CoxICPen {CoxICPen}

Variable Selection for Cox's Model with Interval-Censored Data

Description

Perform variable selection for Cox regression model with interval-censored data by using the methods proposed in Zhao et al. (2020a), Wu et al. (2020) and Zhao et al. (2020b). Can deal with both low-dimensional and high-dimensional data.

Usage

CoxICPen(LR = LR,
         x = x,
         lamb = log(nrow(x))/2-2,
         beta.initial = rep(0,ncol(x)),
         pen = "BAR",
         nfold = 5,
         BernD = 3,
         subj.wt = rep(1,nrow(x)))

Arguments

LR

An n by 2 matrix that contains interval-censored failure times (L, R]. Please set time point R to "Inf" if a subject is right-censored.

x

An n by p covariate matrix.

lamb

The value of the tuning parameter of the penalty term. Can either be a single value or a vector. Cross-validation will be employed to select the optimal lambda if a vector is provided. Default is log(n)/2-2.

beta.initial

The initial values for the regression coefficients in the Cox's model. Default is 0.

pen

The penalty function. Choices include "RIDGE", "BAR", "LASSO", "ALASSO", "SCAD", "MCP", "SICA", "SELO". Default is "BAR".

nfold

Number of folds for cross-validation. Will be ignored if a single lambda value is provided. Default is 5.

BernD

The degree of Bernstein polynomials. Default is 3.

subj.wt

Weight for each subject in the likelihood function. Can be used to incorporate case-cohort design. Default is 1 for each subject.

Value

beta: Penalized estimates of the regression coefficients in the Cox's model.

phi: Estimates of the coefficients in Bernstein Polynomials.

logL: Log likelihood function based on current parameter estimates and lambda value.

Lamb0: Estimate of the cumulative baseline hazard function at each observation time point.

cv.out: Cross-validation outcome for each lambda. Will be NULL if cross-validation is not performed.

References

Zhao, H., Wu, Q., Li, G., Sun, J. (2020a). Simultaneous Estimation and Variable Selection for Interval-Censored Data with Broken Adaptive Ridge Regression. Journal of the American Statistical Association. 115(529):204-216.

Wu, Q., Zhao, H., Zhu, L., Sun, J. (2020). Variable Selection for High-dimensional Partly Linear Additive Cox Model with Application to Alzheimer's disease. Statistics in Medicines.39(23):3120-3134.

Zhao, H., Wu, Q., Gilbert, P. B., Chen, Y. Q., Sun, J. (2020b). A Regularized Estimation Approach for Case-cohort Periodic Follow-up Studies with An Application to HIV Vaccine Trials. Biometrical Journal. 62(5):1176-1191.

Examples

# Generate an example data

require(foreach)

n <- 300  # Sample size
p <- 20   # Number of covariates

bet0 <- c(1, -1, 1, -1, rep(0,p-4))  # True values of regression coefficients

set.seed(1)
x.example <- matrix(rnorm(n*p,0,1),n,p)  # Generate covariates matrix

T.example <- c()
for (i in 1:n){
  T.example[i] <- rexp(1,exp(x.example%*%bet0)[i])  # Generate true failure times
}

timep <- seq(0,3,,10)
LR.example <- c()
for (i in 1:n){
  obsT <- timep*rbinom(10,1,0.5)
  if (max(obsT) < T.example[i]) {LR.example <- rbind(LR.example,c(max(obsT), Inf))} else {
    LR.example <- rbind(LR.example,c(max(obsT[obsT<T.example[i]]), min(obsT[obsT>=T.example[i]])))
  }
}  # Generate interval-censored failure times


# Fit Cox's model with penalized estimation

model1 <- CoxICPen(LR = LR.example, x = x.example, lamb = 100, pen = "RIDGE")
beta.initial <- model1$beta

model2 <- CoxICPen(LR = LR.example, x = x.example, beta.initial = beta.initial, pen = "BAR")
model2$beta

#model3 <- CoxICPen(LR = LR.example, x = x.example, lamb = seq(0.1,1,0.1),
#                   beta.initial = beta.initial, pen = "SELO")
#model3$beta