Bayesian inference from incomplete longitudinal data: a simple method to quantify sensitivity to nonignorable dropout

Bayesian approach has been increasingly used for analyzing longitudinal data. When dropout occurs in the study, analysis often relies on the assumption of ignorable dropout. Because ignorability is a critical and untestable assumption without obtaining additional data or making other unverifiable assumptions, it is important to assess the impact of departures from the ignorability assumption on the key Bayesian inferences. In this paper, we extend the Bayesian index of local sensitivity to non-ignorability (ISNI) method proposed by Zhang and Heitjan to longitudinal data with dropout. We derive formulas for the Bayesian ISNI when the complete longitudinal data follow a linear mixed-effect model. The calculation of the index only requires the posterior draws or summary statistics of these draws from the standard analysis of the ignorable model. Thus, our approach avoids fitting any complicated nonignorable model. One can use the method to evaluate which Bayesian parameter estimates or functions of these estimates in a linear mixed-effect model are susceptible to nonignorable dropout and which ones are not. We illustrate the method using a simulation study and two real examples: rats data set and rheumatoid arthritis clinical trial data set.