A0974
Title: Stochastic interventions, sensitivity analysis, and optimal transport
Authors: Alexander Levis - University of Pennsylvania (United States) [presenting]
Edward Kennedy - Carnegie Mellon University (United States)
Alexander McClean - Carnegie Mellon University (United States)
Sivaraman Balakrishnan - Carnegie Mellon University (United States)
Larry Wasserman - Carnegie Mellon University (United States)
Abstract: Recent methodological research in causal inference has focused on effects of stochastic interventions, which assign treatment randomly, often according to subject-specific covariates. It is demonstrated that the usual notion of stochastic interventions has a surprising property: When there is unmeasured confounding, bounds on their effects do not collapse when the policy approaches the observational regime. As an alternative, the purpose is to study generalized policies, treatment rules that can depend on covariates, the natural value of treatment, and auxiliary randomness. It is shown that certain generalized policy formulations can resolve the "non-collapsing" bound issue: Bounds narrow to a point when the target treatment distribution approaches that in the observed data. Moreover, drawing connections to the theory of optimal transport, generalized policies are characterized that minimize worst-case bound width in various sensitivity analysis models, as well as corresponding sharp bounds on their causal effects. These optimal policies are new and can have a more parsimonious interpretation compared to their usual stochastic policy analogues. Finally, flexible, efficient, and robust estimators are developed for the sharp nonparametric bounds that emerge from the framework.
