  In both the fields of computer science and medicine there is very strong
interest in developing personalized treatment policies for patients who have
variable responses to treatments. In particular, I aim to find an optimal
personalized treatment policy which is a non-deterministic function of the
patient specific covariate data that maximizes the expected survival time or
clinical outcome. I developed an algorithmic framework to solve multistage
decision problem with a varying number of stages that are subject to censoring
in which the "rewards" are expected survival times. In specific, I developed a
novel Q-learning algorithm that dynamically adjusts for these parameters.
Furthermore, I found finite upper bounds on the generalized error of the
treatment paths constructed by this algorithm. I have also shown that when the
optimal Q-function is an element of the approximation space, the anticipated
survival times for the treatment regime constructed by the algorithm will
converge to the optimal treatment path. I demonstrated the performance of the
proposed algorithmic framework via simulation studies and through the analysis
of chronic depression data and a hypothetical clinical trial. The censored
Q-learning algorithm I developed is more effective than the state of the art
clinical decision support systems and is able to operate in environments when
many covariate parameters may be unobtainable or censored.
