Meta-analysis is a statistical approach that integrates data from multiple studies. By aggregating information, it enhances the power to detect the effects of interest and provides an estimate of the effect size with both accuracy and precision. Both fixed-effect and random-effect models are developed and widely used in biomedical research including clinical trials and genomic studies. In the case of rare events data, conventional meta-analysis methods that rely on large sample approximation may not be able to make reliable inferences. There have been various approaches proposed to deal with this situation, in particular, rare binary adverse events in clinical studies.

Genome-wide association studies (GWAS) is the most popular study design of human genetic mapping. Large consortia are organized to increase the power of association detection, and therefore meta-analysis becomes a necessity in GWAS. Advances in sequencing technology enable a complete survey of both common and rare variants. Although numerous statistical methods to analyze rare variants are developed for a single study, there is no meta-analysis approach developed to specifically deal with rare variants. In this dissertation we aim to develop methods to make exact inferences in meta-analysis of rare variants association. The exact methods are based on exact distribution not approximate distribution so it is derived from all known parameters.

We first adapt and implement a fixed-effect exact meta-analysis approach that is based on the concept of p-value function with the specific aim of performing rare variants genetic association studies. It can conduct robust inference on risk difference (RD) and construct a reliable confidence interval (CI) without ignoring studies with zero event, adding arbitrary continuity corrections, or using large sample approximation. We compare the exact method with the commonly used Mantel-Haenszel method in terms of CI coverage probability, CI length, type I error rate, statistical power, and absolute bias in various scenarios of balanced and unbalanced study sample sizes. Simulation results show that the exact methods are more stable when the event rates are extremely rare and sample sizes are unbalanced between case and control groups.

We then extend the exact meta-analysis approach to a random-effect model, which, compared with the fixed-effect model, can handle between-study variances. The proposed method enables an unbiased estimate of odds ratio (OR) and makes exact inferences of CI. We propose a method to shrink the parameter search region, which can substantially reduce the computational cost. Simulation studies are conducted to investigate the performance of the proposed method in terms of CI coverage probability and CI length. The proposed method maintains stable coverage probabilities under various settings of heterogeneity, number of studies, and magnitude of ORs.

We further consider a special study design that there are multiple case groups but there is only one common control group. This may happen when researchers only recruit patients but not controls, and use some large survey database from the general population as the common control group. We propose an exact method to construct CI for the event rate in the case groups and then make inferences on the pooled effect size measures, e.g. RD and OR, compared with the common controls. The proposed exact method shows stable performance regardless of the parameter settings. We particularly recommend applying it when the number of studies is small and the event rate is rare.

Degree Date

Winter 12-18-2021

Document Type


Degree Name



Statistical Science

Subject Area




Creative Commons License

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