SolveLI {SemiPar.depCens}

Cumulative hazard function of survival time under independent censoring

Description

This function estimates the cumulative hazard function of survival time (T) under the assumption of independent censoring. The estimating equation is derived based on martingale ideas.

Usage

SolveLI(theta, resData, X)

Arguments

theta

Estimated parameter values/initial values for finite dimensional parameters

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

Value

This function returns an estimated hazard function, cumulative hazard function and distinct observed survival times;

Examples

n = 200
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))
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)
theta = c(0.3,1,0.3,1)

# Estimate cumulative hazard function

cumFit_ind <- SolveLI(theta, resData,X)

cumhaz = cumFit_ind$cumhaz
time = cumFit_ind$times

# plot hazard vs time

plot(time, cumhaz, type = "l",xlab = "Time",
ylab = "Estimated cumulative hazard function")