variance {CaseCohortCoxSurvival}R Documentation

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 JJ strata), strata.m (vector of length JJ with the numbers of sampled individuals in the strata) and strata.n (vector of length JJ 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)   

[Package CaseCohortCoxSurvival version 0.0.34 Index]