A Bayesian Nonparametic Approach for Estimating Individualized Treatment-Response Curves

We study the problem of estimating the continuous response over time of interventions from observational time series—a retrospective dataset where the policy by which the data are generated are unknown to the learner. We are motivated by applications where response varies by individuals and therefore, estimating responses at the individual-level are valuable for personalizing decisionmaking. We refer to this as the problem of estimating individualized treatment response (ITR) curves. In statistics, G-computation formula (Robins, 1986) has been commonly used for estimating treatment responses from observational data containing sequential treatment assignments. However, past studies have focused predominantly on obtaining point-in-time estimates at the population level. We leverage G-computation formula and develop a novel method based on Bayesian nonparametrics (BNP) that can flexibly model functional data and provide posterior inference over the treatment response curves both at the individual and population level. On a challenging dataset containing time series from patients admitted to a hospital, we estimate treatment responses for treatments used in managing kidney function and show that the resulting fits are more accurate than alternative approaches. Accurate methods for obtaining ITRs from observational data can dramatically accelerate the pace at which personalized treatment plans become possible.