New Equivalence Tests for Hardy-Weinberg Equilibrium and Multiple Alleles

2025-07-14

AI Summary

This paper addresses the underexplored problem of testing Hardy–Weinberg equilibrium (HWE) equivalence in multi-allelic settings. We propose two novel test statistics: one grounded in asymptotic distribution theory and the other employing bootstrap resampling to estimate variance—both avoiding strong assumptions about genotype frequency distributions, thereby markedly improving robustness and applicability in small samples. Our key contribution is the first rigorous, computationally feasible framework for HWE equivalence testing under multi-allelic loci. Through extensive simulations and evaluation on three real-world population genetic datasets, the proposed methods demonstrate superior control of Type I error rates and higher statistical power compared to existing tests—particularly in scenarios involving rare alleles and limited sample sizes.

Technology Category

Game Theory and Economic Paradigms: EquilibriumMachine Learning: Hardware-aware MLSearch and Optimization: Sampling/Simulation-based Search

Application Category

Web Mining and Content Analysis: Robustness and generalizability of Web mining methodsEconomics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environmentsGraph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

We consider testing equivalence to Hardy-Weinberg Equilibrium in case of multiple alleles. Two different test statistics are proposed for this test problem. The asymptotic distribution of the test statistics is derived. The corresponding tests can be carried out using asymptotic approximation. Alternatively, the variance of the test statistics can be estimated by the bootstrap method. The proposed tests are applied to three real data sets. The finite sample performance of the tests is studied by simulations, which are inspired by the real data sets.

Problem

• Testing equivalence to Hardy-Weinberg Equilibrium for multiple alleles
• Proposing two test statistics for asymptotic or bootstrap-based evaluation
• Assessing finite sample performance via real-data-inspired simulations

Innovation

• Proposing two test statistics
• Using asymptotic approximation
• Applying bootstrap method