Local Sensitivity to Nonignorability: Dependence on the Assumed Dropout Mechanism

When a longitudinal study is beset with dropout, and there is concern that the dropout mechanism is nonignorable, a sensitivity analysis is in order. Troxel et al. and Ma et al. proposed to base such an analysis on an index of local sensitivity to nonignorability (ISNI), which measures the sensitivity of estimates to small departures from ignorability. A requirement of their approach is that one must specify a model for the missingness mechanism; applications so far have used either the logit or probit link. Because this assumption is typically of questionable validity, there is concern that a sensitivity analysis that does not account for misspecification of the link function may be misleading. In this article we propose an extended ISNI that relaxes the assumption of a known link by considering larger classes of models that include logistic regression as a special case; specifically, we use two families of power transformations that model symmetric and asymmetric departures from the logistic. We conduct a simulation study that shows the importance of using extended ISNI to account for misspecification of the link function in local sensitivity analysis. We then apply the proposed method to two real examples. In both the simulation study and the examples, we find that conclusions for some parameter estimates can vary in important ways when departure from the logit link is extreme.