Rare binary events data arise frequently in medical research. Due to lack of statistical power in individual studies involving such data, meta-analysis has become an increasingly important tool for combining results from multiple independent studies. However, traditional meta-analysis methods often report severely biased estimates in such rare-event settings. Moreover, many rely on models assuming a pre-specified direction for variability between control and treatment groups for mathematical convenience, which may be violated in practice. In Chapter 1, based on a flexible random-effects model that removes the assumption about the direction, we propose new Bayesian procedures for estimating and testing the overall treatment effect and inter-study heterogeneity. Our Markov chain Monte Carlo algorithm employs Pólya-Gamma augmentation so that all conditionals are known distributions, greatly facilitating computational efficiency. Our simulation shows that the proposed approach generally reports less biased and more stable estimates compared to existing methods. We further illustrate our approach using two real examples, one using rosiglitazone data from 56 studies and the other using stomach ulcer data from 41 studies.

Random-effects (RE) meta-analysis is a crucial approach for combining results from multiple independent studies that exhibit heterogeneity. Recently, two frequentist goodness-of-fit (GOF) tests were proposed to assess the adequacy of RE model fit. However, they tend to perform poorly when encountering rare binary events. In Chapter 2, under a general binomial-normal framework, we propose a Bayesian GOF test for meta-analysis of rare events. Our method is based on pivotal quantities that plays an important role in Bayesian model assessment, and adopts the Cauchy combination idea, newly proposed in a 2019 JASA paper, to combine dependent p-values computed using posterior samples from Markov Chain Monte Carlo. The advantages of our method include straightforward conception and interpretation, incorporation of all data including double zeros without artificial correction, well-controlled Type I error, and generally higher power in detecting model misfits when compared to previous GOF methods. We illustrate the proposed method via simulation and three real data applications.

Replication studies play an essential role in genetic association studies (GAS) for accessing the credibility of original findings. However, existing approaches for measuring replication success often have limitations, such as focusing on single replications, which may not be appropriate in genetic research with multiple replications. Additionally, some methods fail to account for information from the original study or make assumptions that replication studies have the same standard error as the original study, which is not always valid in GAS. To address these limitations, in Chapter 3, we propose a Bayesian approach called OABF that allows for the inclusion of multiple replications and assesses the consistency between the original study and its replications. Our method utilizes a Bayes factor test, where the null hypothesis assumes a zero-effect size, while the alternative hypothesis advocates for consistency between the original study and replications. We show that OABF may alleviate the issue of false positives in GAS and has the potential to address false negatives and correlated replications. We further illustrate the performance of OABF through simulation studies and real GAS datasets of nonalcoholic fatty liver disease (NAFLD), showing its effectiveness in evaluating replication success in genetic research.

Degree Date

Spring 2023

Document Type


Degree Name



Statistical Science


Xinlei Wang

Second Advisor

Chao Xing

Subject Area

Biostatistics, Statistics

Number of Pages




Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License