Multiple imputation under Bayesianly smoothed pattern-mixture models for non-ignorable drop-out

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Abstract
Conventional pattern‐mixture models can be highly sensitive to model misspecification. In many longitudinal studies, where the nature of the drop‐out and the form of the population model are unknown, interval estimates from any single pattern‐mixture model may suffer from undercoverage, because uncertainty about model misspecification is not taken into account. In this article, a new class of Bayesian random coefficient pattern‐mixture models is developed to address potentially non‐ignorable drop‐out. Instead of imposing hard equality constraints to overcome inherent inestimability problems in pattern‐mixture models, we propose to smooth the polynomial coefficient estimates across patterns using a hierarchical Bayesian model that allows random variation across groups. Using real and simulated data, we show that multiple imputation under a three‐level linear mixed‐effects model which accommodates a random level due to drop‐out groups can be an effective method to deal with non‐ignorable drop‐out by allowing model uncertainty to be incorporated into the imputation process. Copyright © 2005 John Wiley & Sons, Ltd.