Constructing treatment decision rules based on scalar and functional predictors when moderators of treatment effect are unknown.

Treatment response heterogeneity poses serious challenges for selecting treatment for many diseases. To better understand this heterogeneity and to help in determining the best patient-specific treatments for a given disease, many clinical trials are collecting large amounts of patient-level data prior to administering treatment in the hope that some of these data can be used to identify moderators of treatment effect. These data can range from simple scalar values to complex functional data such as curves or images. Combining these various types of baseline data to discover "biosignatures" of treatment response is crucial for advancing precision medicine. Motivated by the problem of selecting optimal treatment for subjects with depression based on clinical and neuroimaging data, we present an approach that both (1) identifies covariates associated with differential treatment effect and (2) estimates a treatment decision rule based on these covariates. We focus on settings where there is a potentially large collection of candidate biomarkers consisting of both scalar and functional data. The validity of the proposed approach is justified via extensive simulation experiments and illustrated using data from a placebo-controlled clinical trial investigating antidepressant treatment response in subjects with depression.