Variable selection in semiparametric transformation models for right-censored data

We study variable selection in general transformation models for right-censored data. The models studied can incorporate external time-varying covariates, and they include the proportional hazards model and the proportional odds model as special cases. We propose an estimation method that involves minimizing a weighted negative partial loglikelihood function plus an adaptive lasso penalty, with the initial values obtained from nonparametric maximum likelihood estimation. The objective function is parametric and convex, so the minimization is easy to implement. We show that our selection has oracle properties and that the estimator is semiparametrically efficient. We demonstrate the small-sample performance of the proposed method via simulations, and we use the method to analyse data from the Atherosclerosis Risk in Communities Study. Copyright 2013, Oxford University Press.