B1628
Title: Proximal causal inference under confounded outcome-dependent sampling
Authors: Kendrick Li - University of Michigan (United States) [presenting]
Xu Shi - University of Michigan (United States)
Eric Tchetgen Tchetgen - The Wharton School, University of Pennsylvania (United States)
Wang Miao - Peking University (China)
Abstract: Outcome-dependent sampling is widely used in epidemiology and econometrics to reduce time and effort when studying causal relationships between the exposure and outcome variables. In these types of studies, unmeasured confounding and selection bias are often of concern and may invalidate a causal analysis if not appropriately accounted for. In particular, a latent factor that has causal effects on the treatment, outcome, and sample selection process may cause both unmeasured confounding and selection bias, rendering standard causal parameters unidentifiable without additional assumptions. We introduce the identification and inference of treatment effect under a homogeneous odds ratio model, leveraging a pair of proxies to the source of unmeasured confounding: a negative control exposure (NCE) which is a priori known not to affect the outcome and selection, and a negative control outcome (NCO) which is a priori known not to be affected by the treatment. We introduce three estimators of the odds ratio effect, one of which is doubly robust with respect to the specification of two nuisance functions which restrict the treatment assignment mechanism and outcome distribution, respectively, such that the estimator is consistent and asymptotically normal if either model is correctly specified, without knowing which one is.
