| Title: | Doubly Robust Estimation under Covariate-Induced Dependent Left Truncation |
|---|---|
| Description: | Doubly robust estimation for the mean of an arbitrarily transformed survival time under covariate-induced dependent left truncation and noninformative right censoring. The functions truncAIPW(), truncAIPW_cen1(), and truncAIPW_cen2() compute the doubly robust estimators under the scenario without censoring and the two censoring scenarios, respectively. The package also contains three simulated data sets 'simu', 'simu_c1', and 'simu_c2', which are used to illustrate the usage of the functions in this package. Reference: Wang, Y., Ying, A., Xu, R. (2022) "Doubly robust estimation under covariate-induced dependent left truncation" <arXiv:2208.06836>. |
| Authors: | Yuyao Wang [cre, aut], Andrew Ying [aut], Ronghui Xu [aut] |
| Maintainer: | Yuyao Wang <[email protected]> |
| License: | GPL-3 |
| Version: | 1.0.1 |
| Built: | 2024-10-29 03:30:00 UTC |
| Source: | https://github.com/cran/truncAIPW |
Estimate the conditional cumulative distribution function (CDF) of the event time given covariates evaluated at given time points. The options implemented in this function are: Cox proportional hazards regression using function coxph() from R package ‘survival’, and the hazard model with penalized splines using function survPen() from R package ‘survPen’.
F_est( dat.fit, dat.est = dat.fit, time.eval, model, time.name, Q.name, event.name, cov.names, trim = 0, formula.survPen = NA )F_est( dat.fit, dat.est = dat.fit, time.eval, model, time.name, Q.name, event.name, cov.names, trim = 0, formula.survPen = NA )
dat.fit |
data frame that is used to fit the model for the full data conditional distribution of the event time given the covariates. |
dat.est |
data frame that contains the subjects for which the estimated conditional CDF is computed. |
time.eval |
vector of time points at which the conditional CDF is evaluated. |
model |
method used to estimate the conditional CDF. The options available are "Cox" and "spline", corresponding to Cox proportional hazards regression using function |
time.name |
name of the event time variable. |
Q.name |
name of the left truncation time variable. |
event.name |
name of the event indicator. |
cov.names |
vector of the names of covariates. |
trim |
constant for bounding the estimated conditional CDF from 1. |
formula.survPen |
the formula when applying the hazard model with penalized splines implemented in |
F_est() returns a matrix of the estimated conditional CDF for subjects in 'data.est' evaluated at the time points in the vector 'time.eval'. Each row corresponds to a subject and each column corresponds to a time point. The column names of the matrix are the times in 'time.eval'.
data("simu") u = c(1, 1.5, 2, 2.5, 3, 3.5, 4) Fuz.mx = F_est(simu, simu[1:10,], u, "Cox", "time", "Q", "delta", c("Z1","Z2"))data("simu") u = c(1, 1.5, 2, 2.5, 3, 3.5, 4) Fuz.mx = F_est(simu, simu[1:10,], u, "Cox", "time", "Q", "delta", c("Z1","Z2"))
Estimate the conditional cumulative distribution function (CDF) of the left truncation time given covariates evaluated at given time points. The options implemented in this function are: Cox proportional hazards regression using function coxph() from R package ‘survival’, and the hazard model with penalized splines using function survPen() from R package ‘survPen’.
G_est( dat.fit, dat.est = dat.fit, time.eval, model, time.name, Q.name, event.name, cov.names, trim = 0, weights = rep(1, nrow(dat.fit)), formula.survPen = NA )G_est( dat.fit, dat.est = dat.fit, time.eval, model, time.name, Q.name, event.name, cov.names, trim = 0, weights = rep(1, nrow(dat.fit)), formula.survPen = NA )
dat.fit |
data frame that is used to fit the model for the full data conditional distribution of the event time given the covariates. |
dat.est |
data frame that contains the subjects for which the estimated conditional CDF is computed. |
time.eval |
vector of time points at which the conditional CDF is evaluated. |
model |
method used to estimate the conditional CDF. The options available are "Cox" and "spline", corresponding to Cox proportional hazards regression using function |
time.name |
name of the event time variable. |
Q.name |
name of the left truncation time variable. |
event.name |
name of the event indicator. |
cov.names |
vector of the names of covariates. |
trim |
constant for bounding the estimated conditional CDF from 0. |
weights |
vector of case weights. |
formula.survPen |
the formula when applying the hazard model with penalized splines implemented in |
G_est() returns a matrix of the estimated conditional CDF for subjects in 'data.est' evaluated at the time points in the vector 'time.eval'. Each row corresponds to a subject and each column corresponds to a time point. The column names of the matrix are the times in 'time.eval'.
data("simu") v = c(0.5, 1, 1.5, 2, 2.5, 3) Gvz.mx = G_est(simu, simu[1:10,], v, "Cox", "time", "Q", "delta", c("Z1","Z2"))data("simu") v = c(0.5, 1, 1.5, 2, 2.5, 3) Gvz.mx = G_est(simu, simu[1:10,], v, "Cox", "time", "Q", "delta", c("Z1","Z2"))
A simulated data set under left truncation but no right censoring.
