Pattern-Mixture Models for Multivariate Incomplete Data with Covariates

Pattern-mixture models stratify incomplete data by the pattern of missing values and formulate distinct models within each stratum. Pattern-mixture models are developed for analyzing a random sample on continuous variables y$_{(1)}$, y$_{(2)}$ when values of y$_{(2)}$ are nonrandomly missing. Methods for scalar y$_{(1)}$ and y$_{(2)}$ are here generalized to vector y$_{(1)}$ and y$_{(2)}$ with additional fixed covariates x. Parameters in these models are identified by alternative assumptions about the missing-data mechanism. Models may be underidentified (in which case additional assumptions are needed), just-identified, or overidentified. Maximum likelihood and Bayesian methods are developed for the latter two situations, using the EM and SEM algorithms, direct and iterative simulation methods. The methods are illustrated on a data set involving alternative dosage regimens for the treatment of schizophrenia using haloperidol and on a regression example. Sensitivity to alternative assumptions about the missing-data mechanism is assessed, and the new methods are compared with complete-case analysis and maximum likelihood for a probit selection model.