Set‐valued dynamic treatment regimes for competing outcomes. Issue 1 (8th January 2014) - Laber, Eric B.; Lizotte, Daniel J.; Ferguson, Bradley
Summary Dynamic treatment regimes (DTRs) operationalize the clinical decision process as a sequence of functions, one for each clinical decision, where each function maps up‐to‐date patient information to a single recommended treatment. Current methods for estimating optimal DTRs, for example Q‐learning, require the specification of a single outcome by which the "goodness" of competing dynamic treatment regimes is measured. However, this is an over‐simplification of the goal of clinical decision making, which aims to balance several potentially competing outcomes, for example, symptom relief and side‐effect burden. When there are competing outcomes and patients do not know or cannot communicate their preferences, formation of a single composite outcome that correctly balances the competing outcomes is not possible. This problem also occurs when patient preferences evolve over time. We propose a method for constructing DTRs that accommodates competing outcomes by recommending sets of treatments at each decision point. Formally, we construct a sequence of set‐valued functions that take as input up‐to‐date patient information and give as output a recommended subset of the possible treatments. For a given patient history, the recommended set of treatments contains all treatments that produce non‐inferior outcome vectors. Constructing these set‐valued functions requires solving a non‐trivial enumeration problem. We offer an exact enumeration algorithm by recasting the problem as a linear mixed integer program. The proposed methods are illustrated using data from the CATIE schizophrenia study.