Primary Submission Category: Instrumental Variables
An Instrumental Variable Approach under a Multiplicative Selection Model for Data Missing Not-at-Random
Authors: Yunshu Zhang, Eric Tchetgen Tchetgen,
Presenting Author: Yunshu Zhang*
Instrumental variable (IV) methods offer a valuable approach to account for outcome data missing not-at-random. A valid missing data instrument is a measured factor which (i) predicts the nonresponse process and (ii) is independent of the outcome in the underlying population. For point identification, all existing IV methods for missing data including the celebrated Heckman selection model, a priori restrict the extent of selection bias on the outcome scale, therefore potentially understating uncertainty due to missing data. In this work, we introduce an IV framework which allows the degree of selection bias on the outcome scale to remain completely unrestricted. The new approach instead relies for identification on (iii) a key multiplicative selection model, which posits that the instrument and any hidden correlate of both selection and the outcome, impact the selection mechanism independently on the multiplicative scale. Interestingly, we establish that any regular statistical functional of the missing outcome is nonparametrically identified under (i)-(iii) via a modified Wald ratio estimand reminiscent of the standard Wald ratio estimand in causal inference. For estimation and inference, we characterize the efficient influence function for any functional defined on a nonparametric full data model, which we leverage to develop semiparametric efficient multiply robust IV estimators. Several extensions of the methods are also considered, including the important practical