Variable Selection for Linear Transformation Models via Penalized Marginal Likelihood

We study the problem of variable selection for linear transformation models, a class of general semiparametric models for censored survival data. The penalized marginal likelihood methods with shrinkage-type penalties are proposed to automate variable selection in linear transformation models; we consider the LASSO penalty and propose a new penalty called the adaptive-LASSO (ALASSO). Unlike the LASSO, the ALASSO imposes different penalties on different coefficients: unimportant covariates receive larger penalties than important ones. In this way, important variables can be protectively preserved in models while unimportant ones are more likely to be shrunk to zeros. An efficient iterative algorithm is proposed for optimization. The performance of both penalties is illustrated through simulated examples and one real data, the Veteran’s Administration lung cancer data. In terms of both variable selection and coefficient estimation, we find that both shrinkage estimators outperform the maximum marginal likelihood estimator, and the ALASSO gives better performance than the LASSO.