Penalized Spline-Involved Tree-based (PenSIT) Learning for estimating an optimal dynamic treatment regime using observational data.

Dynamic treatment regimes are a set of time-adaptive decision rules that can be used to personalize treatment across multiple stages of care. Grounded in causal inference methods, dynamic treatment regimes identify variables that differentiate the treatment effect and may be used to tailor treatments across individuals based on the patient's own characteristics - thereby representing an important step toward personalized medicine. In this manuscript we introduce Penalized Spline-Involved Tree-based Learning, which seeks to improve upon existing tree-based approaches to estimating an optimal dynamic treatment regime. Instead of using weights determined from the estimated propensity scores, which may result in unstable estimates when weights are highly variable, we predict missing counterfactual outcomes using regression models that incorporate a penalized spline of the propensity score and other covariates predictive of the outcome. We further develop a novel purity measure applied within a decision tree framework to produce a flexible yet interpretable method for estimating an optimal multi-stage multi-treatment dynamic treatment regime. In simulation experiments we demonstrate good performance of Penalized Spline-Involved Tree-based Learning relative to competing methods and, in particular, we show that Penalized Spline-Involved Tree-based Learning may be advantageous when the sample size is small and/or when the level of confounding of the outcome is high. We apply Penalized Spline-Involved Tree-based Learning to the retrospectively-collected Medical Information Mart for Intensive Care dataset to identify variables that may be used to tailor early fluid resuscitation strategies in septic patients.