 = phase2$weight.true, weights.p2.phase2 = phase2$weight.p2.true, infl2 = infl2.beta.true, infl3 = infl3.beta.true, stratified.p2 = TRUE) # variance estimate for the cumulative baseline hazard estimate variance.missingdata(n = n, casecohort = casecohort, casecohort.phase2 = phase2, weights = casecohort$weight.true, weights.phase2 = phase2$weight.true, weights.p2.phase2 = phase2$weight.p2.true, infl2 = infl2.Lambda0.true, infl3 = infl3.Lambda0.true, stratified.p2 = TRUE) # variance estimate for the pure risk estimate variance.missingdata(n = n, casecohort = casecohort, casecohort.phase2 = phase2, weights = casecohort$weight.true, weights.phase2 = phase2$weight.true, weights.p2.phase2 = phase2$weight.p2.true, infl2 = infl2.Pi.x.true, infl3 = infl3.Pi.x.true, stratified.p2 = TRUE) # Estimation using the stratified case cohort with estimated weights, and # accounting for the estimation through the influences mod.estimated <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.est, id = id, robust = TRUE) est.estimated <- influences.missingdata(mod.estimated, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2, estimated.weights = TRUE, B.phase2 = B.phase2, Tau1 = Tau1, Tau2 = Tau2, x = x) infl.beta.estimated <- est.estimated$infl.beta infl.Lambda0.estimated <- est.estimated$infl.Lambda0.Tau1Tau2 infl.Pi.x.estimated <- est.estimated$infl.Pi.x.Tau1Tau2 infl2.beta.estimated <- est.estimated$infl2.beta infl2.Lambda0.estimated <- est.estimated$infl2.Lambda0.Tau1Tau2 infl2.Pi.x.estimated <- est.estimated$infl2.Pi.x.Tau1Tau2 infl3.beta.estimated <- est.estimated$infl3.beta infl3.Lambda0.estimated <- est.estimated$infl3.Lambda0.Tau1Tau2 infl3.Pi.x.estimated <- est.estimated$infl3.Pi.x.Tau1Tau2 # variance estimate for the log-relative hazard variance.missingdata(n = n, casecohort = casecohort, casecohort.phase2 = phase2, weights = casecohort$weight.est, weights.phase2 = phase2$weight.est, weights.p2.phase2 = phase2$weight.p2.true, infl2 = infl2.beta.estimated, infl3 = infl3.beta.estimated, stratified.p2 = TRUE, estimated.weights = TRUE) # variance estimate for the cumulative baseline hazard estimate variance.missingdata(n = n, casecohort = casecohort, casecohort.phase2 = phase2, weights = casecohort$weight.est, weights.phase2 = phase2$weight.est, weights.p2.phase2 = phase2$weight.p2.true, infl2 = infl2.Lambda0.estimated, infl3 = infl3.Lambda0.estimated, stratified.p2 = TRUE, estimated.weights = TRUE) # variance estimate for the pure risk estimate variance.missingdata(n = n, casecohort = casecohort, casecohort.phase2 = phase2, weights = casecohort$weight.est, weights.phase2 = phase2$weight.est, weights.p2.phase2 = phase2$weight.p2.true, infl2 = infl2.Pi.x.estimated, infl3 = infl3.Pi.x.estimated, stratified.p2 = TRUE, estimated.weights = TRUE)data(dataexample.missingdata.stratified, package="CaseCohortCoxSurvival") cohort <- dataexample.missingdata.stratified$cohort phase2 <- cohort[which(cohort$phase2 == 1),] # the phase-two sample casecohort <- cohort[which(cohort$phase3 == 1),] # the stratified case-cohort B.phase2 <- cbind(1 * (phase2$W3 == 0), 1 * (phase2$W3 == 1)) rownames(B.phase2) <- cohort[cohort$phase2 == 1, "id"] B.phase3 <- cbind(1 * (casecohort$W3 == 0), 1 * (casecohort$W3 == 1)) rownames(B.phase3) <- cohort[cohort$phase3 == 1, "id"] total.B.phase2 <- colSums(B.phase2) J3 <- ncol(B.phase3) n <- nrow(cohort) # Quantities needed for estimation of the cumulative baseline hazard when # covariate data is missing mod.cohort <- coxph(Surv(event.time, status) ~ X2, data = cohort, robust = TRUE) # X2 is available on all cohort members mod.cohort.detail <- coxph.detail(mod.cohort, riskmat = TRUE) riskmat.phase2 <- with(cohort, mod.cohort.detail$riskmat[phase2 == 1,]) rownames(riskmat.phase2) <- cohort[cohort$phase2 == 1, "id"] observed.times.phase2 <- apply(riskmat.phase2, 1, function(v) {which.max(cumsum(v))}) dNt.phase2 <- matrix(0, nrow(riskmat.phase2), ncol(riskmat.phase2)) dNt.phase2[cbind(1:nrow(riskmat.phase2), observed.times.phase2)] <- 