  The development of molecular diagnostic tools to achieve individualized
medicine requires identifying predictive biomarkers associated with subgroups
of individuals who might receive beneficial or harmful effects from different
available treatments. However, due to the large number of candidate biomarkers
in the large-scale genetic and molecular studies, and complex relationships
among clinical outcome, biomarkers and treatments, the ordinary statistical
tests for the interactions between treatments and covariates have difficulties
from their limited statistical powers. In this paper, we propose an efficient
method for detecting predictive biomarkers. We employ weighted loss functions
of Chen et al. (2017) to directly estimate individual treatment scores and
propose synthetic posterior inference for effect sizes of biomarkers. We
develop an empirical Bayes approach, namely, we estimate unknown
hyperparameters in the prior distribution based on data. We then provide
efficient screening methods for the candidate biomarkers via optimal discovery
procedure with adequate control of false discovery rate. The proposed method is
demonstrated in simulation studies and an application to a breast cancer
clinical study in which the proposed method was shown to detect the much larger
numbers of significant biomarkers than existing standard methods.
