A monotone data augmentation algorithm for multivariate nonnormal data: with applications to controlled imputations for longitudinal trials

An efficient monotone data augmentation (MDA) algorithm is proposed for missing data imputation for incomplete multivariate nonnormal data that may contain variables of different types, and are modeled by a sequence of regression models including the linear, binary logistic, multinomial logistic, proportional odds, Poisson, negative binomial, skew-normal, skew-t regressions or a mixture of these models. The MDA algorithm is applied to the sensitivity analyses of longitudinal trials with nonignorable dropout using the controlled pattern imputations that assume the treatment effect reduces or disappears after subjects in the experimental arm discontinue the treatment. We also describe a heuristic approach to implement the controlled imputation, in which the fully conditional specification method is used to impute the intermediate missing data to create a monotone missing pattern, and the missing data after dropout are then imputed according to the assumed nonignorable mechanisms. The proposed methods are illustrated by simulation and real data analyses.