  Variable selection for optimal treatment regime in a clinical trial or an
observational study is getting more attention. Most existing variable selection
techniques focused on selecting variables that are important for prediction,
therefore some variables that are poor in prediction but are critical for
decision-making may be ignored. A qualitative interaction of a variable with
treatment arises when treatment effect changes direction as the value of this
variable varies. The qualitative interaction indicates the importance of this
variable for decision-making. Gunter et al. (2011) proposed S-score which
characterizes the magnitude of qualitative interaction of each variable with
treatment individually. In this article, we developed a sequential advantage
selection method based on the modified S-score. Our method selects
qualitatively interacted variables sequentially, and hence excludes marginally
important but jointly unimportant variables {or vice versa}. The optimal
treatment regime based on variables selected via joint model is more
comprehensive and reliable. With the proposed stopping criteria, our method can
handle a large amount of covariates even if sample size is small. Simulation
results show our method performs well in practical settings. We further applied
our method to data from a clinical trial for depression.
