Bayesian approaches to meta-analysis

The second half of the twentieth century has witnessed an explosive growth in the scientific literature. The challenge to statisticians is to develop effective methodologies for meta-analysis, combining information from related studies in order to perform some overall inference. This dissertation presents Bayesian approaches to meta-analysis modeling, including models for publication bias using weighted distributions, grouped random effects, and dependent covariate subclass effects.^ In meta-analysis, if the sample of study results is not representative of the entire population of such studies, then statistical inference based on this assumption may be unsound. For example, publication bias occurs when investigators or editors base decisions regarding submission or acceptance of manuscripts for publication on the strength of the study findings. Statistical models describing publication bias can be constructed quite naturally using weighted distributions.^ The method of weighted distributions models ascertainment bias by adjusting the probabilities of actual occurrence of events to arrive at a specification of the probabilities of the events as observed and recorded. Here, closed form expressions and Monte Carlo estimates for the Bayes factor are obtained for selection among weighted and unweighted models. The weight function can be a direct representation of the selection probabilities at work in publication bias.^ What happens when results from different subgroups of studies lead to different conclusions? Here, grouped random effects models are developed and compared. The framework for this and for all the modeling in this thesis is the Bayesian hierarchical modeling framework. Markov chain Monte Carlo methods are called upon to generate samples from intractable posterior distributions.^ Finally, the wealth of covariate information available, especially in the form of dependent subclasses, prompted the development herein of models for determining effect size estimates for dependent covariate subclass effects. New meta-analyses were conducted investigating putative links between estrogen exposure and breast and endometrial cancer.