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Type:

Package

Title:

Pseudo Maximum Likelihood Estimation for Semi-Competing Risks Data

Version:

0.1.0

Description:

Implements two-stage pseudo maximum likelihood estimation (PMLE) for copula-based regression models with semi-competing risks data. The marginal distributions are modeled by semiparametric transformation regression models, and the dependence between bivariate event times is specified by a parametric copula function. See Arachchige, Chen and Zhou (2025) <doi:10.1007/s10985-024-09640-z> for details.

License:

MIT + file LICENSE

Encoding:

UTF-8

Imports:

trust, dplyr, rlang, VineCopula

Suggests:

knitr, rmarkdown, kableExtra, SemiCompRisks

RoxygenNote:

7.3.3

VignetteBuilder:

knitr

NeedsCompilation:

Packaged:

2026-06-02 18:03:10 UTC; KHAN GADGET

Author:

Qian M. Zhou [aut], Md. Ismail Hossain [aut, cre]

Maintainer:

Md. Ismail Hossain <mr2618@msstate.edu>

Repository:

CRAN

Date/Publication:

2026-06-08 18:20:19 UTC

Simultaneous maximum likelihood estimation (MLE) of copula-based regression models for semi-competing risks (SCR) data

Description

Perform MLE to simultaneously estimate the parameters associated with a copula-based regression models.

Usage

MLE4SCR(
  data,
  time,
  death,
  status_time,
  status_death,
  T.fmla = ~1,
  D.fmla = ~1,
  Gfun = list(T = "PH", D = "PH"),
  copula.family,
  copula.control = list(link = NULL, formula = ~1),
  initial = NULL
)

Arguments

data

a data frame containing variables names specified in time, death, status_time, status_death, T.fmla, D.fmla, and formula of copula.control.

time

a character string specifying the variable name in the data for the time to a non-terminal event.

death

a character string specifying the variable name in the data for the time to a terminal event.

status_time

a character string specifying the variable name in the data for the censoring indicator for the non-terminal event (take value 1 if the non-terminal event time is observed, and taking value 0 if it is censored).

status_death

a character string specifying the variable name in the data for the censoring indicator for the terminal event (take value 1 if the terminal event time is observed, and taking value 0 if it is censored).

T.fmla

an object of class formula: a symbolic description of the regression model to be fitted for the marginal distribution of the non-terminal event time.

D.fmla

an object of class formula: a symbolic description of the regression model to be fitted for the marginal distribution of the terminal event time.

Gfun

a list of two components T and D, both character strings specifying the link function in the semiparametric transformation (SPT) regression model for the non-terminal and terminal event times, respectively: "PH" (proportional hazards as the default value) or "PO" (proportional odds).

copula.family

a character string: "Clayton", "Gumbel", "Frank", or "Gaussian" specifying the copula family to be used for the dependence between the bivariate event times.

copula.control

a list of two components: link (a character string: "identity", "log", or "log-1", specifying the link function for the regression model of the copula parameter; if link = NULL (default), the link function will be the default function for the specified copula family: "log" for Clayton, "identity" for Frank, "log-1" for Gumbel, and "tanh" for Gaussian), and formula (an object of class formula: a symbolic description of the regression model to be fitted for the copula parameter under the specified link function; if formula = ~ 1 as default, the copula parameter is a constant)

initial

a numerical value or a vector of numerical values for the initial values of the copula parameter or the regression coefficients for the copula parameter. If initial = NULL (default), the initial value is set to be the one corresponding to Kendall's tau being 0.5.

