Continuous Treatment Recommendation with Deep Survival Dose Response Function

We propose a general formulation for continuous treatment recommendation problems in settings with clinical survival data, which we call the Deep Survival Dose Response Function (DeepSDRF). That is, we consider the problem of learning the conditional average dose response (CADR) function solely from historical data in which unobserved factors (confounders) affect both observed treatment and time-to-event outcomes. The estimated treatment effect from DeepSDRF enables us to develop recommender algorithms with explanatory insights. We compared two recommender approaches based on random search and reinforcement learning and found similar performance in terms of patient outcome. We tested the DeepSDRF and the corresponding recommender on extensive simulation studies and two empirical databases: 1) the Clinical Practice Research Datalink (CPRD) and 2) the eICU Research Institute (eRI) database. To the best of our knowledge, this is the first time that confounders are taken into consideration for addressing the continuous treatment effect with observational data in a medical context.