truncAIPW {truncAIPW}

Doubly Robust Estimation under Covariate-induced Dependent Left Truncation and No Censoring

Description

Doubly robust estimation for the mean of an arbitrarily transformed survival time under covariate-induced dependent left truncation and no right censoring.

Usage

truncAIPW(dat, nu, Fuz.mx, Gvz.mx, T.name, Q.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 conditional CDF matrix.

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 conditional CDF matrix.

T.name

name of the event time variable.

Q.name

name of the left truncation time variable.

trim

constant that is used to bound from below for the denominators involved in the computation.

Value

truncAIPW() returns a list of estimators (‘dr’, ‘IPW.Q’, ‘Reg.T1’, ‘Reg.T2’), and the model-based standard errors for the ‘dr’ and ‘IPW.Q’ estimators.

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’.

SE_dr

standard error of the ‘dr’ estimator based on the efficient influence function.

SE_IPW.Q

standard error of the ‘IPW.Q’ estimator computed from the robust sandwich variance estimator assuming the truncation weights are known.

References

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

See Also

See truncAIPW_cen1, truncAIPW_cen2 for the estimations also under noninformative right censoring. See F_est, G_est for examples of computing the input matrices for the conditional CDF's.

Examples

data("simu")
nu <- function(t){ return(as.numeric(t>3)) }
u = c(min(simu$time)-1e-10, sort(simu$time), max(simu$time)+1e-10)
v = c(min(simu$Q)-1e-10, sort(simu$Q), max(simu$Q)+1e-10)
Fuz.mx = F_est(simu, simu, u, "Cox", "time", "Q", "delta", c("Z1","Z2"))
Gvz.mx = G_est(simu, simu, v, "Cox", "time", "Q", "delta", c("Z1","Z2"))

est = truncAIPW(simu, nu, Fuz.mx, Gvz.mx, "time", "Q", trim = 1e-7)
est