  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 trajectories for patients treated with an active
drug and placebo may be very similar but different treatments may exhibit
distinctly different individual trajectory shapes. 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 Divergence 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.
