Set-valued dynamic treatment regimes for competing outcomes

Dynamic treatment regimes operationalize the clinical decision process as a sequence of functions, one for each clinical decision, where each function takes as input up-to-date patient information and gives as output a single recommended treatment. Current methods for estimating optimal dynamic treatment regimes, for example Q-learning, require the specification of a single outcome by which the `goodness’ of competing dynamic treatment regimes are measured. However, this is an over-simplification of the goal of clinical decision making, which aims to balance several potentially competing outcomes. For example, often a balance must be struck between treatment effectiveness and side-effect burden. We propose a method for constructing dynamic treatment regimes 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 are not inferior according to any of the competing outcomes. When there is more than one decision point, 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 a depression study and the CATIE schizophrenia study.

💡 Research Summary

The paper addresses a fundamental limitation of existing dynamic treatment regime (DTR) methods, which typically optimize a single clinical outcome (e.g., symptom reduction) while ignoring other important, often competing, outcomes such as side‑effect burden, cost, or quality of life. To overcome this, the authors introduce set‑valued dynamic treatment regimes—a sequence of decision rules that, at each treatment point, return a set of admissible therapies rather than a single recommendation. A treatment is included in the set if it is not inferior to any other option across all outcomes, i.e., it satisfies a Pareto‑non‑inferiority criterion within a pre‑specified tolerance for each outcome.

Formally, for each decision stage (t), patient history (H_t), and treatment set (\mathcal{A}_t), the authors define Q‑functions (Q_t^{(k)}(H_t,a)=\mathbb{E}