A Pattern-Mixture Model with Nonfuture Dependence and Shift in Current Missing Values

Abstract

For incomplete continuous longitudinal data with a monotone pattern, we study a pattern-mixture model which assumes that missingness only depends on observed data and the current missing value, and that the conditional distribution of the current missing value differ from that of the observed patterns by location and scale shifts. The shift parameters measure the departure from the missing at random mechanism. We show that a numerical or Monte Carlo approximation is needed to obtain the posterior draw of the mean at the final time point as a function of the posterior draw of the observed data model parameters and shift parameters, and that scale shifts have negligible impact on the estimated mean at the final time point. We use multiple imputation to avoid numerical integration and demonstrate that the usual multiple imputation variance estimator is valid for the estimated mean at the final time point when scale shifts are not considered. The multiple imputation method is applied to a clinical study of major depressive disorders.