  A dynamic treatment regime is a sequence of decision rules in which each
decision rule recommends treatment based on features of patient medical history
such as past treatments and outcomes. Existing methods for estimating optimal
dynamic treatment regimes from data optimize the mean of a response variable.
However, the mean may not always be the most appropriate summary of
performance. We derive estimators of decision rules for optimizing
probabilities and quantiles computed with respect to the response distribution
for two-stage, binary treatment settings. This enables estimation of dynamic
treatment regimes that optimize the cumulative distribution function of the
response at a prespecified point or a prespecified quantile of the response
distribution such as the median. The proposed methods perform favorably in
simulation experiments. We illustrate our approach with data from a
sequentially randomized trial where the primary outcome is remission of
depression symptoms.