Value

a list of the following components:

gamma:: a data frame containing the estimates and robust standard errors (SE) of the copula parameter or regression coefficients for the copula parameter.
gamma.cov:: a matrix containing the variance or variance-covariance matrix of the copula parameter estimators.
betaT:: a data frame containing the estimates and robust SEs of the regression coefficients for the marginal distribution of the non-terminal event time.
dLambdaT:: a data frame containing the estimates and robust SEs of the jumps of the baseline function for the marginal distribution of the non-terminal event time.
thetaT.cov:: a matrix containing the variance-covariance matrix of the nonterminal marginal parameter estimators.
betaD:: a data frame containing the estimates and robust SEs of the regression coefficients for the marginal distribution of the terminal event time.
dLambdaD:: a data frame containing the estimates and robust SEs of the jumps of the baseline function for the marginal distribution of the terminal event time.
thetaD.cov:: a matrix containing the variance-covariance matrix of the terminal marginal parameter estimators.
call:: a list containing the specified values of input arguments time, death, status_time, status_death, T.fmla, D.fmla, copula.family, and the following two components:

copula.link:: a list containing three R functions: "h.fun" (the link function used for the copula parameter), "dot.h.fun" (the first-order derivative of "h.fun"), and "ddot.h.fun" (the second-order derivative of "h.fun").
copula.fmla:: the specified value of fomula of the input argument copula.control.

Par2Tau:: a list containing two R functions: "tau.alpha" (transformation from the copula parameter to Kendall's tau), and "Dtau.alpha" (the first-order derivative of "tau.alpha" function)

Examples


data(BMT, package = "SemiCompRisks")
BMT$g <- factor(BMT$g, levels = c(2, 3, 1),
                labels = c("AML-low", "AML-high", "ALL"))
myfit <- MLE4SCR(BMT, time = "T2", death = "T1",
                 status_time = "delta2", status_death = "delta1",
                 T.fmla = ~ g, D.fmla = ~ g,
                 copula.family = "Clayton",
                 copula.control = list(link = NULL, formula = ~ g),
                 initial = NULL)
myfit$gamma
myfit$betaT

Two-stage pseudo maximum likelihood estimation (PMLE) of copula-based regression models for semi-competing risks (SCR) data

Description

Perform two-stage PMLE to estimate the parameters associated with a copula-based regression models.

Usage

PMLE4SCR(
  data,
  time,
  death,
  status_time,
  status_death,
  T.fmla = ~1,
  D.fmla = ~1,
  Gfun = list(T = "PH", D = "PH"),
  copula.family,
  copula.control = list(link = NULL, formula = ~1),
  initial = NULL
)

Arguments

data

a data frame containing variables names specified in time, death, status_time, status_death, T.fmla, D.fmla, and formula of copula.control.

time

a character string specifying the variable name in the data for the time to a non-terminal event.

death

a character string specifying the variable name in the data for the time to a terminal event.

status_time

status_death

T.fmla

an object of class formula: a symbolic description of the regression model to be fitted for the marginal distribution of the non-terminal event time.

D.fmla

an object of class formula: a symbolic description of the regression model to be fitted for the marginal distribution of the terminal event time.

Gfun

copula.family

a character string: "Clayton", "Gumbel", "Frank", or "Gaussian" specifying the copula family to be used for the dependence between the bivariate event times.

copula.control

initial

Value

a list of the following components:

gamma:: a data frame containing the estimates and robust standard errors (SE) of the copula parameter or regression coefficients for the copula parameter.
gamma.cov:: a matrix containing the variance or variance-covariance matrix of the copula parameter estimators.
betaT:: a data frame containing the estimates and robust SEs of the regression coefficients for the marginal distribution of the non-terminal event time.
dLambdaT:: a data frame containing the estimates and robust SEs of the jumps of the baseline function for the marginal distribution of the non-terminal event time.
thetaT.cov:: a matrix containing the variance-covariance matrix of the nonterminal marginal parameter estimators.
betaD:: a data frame containing the estimates and robust SEs of the regression coefficients for the marginal distribution of the terminal event time.
dLambdaD:: a data frame containing the estimates and robust SEs of the jumps of the baseline function for the marginal distribution of the terminal event time.
thetaD.cov:: a matrix containing the variance-covariance matrix of the terminal marginal parameter estimators.
call:: a list containing the specified values of input arguments time, death, status_time, status_death, T.fmla, D.fmla, copula.family, and the following two components:

copula.link:: a list containing three R functions: "h.fun" (the link function used for the copula parameter), "dot.h.fun" (the first-order derivative of "h.fun"), and "ddot.h.fun" (the second-order derivative of "h.fun").
copula.fmla:: the specified value of fomula of the input argument copula.control.

