variance {CaseCohortCoxSurvival}

variance

Description

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.

Usage

  variance(n, casecohort, weights = NULL, infl, calibrated = NULL, 
                     infl2 = NULL, cohort = NULL, stratified = NULL, 
                     variance.phase2 = NULL)

Arguments

n

number of individuals in the whole cohort.

casecohort

If stratified = TRUE, data frame with status (case status), weights (design, if they are not provided in the argument below), W (the J strata), strata.m (vector of length J with the numbers of sampled individuals in the strata) and strata.n (vector of length J with the strata sizes in the cohort), for each individual in the stratified case-cohort data. If stratified = FALSE, data frame with weights (design, if they are not provided in the argument below), m (number of sampled individuals) and n (cohort size), for each individual in the unstratified case-cohort data.

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 calibrated = TRUE, the arguments below need to be provided. Default is FALSE.

infl2

matrix with the phase-two influences on the parameter. Needs to be provided if calibrated = TRUE.

cohort

If stratified = TRUE, data frame with status (case status) and subcohort (subcohort sampling indicators) for each individual in the stratified case-cohort data. If stratified = FALSE, data frame with status (case status) and unstrat.subcohort (subcohort unstratified sampling indicators) for each individual in the unstratified case-cohort data. Needs to be provided if calibrated = TRUE.

stratified

was the sampling of the case-cohort stratified on W? Default is FALSE.

variance.phase2

should the phase-two variance component also be returned? Default is FALSE.

Details

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 (2023). More precisely, as in Section 3.3 if calibrated = FALSE, and as in Section 4.3 if calibrated = TRUE.

Value

variance: variance estimate.

variance.phase2: phase-two variance component.

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

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

Examples

data(dataexample, package="CaseCohortCoxSurvival")

cohort      <- dataexample$cohort # a simulated cohort
n           <- nrow(cohort)
casecohort  <- dataexample$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 design weights 

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

# parameters and influences estimation 
estimation    <- influences(mod, Tau1 = Tau1, Tau2 = Tau2, x = x)
beta.hat      <- estimation$beta.hat
Lambda0.hat   <- estimation$Lambda0.Tau1Tau2.hat
Pi.x.hat      <- estimation$Pi.x.Tau1Tau2.hat
infl.beta     <- estimation$infl.beta
infl.Lambda0  <- estimation$infl.Lambda0.Tau1Tau2
infl.Pi.x     <- estimation$infl.Pi.x.Tau1Tau2

# variance estimate for the log-relative hazard
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)

# Estimation using the stratified case-cohort with calibrated weights 

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

# Parameters and influences estimation 
estimation.calib    <- influences(mod.calib, A = A, calibrated = TRUE, 
                                  Tau1 = Tau1, Tau2 = Tau2, x = x)
beta.hat.calib      <- estimation.calib$beta.hat
Lambda0.hat.calib   <- estimation.calib$Lambda0.Tau1Tau2.hat
Pi.x.hat.calib      <- estimation.calib$Pi.x.Tau1Tau2.hat
infl.beta.calib     <- estimation.calib$infl.beta
infl.Lambda0.calib  <- estimation.calib$infl.Lambda0.Tau1Tau2
infl.Pi.x.calib     <- estimation.calib$infl.Pi.x.Tau1Tau2
infl2.beta.calib    <- estimation.calib$infl2.beta
infl2.Lambda0.calib <- estimation.calib$infl2.Lambda0.Tau1Tau2
infl2.Pi.x.calib    <- estimation.calib$infl2.Pi.x.Tau1Tau2

# variance estimate for the log-relative hazard
variance(n = n, casecohort = casecohort, cohort = cohort, calibrated = TRUE, 
         stratified = TRUE, infl = infl.beta.calib, infl2 = infl2.beta.calib)

# variance estimate for the cumulative baseline hazard estimate
variance(n = n, casecohort = casecohort, cohort = cohort, calibrated = TRUE, 
         stratified = TRUE, infl = infl.Lambda0.calib, 
         infl2 = infl2.Lambda0.calib)

# variance estimate for the pure risk estimate
variance(n = n, casecohort = casecohort, cohort = cohort, calibrated = TRUE, 
         stratified = TRUE, infl = infl.Pi.x.calib,  infl2 = infl2.Pi.x.calib)