Restricted sub-tree learning to estimate an optimal dynamic treatment regime using observational data

Dynamic treatment regimes (DTRs), consisting of a sequence of tailored treatment decision rules that span multiple stages of care, present a unique opportunity in our drive toward personalized medicine. Given that estimation of optimal DTRs is often exploratory and communication with clinicians is vital, robust and flexible methods that yield interpretable results are needed. Tree-based methods utilizing a purity measure defined on the full set of covariates have enjoyed much success in meeting this goal. Often, however, it is necessary for clinical, practical, or ethical reasons to restrict certain covariates that should be used when making treatment decisions. Herein we present restricted sub-tree learning (ReST-L), a flexible and robust, sub-tree-based method to estimate an optimal multi-stage multi-treatment DTR that enables restrictions to the set of prespecified candidate tailoring variables. ReST-L employs a purity measure derived from an augmented inverse probability weighted estimator for the counterfactual mean outcome, using observational data to build multi-stage decision trees that are restricted in sub-tree spaces defined by the corresponding prescriptive covariates. We show that ReST-L is able to correctly estimate the optimal DTR searching over a large number of variables with relatively small sample sizes and improves upon competing estimation methods. We demonstrate the utility of ReST-L to estimate a two-stage fluid resuscitation strategy for patients admitted to an intensive care unit with acute emergent sepsis.