Date of Award

Fall 12-2022

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics & Statistics


Computational and Applied Mathematics

Committee Director

Sinjini Sikdar

Committee Member

N. Rao Chaganty

Committee Member

Yet Nguyen

Committee Member

Hadiza Galadima


Recent developments in high throughput genomic assays have opened up the possibility of testing hundreds and thousands of genes simultaneously. With the availability of vast amounts of public databases, researchers tend to combine genomic analysis results from multiple studies in the form of a meta-analysis. Meta-analysis methods can be broadly classified into two main categories. The first approach is to combine the statistical significance (pvalues) of the genes from each individual study, and the second approach is to combine the statistical estimates (effect sizes) from the individual studies. In this dissertation, we will discuss how adherence to the standard null distributional assumptions in both categories of meta-analysis methods can lead to incorrect significance testing results in detecting the true set of significant genes. To overcome this, we will also propose two robust meta-analysis methods that perform empirical modifications of the summary results. In the first part, we will propose a new meta-analysis method combining p-values for a gene from multiple studies with an aim to detect significance in a consistent pattern in a majority of studies. Our proposed method performs an empirical modification of the individual p-values using an empirical Bayes approach before meta-analyzing them. In the second part, we will propose a meta-analysis method combining effect size estimates for a gene from multiple studies with an aim to detect significance in at least one study. Here we perform empirical modification of the z-scores, obtained from effect size estimates of the genes and their standard errors, using the empirical Bayes approach. Through various simulation studies and real genomic data applications, we will show that our proposed meta-analysis methods outperform the existing meta-analysis methods in terms of accurately identifying the truly significant set of genes by reducing false discoveries, especially in the presence of unobserved confounding variables


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