A Generalized Kruskal-Wallis Test Incorporating Group Uncertainty with Application to Genetic Association Studies

TL;DR

This paper introduces a generalized Kruskal-Wallis test that accounts for group uncertainty, enhancing analysis in genetic association studies with uncertain genotype data, validated through simulations and real GWAS application.

Contribution

It develops a novel extension of the Kruskal-Wallis test incorporating probability weights for group uncertainty, applicable to genetic studies.

Findings

Test maintains validity under finite samples

Robust to genotype uncertainty in simulations

Effective in genome-wide association study

Abstract

Motivated by genetic association studies of SNPs with genotype uncertainty, we propose a generalization of the Kruskal-Wallis test that incorporates group uncertainty when comparing k samples. The extended test statistic is based on probability-weighted rank-sums and follows an asymptotic chi-square distribution with k-1 degrees of freedom under the null hypothesis. Simulation studies confirm the validity and robustness of the proposed test in finite samples. Application to a genome-wide association study of type 1 diabetic complications further demonstrates the utilities of this generalized Kruskal-Wallis test for studies with group uncertainty.