Non-greedy Tree-based Learning for Estimating Global Optimal Dynamic Treatment Decision Rules with Continuous Treatment Dosage

Dynamic treatment regime (DTR) plays a critical role in precision medicine when assigning patient-specific treatments at multiple stages and optimizing a long term clinical outcome. However, most of existing work about DTRs have been focused on categorical treatment scenarios, instead of continuous treatment options. Also, the performances of regular black-box machine learning methods and regular tree learning methods are lack of interpretability and global optimality respectively. In this paper, we propose a non-greedy global optimization method for dose search, namely Global Optimal Dosage Tree-based learning method (GoDoTree), which combines a robust estimation of the counterfactual outcome mean with an interpretable and non-greedy decision tree for estimating the global optimal dynamic dosage treatment regime in a multiple-stage setting. GoDoTree-Learning recursively estimates how the counterfactual outcome mean depends on a continuous treatment dosage using doubly robust estimators at each stage, and optimizes the stage-specific decision tree in a non-greedy way. We conduct simulation studies to evaluate the finite sample performance of the proposed method and apply it to a real data application for optimal warfarin dose finding.