Constructing dynamic treatment regimes with shared parameters for censored data

Dynamic treatment regimes are sequential decision rules that adapt throughout disease progression according to a patient's evolving characteristics. In many clinical applications, it is desirable that the format of the decision rules remains consistent over time. Unlike the estimation of dynamic treatment regimes in regular settings, where decision rules are formed without shared parameters, the derivation of the shared decision rules requires estimating shared parameters indexing the decision rules across different decision points. Estimation of such rules becomes more complicated when the clinical outcome of interest is a survival time subject to censoring. To address these challenges, we propose two novel methods: censored shared-Q-learning and censored shared-O-learning. Both methods incorporate clinical preferences into a qualitative rule, where the parameters indexing the decision rules are shared across different decision points and estimated simultaneously. We use simulation studies to demonstrate the superior performance of the proposed methods. The methods are further applied to the Framingham Heart Study to derive treatment rules for cardiovascular disease.