The left truncation time and the event time are dependent via the two covariates ‘Z1’ and ‘Z2’.
Under the data generating mechanism,
the conditional distribution of the event time given covariates follows a Cox proportional hazards model in the full data, and
the conditional distribution of the left truncation time given covariates follows a Cox proportional hazards model on the reversed time scale in the full data.
The truncation rate is 29.5%;
and the truth .
data(simu)data(simu)
A data frame with 500 subjects (rows) and 5 variables (columns).
the event time
the left truncation time
the event indicator
a continous covariate
a binary covariate
Simulated
data(simu)data(simu)
A simulated data set under left truncation and right censoring where censoring can be before left truncation.
The left truncation time and the event time are dependent via the two covariates ‘Z1’ and ‘Z2’.
Under the data generating mechanism,
the conditional distribution of the censored event time X given covariates follows a Cox proportional hazards model in the full data,
and the conditional distribution of the left truncation time given covariates follows a Cox proportional hazards model on the reversed time scale in the full data.
The truncation rate is 29.5%; the censoring rate is 16.5%; ;
and the truth .
data(simu_c1)data(simu_c1)
A data frame with 500 rows and 5 variables.
the censored event time X = min(T,C)
the left truncation time
the event indicator
a continous covariate
a binary covariate
Simulated
data(simu_c1)data(simu_c1)
A simulated data set under left truncation and right censoring where censoring is always after left truncation.
The left truncation time and the event time are dependent via two covariates ‘Z1’ and ‘Z2’.
Under the data generating mechanism,
the conditional distributions of the event time given covariates follows a Cox model in the full data,
and the conditional distribution of the left truncation time given covariates follows a Cox model on the reversed time scale in the full data.
The truncation rate is 29.5%; the censoring rate is 27.1%;
and the truth .
data(simu_c2)data(simu_c2)
A data frame with 500 rows and 5 variables.
the censored event time X = min(T,C)
the left truncation time
the event indicator
a continous covariate
a binary covariate
Simulated
data(simu_c2)data(simu_c2)
Doubly robust estimation for the mean of an arbitrarily transformed survival time under covariate-induced dependent left truncation and no right censoring.
truncAIPW(dat, nu, Fuz.mx, Gvz.mx, T.name, Q.name, trim = 1e-07)truncAIPW(dat, nu, Fuz.mx, Gvz.mx, T.name, Q.name, trim = 1e-07)
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 |
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 |
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. |
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. |
Wang, Y., Ying, A., Xu, R. (2022) "Doubly robust estimation under covariate-induced dependent left truncation" <arXiv:2208.06836>.
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.
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) estdata("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
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.
truncAIPW_cen1( dat, nu, Fuz.mx, Gvz.mx, Sc, X.name, Q.name, status.name, trim = 1e-07 )truncAIPW_cen1( dat, nu, Fuz.mx, Gvz.mx, Sc, X.name, Q.name, status.name, trim = 1e-07 )
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 |
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 |
Sc |
a function for the censoring survival curve |
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. |
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’. |
Wang, Y., Ying, A., Xu, R. (2022) "Doubly robust estimation under covariate-induced dependent left truncation" <arXiv:2208.06836>.
See also truncAIPW for estimation under no censoring, and truncAIPW_cen2 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.
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$surv)) est = truncAIPW_cen1(simu_c1, nu, Fuz.mx, Gvz.mx, Sc, "X", "Q", "delta", trim = 1e-7) estlibrary(survival) data("simu_c1") simu_c1$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
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.
truncAIPW_cen2( dat, nu, Fuz.mx, Gvz.mx, wd, X.name, Q.name, status.name, trim = 1e-07 )truncAIPW_cen2( dat, nu, Fuz.mx, Gvz.mx, wd, X.name, Q.name, status.name, trim = 1e-07 )
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 |
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 |
wd |
vector for the inverse probability of residual censoring weights |
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. |
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'. |
Wang, Y., Ying, A., Xu, R. (2022) "Doubly robust estimation under covariate-induced dependent left truncation" <arXiv:2208.06836>.
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.
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$wd Fuz.mx = F_est(simu_c2, simu_c2, u, "Cox", "X", "Q", "delta", c("Z1","Z2")) Gvz.mx = G_est(simu_c2.1, simu_c2, v, "Cox", "X", "Q", "delta", c("Z1","Z2"), weights = wd_1) est = truncAIPW_cen2(simu_c2, nu, Fuz.mx, Gvz.mx, wd, "X", "Q", "delta", trim = 1e-7) estlibrary(survival) data("simu_c2") nu <- function(t){ return(as.numeric(t>3)) } u = c(min(simu_c2$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