truncAIPW_cen2 {truncAIPW}

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
)

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.

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'.

References

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

See Also

See also truncAIPW for estimation under no censoring, and truncAIPW_cen1 for estimation under another type of noninformative right censoring. See also F_est, G_est as examples for computing the input matrices of the conditional CDF's.

Examples

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