Variable selection for semiparametric accelerated failure time models with nonignorable missing data

The regularization approach for variable selection was well developed for semiparametric accelerated failure time (AFT) models, where the response variable is right censored. In the presence of missing data, this approach needs to be tailored to different missing data mechanisms. In this paper, we propose a flexible and generally applicable missing data mechanism for AFT models, which contains both ignorable and nonignorable missing data mechanism assumptions. We propose weighted rank (WR) estimators and corresponding penalized estimators of regression parameters under this missing data mechanism. An advantage of the WR estimators and corresponding penalized estimators is that they do not require specifying a missing data model for the proposed missing data mechanism. The theoretical properties of the WR and corresponding penalized estimators are established. Comprehensive simulation studies and a real data application further demonstrate the merits of our approach.