A scalable approach to measuring the impact of nonignorable nonresponse with an EMA application.

There is often a need to assess the dependence of standard analyses on the strong untestable assumption of ignorable missingness. To tackle this problem, past research developed simple sensitivity index measures assuming a linear impact of nonignorability and missingness in outcomes only. These restrictions limit their applicability for studies with missingness in both outcome and covariates. Nonignorable missingness in this setting poses significant new analytic challenges and calls for more general and flexible methods that are also computationally tractable even for large datasets. In this paper, we relax the restrictions of extant linear sensitivity index methods and develop nonlinear sensitivity indices that maintain computational simplicity and perform equally well when the impact of nonignorability is locally linear. On the other hand, they can substantially improve the effectiveness of local sensitivity analysis when regression outcomes and covariates are subject to concurrent missingness. In this situation, the local linear sensitivity analysis fails to detect the impact of nonignorability while the proposed nonlinear sensitivity measures can. Because the new sensitivity indices avoid fitting complicated nonignorable models, they are computationally tractable (i.e., scalable) for use in large datasets. We develop general formula for nonlinear sensitivity index measures, and evaluate the new measures in simulated data and a real dataset collected using the ecological momentary assessment method.