Statistics and Its Interface

Volume 9 (2016)

Number 3

Search for risk haplotype segments with GWAS data by use of finite mixture models

Pages: 267 – 280



Fadhaa Ali (School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent, United Kingdom)

Jian Zhang (School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent, United Kingdom)


The region-based association analysis has been proposed to capture the collective behavior of sets of variants by testing the association of each set instead of individual variants with the disease. Such an analysis typically involves a list of unphased multiple-locus genotypes with potentially sparse frequencies in cases and controls. To tackle the problem of the sparse distribution, a two-stage approach was proposed in literature: In the first stage, haplotypes are computationally inferred from genotypes, followed by a haplotype coclassification. In the second stage, the association analysis is performed on the inferred haplotype groups. If a haplotype is unevenly distributed between the case and control samples, this haplotype is labeled as a risk haplotype. Unfortunately, the in-silico reconstruction of haplotypes might produce a proportion of false haplotypes which hamper the detection of rare but true haplotypes. Here, to address the issue, we propose an alternative approach: In Stage 1, we cluster genotypes instead of inferred haplotypes and estimate the risk genotypes based on a finite mixture model. In Stage 2, we infer risk haplotypes from risk genotypes inferred from the previous stage. To estimate the finite mixture model, we propose an EM algorithm with a novel data partition-based initialization. The performance of the proposed procedure is assessed by simulation studies and a real data analysis. Compared to the existing multiple Z-test procedure, we find that the power of genome-wide association studies can be increased by using the proposed procedure.


region-based association analysis, genotype mixture models, odds ratios, genome wide association studies, expectation-maximization algorithm

2010 Mathematics Subject Classification


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Published 27 January 2016