A Flexible Bayesian Approach to Monotone Missing Data in Longitudinal Studies with Informative Missingness

• Activity Number: 381
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Antonio Linero*+ and Michael Daniels
• Companies: University of Florida and University of Texas at Austin
• Keywords: Identifiability ; Identifying restrictions ; Sensitivity analysis ; Nonparametric Bayes

Abstract

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 spae of missing data assumptions can be specified to combine inferences under many different assumptions into a final inference and accurately characterize uncertainty.