Stability enhanced variable selection for a semiparametric model with flexible missingness mechanism and its application to the ChAMP study

This paper is motivated by the analytical challenges we encounter when analyzing the ChAMP (Chondral Lesions And Meniscus Procedures) study, a randomized controlled trial to compare debridement to observation of chondral lesions in arthroscopic knee surgery. The main outcome, WOMAC (Western Ontario and McMaster Universities Osteoarthritis Index) pain score, is derived from the patient's responses to the questionnaire collected in the study. The major goal is to identify potentially important variables that contribute to this outcome. In this paper, the model of interest is a semiparametric model for the pain score. To address the missing data issue, we adopt a flexible missingness mechanism that is much more versatile in practice than a single parametric model. Then we propose a pairwise conditional likelihood approach to estimate the unknown parameter in the semiparametric model without the need of modeling its nonparametric counterpart nor the missingness mechanism. For variable selection, we apply a regularization approach with a variety of stability enhanced tuning parameter selection methods. We conduct comprehensive simulation studies to evaluate the performance of the proposed method. We also apply the proposed method to the ChAMP study to demonstrate its usefulness.