Analyzing the Sensitivity of Generalized Linear Models to Incomplete Outcomes via the IDE Algorithm

Incomplete data models typically involve strong untestable assumptions about the missing data distribution. As inference may critically depend on them, the importance of sensitivity analysis is well recognized. Molenberghs, Kenward, and Goetghebeur proposed a formal frequentist approach to sensitivity analysis which distinguishes ignorance due to unintended incompleteness from imprecision due to finite sampling by design. They combine both sources of variation into uncertainty. This article develops estimation tools for ignorance and uncertainty concerning regression coefficients in a complete data model when some of the intended outcome values are missing. Exhaustive enumeration of all possible imputations for the missing data requires enormous computational resources. In contrast, when the boundary of the occupied region is of greatest interest, reasonable computational efficiency may be achieved via the imputation towards directional extremes (IDE) algorithm. This is a special imputation method designed to mark the boundary of the region by maximizing the direction of change of the complete data estimator caused by perturbations to the imputed outcomes. For multi-dimensional parameters, a dimension reduction approach is considered. Additional insights are obtained by considering structures within the region, and by introducing external knowledge to narrow the boundary to useful proportions. Special properties hold for the generalized linear model. Examples from a Kenyan HIV study will illustrate the points.

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