Learning Treatment Allocations with Risk Control Under Partial Identifiability

Learning beneficial treatment allocations for a patient population is an important problem in precision medicine. For such allocations, a certain proportion of treated patients may not receive any benefit. This proportion of unnecessary treated represents a `treatment risk' which is a waste of resources and may, in addition, expose patients to unnecessary adverse effects. Therefore, we aim to control the treatment risk when learning beneficial allocations. This learning problem is complicated by the fact that the treatment risk is generally not identifiable from either randomized trial or observational data. We propose a certifiable learning method that controls treatment risk, using finite samples in the partially identified setting. The method is illustrated using both simulated and real data.