A Flexible Bayesian Approach to Monotone Missing Data in Longitudinal Studies With Nonignorable Missingness With Application to an Acute Schizophrenia Clinical Trial
Antonio R. Linero, Michael J. Daniels · Journal of the American Statistical Association · 2014
Antonio R. Linero & Michael J. DanielsAntonio R. Linero, Department of Statistics, University of Florida, Gainesville, FL, 32611 (E-mail: [email protected]), Michael J. Daniels, Department of Integrative Biology, Department of Statistics and Data Sciences, University of Texas at Austin, Austin, TX 78712 (E-mail: [email protected]) This work was partially supported by NIH grant CA 85295 and CA 183854. The authors thank the Bayes Missing Data Working Group for providing the data and important insights about the clinical trial, as well as Merck & Co., Inc. for allowing us the use of the data from their clinical trial.Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/jasa.We develop a Bayesian nonparametric model for a longitudinal response in the presence of nonignorable missing data. Our general approach is to first specify a working model that flexibly models the missingness and full outcome processes jointly. We specify a Dirichlet process mixture of missing at random (MAR) models as a prior on the joint distribution of the working model. This aspect of the model governs the fit of the observed data by modeling the observed data distribution as the marginalization over the missing data in the working model. We then separately specify the conditional distribution of the missing data given the observed data and dropout. This approach allows us to identify the distribution of the missing data using identifying restrictions as a starting point. We propose a framework for introducing sensitivity parameters, allowing us to vary the untestable assumptions about the missing data mechanism smoothly. Informative priors on the space of missing data assumptions can be specified to combine inferences under many different assumptions into a final inference and accurately characterize uncertainty. These methods are motivated by, and applied to, data from a clinical trial assessing the efficacy of a new treatment for acute schizophrenia. Supplementary materials for this article are available online.