Statistica Sinica 14(2004), 1221-1237

AN INDEX OF LOCAL SENSITIVITY TO

NONIGNORABILITY

Andrea B. Troxel$^1$, Guoguang Ma$^2$ and Daniel F. Heitjan$^1$

$^1$University of Pennsylvania School of Medicine and

$^2$Clinical Biostatistics, Merck & Co., Inc.

Abstract: Standard methods of analysis can give misleading results when some observations are nonignorably missing. Analysts currently assess nonignorability by performing sensitivity analyses using models with and without a nonignorable component. Because this approach can involve complicated modeling and arduous computation, and can yield results that are highly sensitive to untestable model assumptions, there is a need for a simple screening tool that measures the potential impact of nonignorability on an analysis. We propose a measure based on a Taylor-series approximation to the nonignorable likelihood, evaluated at the parameter estimates under the assumption of ignorability. From this approximate likelihood, we derive an index of sensitivity to nonignorability, or ISNI. One can compute ISNI without estimating a nonignorable model or positing specific values of a nonignorability parameter. We interpret ISNI in terms of an intuitive parameter that captures the extent of sensitivity. We derive a general expression for ISNI in the generalized linear model with fully observed predictors and potentially missing outcomes. We illustrate the method with two regression examples.

Key words and phrases: Ignorability, missing at random, missing data, sensitivity analysis.