truncAIPW_cen2: Doubly Robust Estimation under Covariate-induced Dependent Left Truncation and Noninformative Right Censoring where Censoring is always after Left Truncation

Description

Doubly robust estimation of the mean of an arbitrarily transformed survival time under covariate-induced dependent left truncation and noninformative right censoring where censoring is always after left truncation. Inverse probability of censoring weighting is used to handle the right censoring.

Usage

truncAIPW_cen2(
  dat,
  nu,
  Fuz.mx,
  Gvz.mx,
  wd,
  X.name,
  Q.name,
  status.name,
  trim = 1e-07
)

Value

truncAIPW_cen2() returns a list of estimators (`dr', `IPW.Q', `Reg.T1', `Reg.T2').

dr: doubly robust estimator 'dr'.
IPW.Q: inverse probability of truncation weighted estimator 'IPW.Q'.
Reg.T1: regression based estimator 'Reg.T1'.
Reg.T2: regression based estimator 'Reg.T2'.

Arguments

dat: data frame that contains the data for constructing the estimating equation.
nu: transformation that defines the parameter of interest.
Fuz.mx: matrix for the estimated conditional CDF of the event time given covariates. Each row corresponds to a subject, and each column corresponds to a time point. The column names of the matrix are the time points. See F_est for an example of computing this input matrix for the conditional CDF.
Gvz.mx: matrix for the estimated conditional CDF of the truncation time given covariates. Each row corresponds to a subject, and each column corresponds to a time point. The column names of the matrix are the time points. See G_est for an example of computing this input matrix for the conditional CDF.
wd: vector for the inverse probability of residual censoring weights \(\Delta/\hat S_D(X-Q)\).
X.name: name of the censored event time variable X = min(T, C).
Q.name: name of the left truncation time variable.
status.name: name of the event time indicator.
trim: constant that is used to bound from below for the denominators involved in the computation.

References

Wang, Y., Ying, A., Xu, R. (2022) "Doubly robust estimation under covariate-induced dependent left truncation" <arXiv:2208.06836>.

Examples

Run this code

library(survival)
data("simu_c2")
nu <- function(t){ return(as.numeric(t>3)) }

u = c(min(simu_c2$X)-1e-10, sort(simu_c2$X), max(simu_c2$X)+1e-10)
v = c(min(simu_c2$Q)-1e-10, sort(simu_c2$Q), max(simu_c2$Q)+1e-10)

kmfit.D = survfit(Surv(X-Q, 1-delta)~1, data = simu_c2, type = "kaplan-meier")
Sd = stepfun(kmfit.D$time,  c(1, kmfit.D$surv))
wd = rep(0, nrow(simu_c2))
wd[which(simu_c2$delta == 1)] = 1/Sd(simu_c2$X - simu_c2$Q)[which(simu_c2$delta == 1)]

simu_c2$wd = wd
simu_c2.1 = simu_c2[simu_c2$delta==1,]
wd_1 = simu_c2.1$wd

Fuz.mx = F_est(simu_c2, simu_c2, u, "Cox", "X", "Q", "delta", c("Z1","Z2"))
Gvz.mx = G_est(simu_c2.1, simu_c2, v, "Cox", "X", "Q", "delta", c("Z1","Z2"), weights = wd_1)

est = truncAIPW_cen2(simu_c2, nu, Fuz.mx, Gvz.mx, wd, "X", "Q", "delta", trim = 1e-7)
est