dependCox.reg.CV {compound.Cox} | R Documentation |
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).
dependCox.reg.CV(t.vec, d.vec, X.mat, K = 5, G = 20)
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) |
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.
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 |
Takeshi Emura
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
### 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 #