Identifying predictive markers for personalized treatment selection.

It is now well recognized that the effectiveness and potential risk of a treatment often vary by patient subgroups. Although trial-and-error and one-size-fits-all approaches to treatment selection remain a common practice, much recent focus has been placed on individualized treatment selection based on patient information (La Thangue and Kerr, 2011; Ong et al., 2012). Genetic and molecular markers are becoming increasingly available to guide treatment selection for various diseases including HIV and breast cancer (Mallal et al., 2008; Zujewski and Kamin, 2008). In recent years, many statistical procedures for developing individualized treatment rules (ITRs) have been proposed. However, less focus has been given to efficient selection of predictive biomarkers for treatment selection. The standard Wald test for interactions between treatment and the set of markers of interest may not work well when the marker effects are nonlinear. Furthermore, interaction-based test is scale dependent and may fail to capture markers useful for predicting individualized treatment differences. In this article, we propose to overcome these difficulties by developing a kernel machine (KM) score test that can efficiently identify markers predictive of treatment difference. Simulation studies show that our proposed KM-based score test is more powerful than the Wald test when there is nonlinear effect among the predictors and when the outcome is binary with nonlinear link functions. Furthermore, when there is high-correlation among predictors and when the number of predictors is not small, our method also over-performs Wald test. The proposed method is illustrated with two randomized clinical trials.