Date of Completion
Probit Model; Latent Variable; Jeffreys Prior; Collapsed Gibbs Sampler; Identifiability; DIC; LPML
Elizabeth D. Schifano
Field of Study
Missing data are frequently encountered in longitudinal clinical trials. To better monitor and understand the progress over time, we must handle the missing data appropriately and thus examine whether the missing data mechanism is ignorable or nonignorable.
In this dissertation research, we develop models and carry out Bayesian inferences for both longitudinal binary response and count response data. For longitudinal binary response data, we develop a new probit model. It resolves the well-known weak identifiability issue of the variance of the random effects, and substantially improves the convergence and mixing of the Gibbs sampling algorithm. We adopt a sequence of one-dimensional conditional distributions for the missing data indicators via a logistic regression model. For the longitudinal count response data, we use the zero-inflated Poisson model for the response measurements, and propose a new conditional model for the missing data mechanism. The new model has the potential of reducing the number of nuisance parameters, allows us to model dropout and intermittent missing jointly, and provides a broad class of missing data mechanisms. We then investigate and characterize the conditions for propriety of the joint posterior distribution under both binary and Poisson cases, and propose a variation of Jeffreys's prior as a remedy for impropriety of the posterior. In addition, we develop two efficient Gibbs sampling algorithms for both binary and Poisson cases, which allow us to conveniently sample missing responses and to apply the collapsed Gibbs technique as well as the hierarchical centering technique within the Gibbs sampling framework.
The proposed methodologies and the sampling techniques are illustrated using real data from an HIV prevention clinical trial. A sensitivity analysis is carried out to assess the robustness of the posterior estimates under different prior specifications and missing data mechanisms. Two model assessment criteria, the deviance information criterion (DIC) and the logarithm of the pseudomarginal likelihood (LPML), are used to examine model fit. Extensive real data analyses are conducted to assess the performances of missing data mechanisms under different scenarios.
Wu, Jing, "Bayesian Modeling and Inference for Nonignorably Missing Longitudinal Response Data" (2017). Doctoral Dissertations. 1411.