A Model Selection Approach for Variable Selection with Censored Data

Abstract

We consider the variable selection problem when the response is subject to censoring. A main particularity of this context is that information content of sampled units varies depending on the censoring times. Our approach is based on model selection where all $2^k$ possible models are entertained and we adopt an objective Bayesian perspective where the choice of prior distributions is a delicate issue given the well-known sensitivity of Bayes factors to these prior inputs. We show that borrowing priors from the ‘uncensored’ literature may lead to unsatisfactory results as this default procedure implicitly assumes a uniform contribution of all units independently on their censoring times. In this paper, we develop specific methodology based on a generalization of the g-priors, explicitly addressing the particularities of survival problems arguing that it behaves comparatively better than standard approaches on the basis of arguments specific to variable selection problems (like e.g. predictive matching) in the particular case of the accelerated failure time model with lognormal errors. We apply the methodology to a recent large epidemiological study about breast cancer survival rates in Castellón, a province of Spain.