A single index model for longitudinal outcomes to optimize individual treatment decision rules

A pressing challenge in medical research is to identify optimal treatments for individual patients. This is particularly challenging in mental health settings where mean responses are often similar across multiple treatments. For example, the mean longitudinal trajectory for patients treated with an active drug versus placebo may be similar trajectories, but different treatments may exhibit trajectory shapes that are distinct from trajectories in other treatment groups. Most precision medicine approaches using longitudinal data often ignore information from the longitudinal data structure. This paper investigates a powerful precision medicine approach by examining the impact of baseline covariates on longitudinal outcome trajectories to guide treatment decisions instead of traditional scalar outcome measures derived from longitudinal data, such as a change score. We introduce a method of estimating "biosignatures" defined as linear combinations of baseline characteristics (i.e., a single index) that optimally separate longitudinal trajectories among different treatment groups. The criterion used is to maximize the Kullback-Leibler Divergences between different treatment outcome distributions. The approach is illustrated via simulation studies and a depression clinical trial. The approach is also contrasted with more traditional methods and compares performance in the presence of missing data.