dependCox.reg.CV {compound.Cox}

Cox regression under dependent censoring.

Description

This function performs estimation and significance testing for survival data under a copula-based dependent censoring model proposed in Emura and Chen (2016). The dependency between the failure and censoring times is modeled via the Clayton copula. The method is based on the semiparametric maximum likelihood estimation, where the association parameter is estimated by maximizing the cross-validated c-index (see Emura and Chen 2016 for details).

Usage

dependCox.reg.CV(t.vec, d.vec, X.mat, K = 5, G = 20)

Arguments

t.vec

A vector of survival times (time-to-death or censoring)

d.vec

A vector of censoring indicators, 1=death, 0=censoring

X.mat

An (n*p) matrix of covariates, where n is the sample size and p is the number of covariates

K

The number of cross-validation folds

G

The number of grids to optimize c-index (c-index is computed for G different values of copula parameters)

Details

The Clayton model yields positive association between survival time and censoring time with Kendall's tau being equal to alpha/(alpha+2), where alpha > 0 is a copula parameter. The independence copula corresponds to alpha = 0.

If the number of covariates p is large (p>=100), the computational time becomes very long. We suggest using "uni.selection" to reduce the number such that p<100.

If the number of grids G is large, the computational time becomes very long. Please take 5<=G<=20.

Value

beta

The estimated regression coefficients

SE

The standard errors for the estimated regression coefficients

Z

The Z-values for testing the null hypothesis of "beta=0" (the Wald test)

P

The P-values for testing the null hypothesis of "beta=0" (the Wald test)

alpha

The estimated copula parameter by optimizing c-index

c_index

The optimized value of c_index

Author(s)

Takeshi Emura

References

Emura T, Chen YH (2016). Gene Selection for Survival Data Under Dependent Censoring: a Copula-based Approach, Stat Methods Med Res 25(No.6): 2840-57

Examples

### Reproduce Section 5 of Emura and Chen (2016) ###
data(Lung)
temp=Lung[,"train"]==TRUE
t.vec=Lung[temp,"t.vec"]
d.vec=Lung[temp,"d.vec"]
X.mat=as.matrix(Lung[temp,-c(1,2,3)])
#dependCox.reg.CV(t.vec,d.vec,X.mat,G=20) # time-consuming process #