truncAIPW_cen1: Doubly Robust Estimation under Covariate-induced Dependent Left Truncation and Noninformative Right Censoring where Censoring can be before 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 can be before left truncation. Inverse probability of censoring weighting is used to handle the right censoring.

Usage

truncAIPW_cen1(
  dat,
  nu,
  Fuz.mx,
  Gvz.mx,
  Sc,
  X.name,
  Q.name,
  status.name,
  trim = 1e-07
)

Value

truncAIPW_cen1() 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.
Sc: a function for the censoring survival curve \(S_c(\cdot)\).
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_c1")
simu_c1$delta.1 = 1

nu <- function(t){ return(as.numeric(t>3)) }
u = c(min(simu_c1$X)-1e-10, sort(simu_c1$X), max(simu_c1$X)+1e-10)
v = c(min(simu_c1$Q)-1e-10, sort(simu_c1$Q), max(simu_c1$Q)+1e-10)

Fuz.mx = F_est(simu_c1, simu_c1, u, "Cox", "X", "Q", "delta.1", c("Z1","Z2"))
Gvz.mx = G_est(simu_c1, simu_c1, v, "Cox", "X", "Q", "delta.1", c("Z1","Z2"))

# KM curve for Sc
kmfit.C = survfit(Surv(Q, X, 1-delta)~1, data = simu_c1, type = "kaplan-meier")
Sc = stepfun(kmfit.C$time,  c(1, kmfit.C$surv))

est = truncAIPW_cen1(simu_c1, nu, Fuz.mx, Gvz.mx, Sc, "X", "Q", "delta", trim = 1e-7)
est