  We use a Stochastic Hybrid Automaton (SHA) model of prostate cancer evolution
under intermittent androgen suppression (IAS) to study a threshold-based policy
for therapy design. IAS is currently one of the most widely used treatments for
advanced prostate cancer. Patients undergoing IAS are submitted to cycles of
treatment (in the form of androgen deprivation) and off-treatment periods in an
alternating manner. One of the main challenges in IAS is to optimally design a
therapy scheme, i.e., to determine when to discontinue and recommence androgen
suppression. The level of prostate specific antigen (PSA) in a patient's serum
is frequently monitored to determine when the patient will be taken off therapy
and when therapy will resume. The threshold-based policy we propose is
parameterized by lower and upper PSA threshold values and is associated with a
cost metric that combines clinically relevant measures of therapy success.
Using Infinitesimal Perturbation Analysis (IPA), we derive unbiased gradient
estimators of this cost metric with respect to the controllable PSA threshold
values based on actual data and show how these estimators can be used to
adaptively adjust controllable parameters so as to improve therapy outcomes
based on the cost metric defined.
