Set Valued Dynamic Treatment Regimes.

Abstract

Dynamic Treatment Regimes (DTR)s are composed of sequences of decision rules, one per stage of treatment. Each decision rule inputs patient information and outputs a single recommended treatment. While the majority of present studies are focused on finding the optimal DTR, we take another approach. Instead of trying to determine the true best DTR, we aim to construct a set of DTRs such that the true best DTR is contained in this set with a desired probability. The reasons are as follows: (1) Usually we do not have enough data to identify the best DTR and (2) we want to give patients and clinicians more options. To discuss the second reason in more detail, patients and clinicians might have treatment preferences related to cost, side eects or convenience, etc. Thus, our goal is to provide a recommended set of DTRs, such that the DTRs contained in the set are those we cannot distinguish from the best, while the DTRs we exclude are those that are certain to be inferior with high condence. This idea comes from decision support: we do not tell patients and clinicians what to do; we do not offer treatments known to be inferior. Rather we offer a set of treatments that excludes inferior treatments. In this thesis we develop a set valued DTR in which the decision rules at each stage can output a set of treatments. Second we develop an approach for constructing a recommended set of DTRs. In the appendix we prove the relevant theorems.