fitDepCens {SemiPar.depCens}

Fit Dependent Censoring Models

Description

This function allows to estimate the dependency parameter along all other model parameters. First, estimates the cumulative hazard function, and then at the second stage it estimates other model parameters assuming that the cumulative hazard function is known. The details for implementing the dependent censoring methodology can be found in Deresa and Van Keilegom (2023).

Usage

fitDepCens(
  resData,
  X,
  W,
  cop = c("Frank", "Gumbel", "Normal"),
  dist = c("Weibull", "lognormal"),
  start = NULL,
  n.iter = 20,
  bootstrap = TRUE,
  n.boot = 50,
  eps = 0.001
)

Arguments

resData

Data matrix with three columns; Z = the observed survival time, d1 = the censoring indicator of T and d2 = the censoring indicator of C.

X

Data matrix with covariates related to T.

W

Data matrix with covariates related to C. First column of W should be a vector of ones.

cop

Which copula should be computed to account for dependency between T and C. This argument can take one of the values from c("Gumbel", "Frank", "Normal").

dist

The distribution to be used for the censoring time C. Only two distributions are allowed, i.e, Weibull and lognormal distributions. With the value "Weibull" as the default.

start

Initial values for the finite dimensional parameters. If start is NULL, the initial values will be obtained by fitting a Cox model for survival time T and a Weibull model for dependent censoring C.

n.iter

Number of iterations; the default is n.iter = 20. The larger the number of iterations, the longer the computational time.

bootstrap

A boolean indicating whether to compute bootstrap standard errors for making inferences.

n.boot

Number of bootstrap samples to use in the estimation of bootstrap standard errors if bootstrap = TRUE. The default is n.boot = 50. But, higher values of n.boot are recommended for obtaining good estimates of bootstrap standard errors.

eps

Convergence error. This is set by the user in such away that the desired convergence is met; the default is eps = 1e-3.

Value

This function returns a fit of dependent censoring model; parameter estimates, estimate of the cumulative hazard function, bootstrap standard errors for finite-dimensional parameters, the nonparametric cumulative hazard function, etc.

References

Deresa and Van Keilegom (2023). Copula based Cox proportional hazards models for dependent censoring, Journal of the American Statistical Association (in press).

Examples

# Toy data example to illustrate implementation
n = 300
beta = c(0.5)
lambd = 0.35
eta = c(0.9,0.4)
X = cbind(rbinom(n,1,0.5))
W = cbind(rep(1,n),rbinom(n,1,0.5))
# generate dependency structure from Frank
frank.cop <- copula::frankCopula(param = 5,dim = 2)
U = copula::rCopula(n,frank.cop)
T1 = (-log(1-U[,1]))/(lambd*exp(X*beta))           # Survival time
T2 = (-log(1-U[,2]))^(1.1)*exp(W%*%eta)            # Censoring time
A = runif(n,0,15)                                  # administrative censoring time
Z = pmin(T1,T2,A)
d1 = as.numeric(Z==T1)
d2 = as.numeric(Z==T2)
resData = data.frame("Z" = Z,"d1" = d1, "d2" = d2)   # should be data frame
colnames(W) <- c("ones","cov1")
colnames(X) <- "cov.surv"

# Fit dependent censoring model

fit <- fitDepCens(resData = resData, X = X, W = W, bootstrap = FALSE)

# parameter estimates

fit$parameterEstimates

# summary fit results
summary(fit)

# plot cumulative hazard vs time

plot(fit$observedTime, fit$cumhazardFunction, type = "l",xlab = "Time",
ylab = "Estimated cumulative hazard function")