Testing homogeneity of proportions from sparse binomial data with a large number of groups

TL;DR

This paper develops and evaluates new statistical tests for assessing the homogeneity of proportions across many sparse binomial groups, combining theoretical analysis, simulations, and real data application.

Contribution

It introduces novel tests for homogeneity in sparse binomial data, with asymptotic properties and performance comparisons to existing methods.

Findings

Proposed tests control sizes and have good power in simulations

No single test dominates across all scenarios

Real data application demonstrates practical utility

Abstract

In this paper, we consider testing the homogeneity for proportions in independent binomial distributions especially when data are sparse for large number of groups. We provide broad aspects of our proposed tests such as theoretical studies, simulations and real data application. We present the asymptotic null distributions and asymptotic powers for our proposed tests and compare their performance with existing tests. Our simulation studies show that none of tests dominate the others, however our proposed test and a few tests are expected to control given sizes and obtain significant powers. We also present a real example regarding safety concerns associated with Avandiar (rosiglitazone) in Nissen and Wolsky (2007).