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An efficient monotone data augmentation (MDA) algorithm is proposed formissing data imputation for incomplete multivariate nonnormal data that maycontain variables of different types, and are modeled by a sequence ofregression models including the linear, binary logistic, multinomial logistic,proportional odds, Poisson, negative binomial, skew-normal, skew-t regressionsor a mixture of these models. The MDA algorithm is applied to the sensitivityanalyses of longitudinal trials with nonignorable dropout using the controlledpattern imputations that assume the treatment effect reduces or disappearsafter subjects in the experimental arm discontinue the treatment. We alsodescribe a heuristic approach to implement the controlled imputation, in whichthe fully conditional specification method is used to impute the intermediatemissing data to create a monotone missing pattern, and the missing data afterdropout are then imputed according to the assumed nonignorable mechanisms. Theproposed methods are illustrated by simulation and real data analyses.

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