An efficient monotone data augmentation algorithm for multiple imputation in a class of pattern mixture models

Abstract

We develop an efficient Markov chain Monte Carlo algorithm for the mixed-effects model for repeated measures (MMRM) and a class of pattern mixture models (PMMs) via monotone data augmentation (MDA). The proposed algorithm is particularly useful for multiple imputation in PMMs and is illustrated by the analysis of an antidepressant trial. We also describe the full data augmentation (FDA) algorithm for MMRM and PMMs and show that the marginal posterior distributions of the model parameters are the same in the MDA and FDA algorithms.

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

“…If the imputation contains only the normal linear models with the conditional mean , the MH sampler for y i c becomes a Gibbs sampler ( A j y ≡1) and the proposed algorithm reduced to the MDA algorithm for multivariate normal data (except that the priors may be different). For longitudinal binary or ordinal outcomes, the above algorithm is identical to that of Tang …”

“…The MDA algorithm iterates between an imputation I‐step, in which the intermittent missing data are imputed given the current draw of the model parameters, and a posterior P‐step, in which the model parameters are updated given the current imputed monotone data. It tends to converge faster with smaller autocorrelation between posterior samples than a full data augmentation algorithm that imputes both the intermittent missing data and missing data after dropout during the I‐step . Schafer's algorithm was recently improved by Tang .…”

“…Schafer's algorithm was recently improved by Tang . Tang's approach allows the use of a more general prior distribution, imputes the intermittent missing outcomes in a more computationally efficient way, and enables more flexible modeling of the mean and covariance matrix …”

“…There is no restriction on the order of the response variables. The MDA algorithms of Tang are special cases of the proposed algorithm when the data contain only one type of response variable (continuous, binary, or ordinal). Section 2.2 extends the algorithm to incorporate the skew‐normal and skew‐t regressions for nonnormal continuous outcomes and discusses the potential extension to include other types of regression models.…”

“…The regulatory guidelines and a FDA‐mandated panel report from the National Research Council recommend sensitivity analysis under missing not at random (MNAR) in the sense that the response profiles for subjects who withdraw are systematically different from those who remain on the treatment. The controlled pattern imputations, pioneered by Little and Yau, assume that the treatment effect reduces or disappears after the treatment discontinuation by taking into account of the treatment actually received after dropout . These methods have become increasingly popular in clinical trials because the underlying MNAR assumption is clinically plausible and easy to interpret.…”