1 dNt.phase2 <- sweep(dNt.phase2, 1, phase2$status, "*") colnames(dNt.phase2) <- colnames(riskmat.phase2) rownames(dNt.phase2) <- rownames(riskmat.phase2) Tau1 <- 0 # given time interval for the pure risk Tau2 <- 8 x <- c(-1, 1, -0.6) # given covariate profile for the pure risk # Estimation using the stratified case cohort with true known design weights mod.true <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.true, id = id, robust = TRUE) est.true <- influences.missingdata(mod = mod.true, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2, Tau1 = Tau1, Tau2 = Tau2, x = x) infl.beta.true <- est.true$infl.beta infl.Lambda0.true <- est.true$infl.Lambda0.Tau1Tau2 infl.Pi.x.true <- est.true$infl.Pi.x.Tau1Tau2 infl2.beta.true <- est.true$infl2.beta infl2.Lambda0.true <- est.true$infl2.Lambda0.Tau1Tau2 infl2.Pi.x.true <- est.true$infl2.Pi.x.Tau1Tau2 infl3.beta.true <- est.true$infl3.beta infl3.Lambda0.true <- est.true$infl3.Lambda0.Tau1Tau2 infl3.Pi.x.true <- est.true$infl3.Pi.x.Tau1Tau2 # variance estimate for the log-relative hazard estimate variance.missingdata(n = n, casecohort = casecohort, casecohort.phase2 = phase2, weights = casecohort$weight.true, weights.phase2 = phase2$weight.true, weights.p2.phase2 = phase2$weight.p2.true, infl2 = infl2.beta.true, infl3 = infl3.beta.true, stratified.p2 = TRUE) # variance estimate for the cumulative baseline hazard estimate variance.missingdata(n = n, casecohort = casecohort, casecohort.phase2 = phase2, weights = casecohort$weight.true, weights.phase2 = phase2$weight.true, weights.p2.phase2 = phase2$weight.p2.true, infl2 = infl2.Lambda0.true, infl3 = infl3.Lambda0.true, stratified.p2 = TRUE) # variance estimate for the pure risk estimate variance.missingdata(n = n, casecohort = casecohort, casecohort.phase2 = phase2, weights = casecohort$weight.true, weights.phase2 = phase2$weight.true, weights.p2.phase2 = phase2$weight.p2.true, infl2 = infl2.Pi.x.true, infl3 = infl3.Pi.x.true, stratified.p2 = TRUE) # Estimation using the stratified case cohort with estimated weights, and # accounting for the estimation through the influences mod.estimated <- coxph(Surv(event.time, status) ~ X1 + X2 + X3, data = casecohort, weight = weight.est, id = id, robust = TRUE) est.estimated <- influences.missingdata(mod.estimated, riskmat.phase2 = riskmat.phase2, dNt.phase2 = dNt.phase2, estimated.weights = TRUE, B.phase2 = B.phase2, Tau1 = Tau1, Tau2 = Tau2, x = x) infl.beta.estimated <- est.estimated$infl.beta infl.Lambda0.estimated <- est.estimated$infl.Lambda0.Tau1Tau2 infl.Pi.x.estimated <- est.estimated$infl.Pi.x.Tau1Tau2 infl2.beta.estimated <- est.estimated$infl2.beta infl2.Lambda0.estimated <- est.estimated$infl2.Lambda0.Tau1Tau2 infl2.Pi.x.estimated <- est.estimated$infl2.Pi.x.Tau1Tau2 infl3.beta.estimated <- est.estimated$infl3.beta infl3.Lambda0.estimated <- est.estimated$infl3.Lambda0.Tau1Tau2 infl3.Pi.x.estimated <- est.estimated$infl3.Pi.x.Tau1Tau2 # variance estimate for the log-relative hazard variance.missingdata(n = n, casecohort = casecohort, casecohort.phase2 = phase2, weights = casecohort$weight.est, weights.phase2 = phase2$weight.est, weights.p2.phase2 = phase2$weight.p2.true, infl2 = infl2.beta.estimated, infl3 = infl3.beta.estimated, stratified.p2 = TRUE, estimated.weights = TRUE) # variance estimate for the cumulative baseline hazard estimate variance.missingdata(n = n, casecohort = casecohort, casecohort.phase2 = phase2, weights = casecohort$weight.est, weights.phase2 = phase2$weight.est, weights.p2.phase2 = phase2$weight.p2.true, infl2 = infl2.Lambda0.estimated, infl3 = infl3.Lambda0.estimated, stratified.p2 = TRUE, estimated.weights = TRUE) # variance estimate for the pure risk estimate variance.missingdata(n = n, casecohort = casecohort, casecohort.phase2 = phase2, weights = casecohort$weight.est, weights.phase2 = phase2$weight.est, weights.p2.phase2 = phase2$weight.p2.true, infl2 = infl2.Pi.x.estimated, infl3 = infl3.Pi.x.estimated, stratified.p2 = TRUE, estimated.weights = TRUE)