influences.CumBH.missingdata {CaseCohortCoxSurvival}

influences.CumBH.missingdata

Description

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.

Usage

  influences.CumBH.missingdata(mod, riskmat.phase2, dNt.phase2 = NULL, 
status.phase2 = NULL, Tau1 = NULL, Tau2 = 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.

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 estimated.weights = TRUE, the argument below needs to be provided. 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.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 (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.

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 p 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].

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.RH.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.CumBH.missingdata(mod = mod, 
                                           riskmat.phase2 = riskmat.phase2, 
                                           dNt.phase2 = dNt.phase2, Tau1 = 0, 
                                           Tau2 = 8)

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

# print the influences on the cumulative baseline hazard estimate
#estimation$infl.Lambda0.Tau1Tau2

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

# print the phase-two influences on the cumulative baseline hazard estimate
#estimation$infl2.Lambda0.Tau1Tau2

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

# print the phase-three influences on the cumulative baseline hazard estimate
#estimation$infl3.Lambda0.Tau1Tau2

# 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.CumBH.missingdata(mod.est, 
                                                riskmat.phase2 = riskmat.phase2, 
                                                dNt.phase2 = dNt.phase2, 
                                                estimated.weights = TRUE,
                                                B.phase2 = B.phase2, 
                                                Tau1 = 0, Tau2 = 8)