depCensoring (version 0.1.7)

NonParTrans: Fit a semiparametric transformation model for dependent censoring

Description

This function allows to estimate the dependency parameter along all other model parameters. First, estimates a non-parametric transformation function, and then at the second stage it estimates other model parameters assuming that the non-parametric function is known. The details for implementing the dependent censoring methodology can be found in Deresa and Van Keilegom (2021).

Usage

NonParTrans(
  resData,
  X,
  W,
  start = NULL,
  n.iter = 15,
  bootstrap = FALSE,
  n.boot = 50,
  eps = 0.001
)

Value

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

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

start

Initial values for the finite dimensional parameters. If start is NULL, the initial values will be obtained by fitting an Accelerated failure time models.

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.

References

Deresa, N. and Van Keilegom, I. (2021). On semiparametric modelling, estimation and inference for survival data subject to dependent censoring, Biometrika, 108, 965–979.

Examples

# \donttest{
# Toy data example to illustrate implementation
n = 300
beta = c(0.5, 1); eta = c(1,1.5); rho = 0.70
sigma = matrix(c(1,rho,rho,1),ncol=2)
err = MASS::mvrnorm(n, mu = c(0,0) , Sigma=sigma)
err1 = err[,1]; err2 = err[,2]
x1 = rbinom(n,1,0.5); x2 = runif(n,-1,1)
X = matrix(c(x1,x2),ncol=2,nrow=n); W = X   # data matrix
T1 = X%*%beta+err1
C =  W%*%eta+err2
T1 = exp(T1); C = exp(C)
A = runif(n,0,8); Y = pmin(T1,C,A)
d1 = as.numeric(Y==T1)
d2 = as.numeric(Y==C)
resData = data.frame("Z" = Y,"d1" = d1, "d2" = d2)   # should be data frame
colnames(X) = c("X1", "X2")
colnames(W) = c("W1","W2")

#  Bootstrap is false by default
output = NonParTrans(resData = resData, X = X, W = W, n.iter = 2)
output$parameterEstimates

# }