An index of local sensitivity to non-ignorability for parametric survival models with potential non-random missing covariate: an application to the SEER cancer registry data

Bayesian second-order sensitivity of longitudinal inferences to non-ignorability: an application to antidepressant clinical trial data

Incomplete data is a prevalent complication in longitudinal studies due to individuals' drop-out before intended completion time. Currently available methods via commercial software for analyzing incomplete longitudinal data at best rely on the ignorability of the drop-outs. If the underlying missing mechanism was non-ignorable, potential bias arises in the statistical inferences. To remove the bias when the drop-out is non-ignorable, joint complete-data and drop-out models have been proposed which involve computational difficulties and untestable assumptions. Since the critical ignorability assumption is unverifiable based on the observed part of the sample, some local sensitivity indices have been proposed in the literature. Specifically, Eftekhari Mahabadi (Second-order local sensitivity to non-ignorability in Bayesian inferences. Stat Med 2018;59:55-95) proposed a second-order local sensitivity tool for Bayesian analysis of cross-sectional studies and show its better performance for handling bias compared with the first-order ones. In this paper, we aim to extend this index for the Bayesian sensitivity analysis of normal longitudinal studies with drop-outs. The index is driven based on a selection model for the drop-out mechanism and a Bayesian linear mixed-effect complete-data model. The presented formulas are calculated using the posterior estimation and draws from the simpler ignorable model. The method is illustrated via some simulation studies and sensitivity analysis of a real antidepressant clinical trial data. Overall, the numerical analysis showed that when repeated outcomes are subject to missingness, regression coefficient estimates are nearly approximated well by a linear function in the neighbourhood of MAR model, but there are a considerable amount of second-order sensitivity for the error term and random effect variances in Bayesian linear mixed-effect model framework.

Second-order local sensitivity to non-ignorability in Bayesian inferences

The sensitivity of Bayesian inferences to non-ignorability is an important issue which should be carefully handled when analyzing incomplete data sets. Generally, sensitivity analysis quantifies the effect that non-ignorability parameter variations have on model outputs or inferences. This sensitivity can be achieved locally around the ignorable model. Previously, some local sensitivity measures to assess the impact of non-ignorable coarsening on Bayesian inferences have been established based on the first-order derivation of the posterior expectations. This may not be adequate to show potential sensitivity when there is a considerable amount of curvature around the ignorable model estimate. Specifically, it becomes more important when the posterior expectation is U-shaped near the ignorable estimate so that the first-order sensitivity index is approximately zero even if the posterior mean might be highly curved around the ignorable model and hence sensitive to the ignorability assumption. In this paper, we present a method for determining the second-order sensitivity to non-ignorability of Bayesian inferences locally around the ignorable model in GLMs which perform equally well when the impact of non-ignorability is locally linear. Calculation of the proposed second-order sensitivity index only requires some posterior covariances of the simple ignorable model and is conducted efficiently and with minimal computational overhead compared with the first-order sensitivity index. To show the need for the second-order sensitivity index as a more precise screening tool, some simulation studies are conducted. Also, the approach is applied to analyze a real data example with CD4 cell counts as an incomplete response variable.