robustvariance {CaseCohortCoxSurvival}

robustvariance

Description

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.

Usage

 robustvariance(infl) 

Arguments

infl

overall influences on a parameter such as log-relative hazard, cumulative baseline hazard or covariate specific pure-risk.

Details

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).

Value

robust.var: robust variance estimate.

References

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. (2023). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Submitted.

See Also

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

Examples

data(dataexample, package="CaseCohortCoxSurvival")

casecohort  <- dataexample$casecohort # a simulated stratified case cohort
A           <- dataexample$A # matrix with auxiliary variables values in the cohort

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 weights calibrated on A 

mod.calib <- coxph(Surv(times, status) ~ X1 + X2 + X3, data = casecohort, 
                   weight = weights.calib, id = id, robust = TRUE)
estimation.calib    <- influences(mod.calib, A = A, calibrated = TRUE, 
                                  Tau1 = Tau1, Tau2 = Tau2, x = x)

# robust variance estimate for the log-relative hazard
robustvariance(estimation.calib$infl.beta)

# robust variance estimate for the cumulative baseline hazard estimate
robustvariance(estimation.calib$infl.Lambda0.Tau1Tau2)

# robust variance estimate for the pure risk estimate
robustvariance(estimation.calib$infl.Pi.x.Tau1Tau2)