TitleBayesian methods for non-standard missing data problems
NameCheng, Jerry Q. (author), Madigan, David (chair), Xie, Minge (co-chair), Hoover, Donald (internal member), Carpenter, Tamra (outside member), Rutgers University, Graduate School - New Brunswick,
SubjectStatistics and Biostatistics,
Bayesian statistical decision theory,
Missing observations (Statistics)--Mathematical models
DescriptionMissing data presents challenges to statistical analysis in many applications such as clinical trials, cluster detection, etc. This thesis analyzes and develops methodologies in some non-standard missing data problems. We first consider non-ignorable drop-out in longitudinal clinical trials. Common simple approaches such as complete case analysis or last observation carried forward can lead to biased estimates and underestimation of uncertainty. We pursue a model-based approach in the context of Bayesian framework to provide more useful inferences. Second, non-compliance is another way to deviate from pre-designed protocols. Traditional methods circumvent the issue with simplifying assumptions such as intention to treat. Consequently they might produce misleading results. We adopt a counter-factual approach, known as the Rubin Causal Model, essentially reducing the analysis to a missing data problem. We address the issue in particular when drop-out is also involved. In relation to the first two research topics to provide better and more accurate assessment of a treatment or procedure, we develop a Bayesian sequential meta-analysis framework to aggregate results from all available studies. We conduct a case study and build a risk profile of a treatment to provide early alert of emerging problems. Last, the question whether a spatial pattern is randomly distributed has been of interest in many applications. We extend and generalize a latent model approach to overlapping cluster detection. We employ this methodology to design an urban mobile sensor network for the surveillance of nuclear materials. With simulation studies, we demonstrate that the method is efficient and powerful in detection of overlapping clusters.
NoteIncludes bibliographical references
Noteby Jerry Q. Cheng
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.