estimation.CumBH {CaseCohortCoxSurvival}R Documentation

estimation.CumBH

Description

Estimates the log-relative hazard, baseline hazards at each unique event time and cumulative baseline hazard in a given time interval [Tau1, Tau2].

Usage

estimation.CumBH(mod, Tau1 = NULL, Tau2 = NULL, missing.data = FALSE,
riskmat.phase2 = NULL, dNt.phase2 = NULL, status.phase2 = NULL)

Arguments

mod

a Cox model object, result of function coxph.

Tau1

left bound of the time interval considered for the cumulative baseline hazard. Default is the first event time.

Tau2

right bound of the time interval considered for the cumulative baseline hazard. Default is the last event time.

missing.data

was data on the p covariates missing for certain individuals in the phase-two data (i.e., was a third phase of sampling performed)? If missing.data = TRUE, the arguments below need to be provided. Default is FALSE.

riskmat.phase2

at risk matrix for the phase-two data at all of the case event times, even those with missing covariate data. Needs to be provided if missing.data = TRUE.

dNt.phase2

counting process matrix for failures in the phase-two data. Needs to be provided if missing.data = TRUE and status.phase2 = NULL.

status.phase2

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

Details

estimation.CumBH returns the log-relative hazard estimates provided by mod, and estimates the baseline hazard point mass at any event time non-parametrically.

estimation.CumBH works for estimation from a case-cohort with design weights or calibrated weights, when the case-cohort consists of the subcohort and cases not in the subcohort (i.e., case-cohort obtained from two phases of sampling), as well as with design weights when covariate data was missing for certain individuals in the phase-two data (i.e., case-cohort obtained from three phases of sampling).

Value

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

Breslow, N. (1974). Covariance Analysis of Censored Survival Data. Biometrics, 30, 89-99.

Etievant, L., Gail, M. H. (2024). Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data. Lifetime Data Analysis, 30, 572-599.

See Also

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

Examples


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

  cohort <- dataexample.missingdata.stratified$cohort
  phase2 <- cohort[which(cohort$phase2 == 1),] # the phase-two sample
  casecohort <- cohort[which(cohort$phase3 == 1),] # the stratified case-cohort

  B.phase2 <- cbind(1 * (phase2$W3 == 0), 1 * (phase2$W3 == 1))
  rownames(B.phase2)  <- cohort[cohort$phase2 == 1, "id"]
  B.phase3 <- cbind(1 * (casecohort$W3 == 0), 1 * (casecohort$W3 == 1))
  rownames(B.phase3)  <- cohort[cohort$phase3 == 1, "id"]
  total.B.phase2 <- colSums(B.phase2)
  J3 <- ncol(B.phase3)
  n <- nrow(cohort)

  # Quantities needed for estimation of the cumulative baseline hazard when
  # covariate data is missing
  mod.cohort <- coxph(Surv(event.time, status) ~ X2, data = cohort,
                      robust = TRUE) # X2 is available on all cohort members
  mod.cohort.detail <- coxph.detail(mod.cohort, riskmat = TRUE)

  riskmat.phase2 <- with(cohort, mod.cohort.detail$riskmat[phase2 == 1,])
  rownames(riskmat.phase2) <- cohort[cohort$phase2 == 1, "id"]
  observed.times.phase2 <- apply(riskmat.phase2, 1,
                                 function(v) {which.max(cumsum(v))})
  dNt.phase2 <- matrix(0, nrow(riskmat.phase2), ncol(riskmat.phase2))
  dNt.phase2[cbind(1:nrow(riskmat.phase2), observed.times.phase2)] <- 1
  dNt.phase2 <- sweep(dNt.phase2, 1, phase2$status, "*")
  colnames(dNt.phase2) <- colnames(riskmat.phase2)
  rownames(dNt.phase2) <- rownames(riskmat.phase2)

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

  est.true <- estimation(mod.true, Tau1 = Tau1, Tau2 = Tau2, x = x,
                         missing.data = TRUE,
                         riskmat.phase2 = riskmat.phase2,
                         dNt.phase2 = dNt.phase2)

  est.true <- estimation.CumBH(mod.true, Tau1 = Tau1, Tau2 = Tau2,
                                            missing.data = TRUE,
                                            riskmat.phase2 = riskmat.phase2,
                                            dNt.phase2 = dNt.phase2)

  # print the cumulative baseline hazard estimate
  est.true$Lambda0.Tau1Tau2.hat

[Package CaseCohortCoxSurvival version 0.0.36 Index]