Par2Tau:: a list containing two R functions: "tau.alpha" (transformation from the copula parameter to Kendall's tau), and "Dtau.alpha" (the first-order derivative of "tau.alpha" function)

Examples


data(BMT, package = "SemiCompRisks")
BMT$g = factor(BMT$g, levels = c(2, 3, 1),
               labels = c("AML-low", "AML-high", "ALL"))
myfit = PMLE4SCR(BMT, time = "T2", death = "T1",
                  status_time = "delta2", status_death = "delta1",
                  T.fmla = ~ g, D.fmla = ~ g,
                  copula.family = "Clayton",
                  copula.control = list(link = NULL, formula = ~ g),
                  initial = NULL)
myfit$gamma
myfit$betaT

Fit a semi-parametric transformation (SPT) regression model

Description

Fit a semiparametric transformation regression model, where the unspecified baseline function is estimated via nonparametric maximum likelihood estimation (NPMLE) method.

Usage

fitSPT(data, time, status, formula = ~1, Gfun = "PH")

Arguments

data

a data frame containing variables names specified in time, status, and formula.

time

a character string specifying the variable name in the data for the event time.

status

a character string specifying the variable name in the data for the censoring indicator (taking value 1 if the time is observed, and taking value 0 when it is censored).

formula

an object of class formula: a symbolic description of the model to be fitted.

Gfun

a character string specifying the link function, Gfun = "PH" (proportional hazards as default) or Gfun = "PO" (proportional odds) in the SPT model.

Value

a list of the following components:

beta: a data frame containing the estimates, model-based standard erors (SE), and robust SEs for regresson coefficients.
dLambda: a data frame containing the estimates, model-based SEs, and robust SEs for the jumps of the baseline function at observed time points.
Lambda: a data frame containing the estimates, model-based SEs, and robust SEs for the baseline function at observed time points.
varcov: a list of two elements: model, the model-based variance-covariance matrix for all regression and baseline function parameter estimators, and robust, the robust variance-covariance matrix for parameter estimators.
Psi.theta: a data frame containing the estimated asymptotic expansion of the NPMLE estimator.
call: a list containing the specified values of the input arguments.
convergence: a logical value indicating whether the maximization of the log-likelihood converges or not.
niter: an interger which is the number of iterations for the maximization of the log-likelihood.

Examples


data(BMT, package = "SemiCompRisks")
BMT$g <- factor(BMT$g, levels = c(2, 3, 1),
                labels = c("AML-low", "AML-high", "ALL"))
fitSPT(BMT, time = "T1", status = "delta1",
       formula = ~ g, Gfun = "PH")$beta

Survival estimation under semi-parametric transformation regression model (SPT) for a given data

Description

Computes survival probability estimates for new data using a fitted fitSPT object.

Usage

predictFitSPT(obj, newdata)

Arguments

obj

an object of fitSPT.

newdata

a data frame containing the same variables in the formula of fitSPT.

Value

a list of the following components:

surv: a data frame containing the estimate, model-based standard eror (SE), and robust SE for the survival probabilities for a given data.
Psi.surv: a data frame containing the estimated asymptotic expansion of the estimator of the survival probabilities.

Examples


data(BMT, package = "SemiCompRisks")
BMT$g <- factor(BMT$g, levels = c(2, 3, 1),
                labels = c("AML-low", "AML-high", "ALL"))
fit <- fitSPT(BMT, time = "T1", status = "delta1",
              formula = ~ g, Gfun = "PH")
predictFitSPT(fit, BMT)$surv

Package {PMLE4SCR}

Simultaneous maximum likelihood estimation (MLE) of copula-based regression models for semi-competing risks (SCR) data

Description

Usage

Arguments

Value

Examples

Two-stage pseudo maximum likelihood estimation (PMLE) of copula-based regression models for semi-competing risks (SCR) data

Description

Usage

Arguments

Value

Examples

Fit a semi-parametric transformation (SPT) regression model

Description

Usage

Arguments

Value

Examples

Survival estimation under semi-parametric transformation regression model (SPT) for a given data

Description

Usage

Arguments

Value

Examples