Gamma Approximation of Stratified Truncated Exact test (GASTE-test) & Application

The analysis of binary outcomes and features, such as the effect of vaccination on health, often rely on 2 × 2 contingency tables. However, confounding factors such as age or gender call for stratified analysis, by creating sub-tables, which is common in bioscience, epidemiological, and social research, as well as in meta-analyses. Traditional methods for testing associations across strata, such as the Cochran-Mantel-Haenszel (CMH) test, struggle with small sample sizes and heterogeneity of effects between strata. Exact tests can address these issues, but are computationally expensive. To address these challenges, the Gamma Approximation of Stratified Truncated Exact (GASTE) test is proposed. It approximates the exact statistic of the combination of p-values with discrete support, leveraging the gamma distribution to approximate the distribution of the test statistic under stratification, providing fast and accurate p-value calculations, even when effects vary between strata. The GASTE method maintains high statistical power and low type I error rates, outperforming traditional methods by offering more sensitive and reliable detection. It is computationally efficient and broadens the applicability of exact tests in research fields with stratified binary data. The GASTE method is demonstrated through two applications: an ecological study of Alpine plant associations and a 1973 case study on admissions at the University of California, Berkeley. The GASTE method offers substantial improvements over traditional approaches and is available as an open-source package at https://github.com/AlexandreWen/gaste .