influences.RH.missingdata {CaseCohortCoxSurvival}

influences.RH.missingdata

Description

Computes the influences on the log-relative hazard, when covariate data is missing for certain individuals in the phase-two data.

Usage

influences.RH.missingdata(mod, riskmat.phase2, dNt.phase2 = NULL, 
status.phase2 = NULL, estimated.weights = FALSE, B.phase2 = NULL)

Arguments

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 = NULL.

status.phase2

vector indicating the case status in the phase-two data. Needs to be provided if dNt.phase2 = NULL.

estimated.weights

are the weights for the third phase of sampling (due to missingness) estimated? If estimated.weights = TRUE, the argument below needs to beprovided. Default is FALSE.

B.phase2

matrix for the phase-two data, with phase-three sampling strata indicators. It should have as many columns as phase-three strata (J^{(3)}), with one 1 per row, to indicate the phase-three stratum position. Needs to be provided if estimated.weights = TRUE.

Details

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 (2023). More precisely, as in Section 5.4 if estimated.weights = TRUE, and as in Web Appendix H if estimated.weights = FALSE.

Value

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 p with log-relative hazard estimates.

References

Etievant, L., Gail, M.H. (2023). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Submitted.

See Also

estimation, estimation.CumBH, estimation.PR, influences.missingdata, influences.CumBH.missingdata, influences.PR.missingdata, influences, influences.RH, influences.CumBH, influences.PR, robustvariance and variance.

Examples

data(dataexample.missingdata, package="CaseCohortCoxSurvival")

cohort          <- dataexample.missingdata$cohort # a simulated cohort
casecohort      <- dataexample.missingdata$casecohort # a simulated stratified case-cohort
# phase-two data: dataexample.missingdata$casecohort.phase2 
riskmat.phase2  <- dataexample.missingdata$riskmat.phase2
dNt.phase2      <- dataexample.missingdata$dNt.phase2
B.phase2        <- dataexample.missingdata$B.phase2

# Estimation using the stratified case-cohort with true known design weights 

mod <- coxph(Surv(times, status) ~ X1 + X2 + X3, data = casecohort, 
             weight = weights.true, id = id, robust = TRUE)

estimation <- influences.RH.missingdata(mod = mod, 
                                           riskmat.phase2 = riskmat.phase2, 
                                           dNt.phase2 = dNt.phase2)

# print the influences on the log-relative hazard estimates
#estimation$infl.beta

# print the phase-two influences on the log-relative hazard estimates
#estimation$infl2.beta

# print the phase-three influences on the log-relative hazard estimates
#estimation$infl3.beta

# Estimation using the stratified case-cohort with estimated weights, and
# accounting for the estimation through the influences

mod.est <- coxph(Surv(times, status) ~ X1 + X2 + X3, data = casecohort, 
                 weight = weights.est, id = id, robust = TRUE)

estimation.est  <- influences.RH.missingdata(mod.est, 
                                                riskmat.phase2 = riskmat.phase2, 
                                                dNt.phase2 = dNt.phase2, 
                                                estimated.weights = TRUE,
                                                B.phase2 = B.phase2)