Variable selection is gaining more attention because it plays an important role in deriving practical and reliable optimal treatment regimes for personalized medicine, especially when there are a large number of predictors. Most existing variable selection techniques focus on selecting variables that are important for prediction. With such methods, some variables that are poor in prediction but are critical for treatment decision making may be ignored. A qualitative interaction of a variable with treatment arises when the treatment effect changes direction as the value of the variable varies. Variables that have qualitative interactions with treatment are of clinical importance for treatment decision making. Gunter, Zhu and Murphy [Stat. Methodol. 8 (2011) 42–55] proposed the S-score method to characterize the magnitude of qualitative interaction of an individual variable with treatment. In this paper, we develop a sequential advantage selection method based on a modified S-score. Our method sequentially selects variables with a qualitative interaction and can be applied in multiple decision-point settings. To select the best candidate subset of variables for decision making, we also propose a BIC-type criterion that is based on the sequential advantage. The empirical performance of the proposed method is evaluated by simulation and an application to depression data from a clinical trial.
"Sequential advantage selection for optimal treatment regime." Ann. Appl. Stat. 10 (1) 32 - 53, March 2016. https://doi.org/10.1214/15-AOAS849