Type: Package
Title: Doubly Robust Estimation under Covariate-Induced Dependent Left Truncation
Version: 1.0.1
Author: Yuyao Wang [cre, aut], Andrew Ying [aut], Ronghui Xu [aut]
Maintainer: Yuyao Wang <yuw079@ucsd.edu>
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" <doi:10.48550/arXiv.2208.06836>.
Depends: R (≥ 3.5.0)
License: GPL-3
Encoding: UTF-8
URL: https://arxiv.org/pdf/2208.06836.pdf
LazyData: true
Imports: stats, survival, survPen
RoxygenNote: 7.2.3
NeedsCompilation: no
Packaged: 2023-08-30 20:36:26 UTC; wangyuyao
Repository: CRAN
Date/Publication: 2023-08-31 13:50:02 UTC

Estimate the Conditional CDF of the Event Time given Covariates

Description

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’.

Usage

F_est(
  dat.fit,
  dat.est = dat.fit,
  time.eval,
  model,
  time.name,
  Q.name,
  event.name,
  cov.names,
  trim = 0,
  formula.survPen = NA
)

Arguments

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 coxph() from R package ‘survival’, and the hazard model with penalized splines using function survPen() from R package ‘survPen’, respectively.

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 survPen::survPen.

Value

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'.

See Also

G_est

Examples

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 CDF for the Left Truncation Time given Covariates

Description

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’.

Usage

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
)

Arguments

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 coxph() from R package ‘survival’, and the hazard model with penalized splines using function survPen() from R package ‘survPen’, respectively.

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 survPen::survPen.

Value

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'.

See Also

F_est

Examples

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

Description

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 P^*(T>3) = 0.5755753.

Usage

data(simu)

Format

A data frame with 500 subjects (rows) and 5 variables (columns).

time

the event time

Q

the left truncation time

delta

the event indicator

Z1

a continous covariate

Z2

a binary covariate

Source

Simulated

Examples

data(simu)

A Simulated Data Set under Left Truncation and Right Censoring where Censoring can be before Truncation

Description

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%; P^*(C<Q) = 0.6057; and the truth P^*(T>3) = 0.623955.

Usage

data(simu_c1)

Format

A data frame with 500 rows and 5 variables.

X

the censored event time X = min(T,C)

Q

the left truncation time

delta

the event indicator

Z1

a continous covariate

Z2

a binary covariate

Source

Simulated

Examples

data(simu_c1)

A Simulated Data Set under Left Truncation and Right Censoring where Censoring is always after Truncation

Description

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 P^*(T>3) = 0.576547.

Usage

data(simu_c2)

Format

A data frame with 500 rows and 5 variables.

X

the censored event time X = min(T,C)

Q

the left truncation time

delta

the event indicator

Z1

a continous covariate

Z2

a binary covariate

Source

Simulated

Examples

data(simu_c2)

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

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
)

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.

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’.

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_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.

Examples

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

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