Proximal Causal Inference with Some Invalid Proxies

Oregon Convention Center 

In observational studies researchers have recently adopted proximal causal learning to identify and estimate causal effects subject to confounding bias.This approach realizes that covariate measurements,even in well-designed studies, may at best be proxies for underlying confounding mechanisms.Traditional proximal causal learning relies on prior knowledge of the validity and relevance of these proxies:a valid treatment inducing proxy should not directly impact the outcome,a relevant outcome inducing proxy must be linked to treatment only to the extent that it relates to an unmeasured confounder.But obtaining complete ex-ante knowledge about proxy validity is impractical.We state necessary-sufficient conditions to identify a causal effect when such apriori knowledge is lacking.We propose a LASSO based 2-stage estimator and offer theoretical guarantees on its performance.To address scenarios where LASSO variable selection is inconsistent a 2-stage adaptive LASSO based estimator is suggested,incorporating adaptive weights in the penalty.It is shown to have oracle properties.We then correct the bias introduced by penalization & establish limiting distribution of the debiased estimator.

Proximal causal inference

Invalid proxies

Two stage estimator

Adaptive Lasso

Oracle property

Debiasing 

IMS