  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 observed factors (confounders) affect both observed
treatment and time-to-event outcomes. The estimated treatment effect from
DeepSDRF enables us to develop recommender algorithms with the correction for
selection bias. 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 the eICU Research Institute (eRI) database. To the best
of our knowledge, this is the first time that causal models are used to address
the continuous treatment effect with observational data in a medical context.
