Search for Risk Haplotype Segments with GWAS Data by Use of Finite Mixture Models

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 co-classification. 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

Screening tests for Disease Risk Haplotype Segments in Genome by Use of Permutation

The haplotype 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. It starts with inferring haplotypes from genotypes followed by a haplotype co-classification and marginal screening for disease-associated haplotypes. Unfortunately, phasing uncertainty may have a strong effects on the haplotype co-classification and therefore on the accuracy of predicting risk haplotypes. Here, to address the issue, we propose an alternative approach: In Stage 1, we select potential risk genotypes instead of co-classification of the inferred haplotypes. In Stage 2, we infer risk haplotypes from the genotypes inferred from the previous stage. 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

Mixture Model-Based Association Analysis with Case-Control Data in Genome Wide Association Studies

Multilocus haplotype analysis of candidate variants with genome wide association studies (GWAS) data may provide evidence of association with disease, even when the individual loci themselves do not. Unfortunately, when a large number of candidate variants are investigated, identifying risk haplotypes can be very difficult. To meet the challenge, a number of approaches have been put forward in recent years. However, most of them are not directly linked to the disease-penetrances of haplotypes and thus may not be efficient. To fill this gap, we propose a mixture model-based approach for detecting risk haplotypes. Under the mixture model, haplotypes are clustered directly according to their estimated disease penetrances. A theoretical justification of the above model is provided. Furthermore, we introduce a hypothesis test for haplotype inheritance patterns which underpin this model. The performance of the proposed approach is evaluated by simulations and real data analysis. The simulation results show that the proposed approach outperforms an existing multiple testing method in terms of average specificity and sensitivity. We apply the proposed approach to analyzing two datasets on coronary artery disease and hypertension in the Wellcome Trust Case Control Consortium, identifying many more disease associated haplotype blocks than does the existing method

Statistical Methods For Detecting Genetic Risk Factors of a Disease with Applications to Genome-Wide Association Studies

This thesis aims to develop various statistical methods for analysing the data derived from genome wide association studies (GWAS). The GWAS often involves genotyping individual human genetic variation, using high-throughput genome-wide single nucleotide polymorphism (SNP) arrays, in thousands of individuals and testing for association between those variants and a given disease under the assumption of common disease/common variant. Although GWAS have identified many potential genetic factors in the genome that affect the risks to complex diseases, there is still much of the genetic heritability that remains unexplained. The power of detecting new genetic risk variants can be improved by considering multiple genetic variants simultaneously with novel statistical methods. Improving the analysis of the GWAS data has received much attention from statisticians and other scientific researchers over the past decade. There are several challenges arising in analysing the GWAS data. First, determining the risk SNPs might be difficult due to non-random correlation between SNPs that can inflate type I and II errors in statistical inference. When a group of SNPs are considered together in the context of haplotypes/genotypes, the distribution of the haplotypes/genotypes is sparse, which makes it difficult to detect risk haplotypes/genotypes in terms of disease penetrance. In this work, we proposed four new methods to identify risk haplotypes/genotypes based on their frequency differences between cases and controls. To evaluate the performances of our methods, we simulated datasets under wide range of scenarios according to both retrospective and prospective designs. In the first method, we first reconstruct haplotypes by using unphased genotypes, followed by clustering and thresholding the inferred haplotypes into risk and non-risk groups with a two-component binomial-mixture model. In the method, the parameters were estimated by using the modified Expectation-Maximization algorithm, where the maximisation step was replaced the posterior sampling of the component parameters. We also elucidated the relationships between risk and non-risk haplotypes under different modes of inheritance and genotypic relative risk. In the second method, we fitted a three-component mixture model to genotype data directly, followed by an odds-ratio thresholding. In the third method, we combined the existing haplotype reconstruction software PHASE and permutation method to infer risk haplotypes. In the fourth method, we proposed a new way to score the genotypes by clustering and combined it with a logistic regression approach to infer risk haplotypes. The simulation studies showed that the first three methods outperformed the multiple testing method of (Zhu, 2010) in terms of average specificity and sensitivity (AVSS) in all scenarios considered. The logistic regression methods also outperformed the standard logistic regression method. We applied our methods to two GWAS datasets on coronary artery disease (CAD) and hypertension (HT), detecting several new risk haplotypes and recovering a number of the existing disease-associated genetic variants in the literature

Bayesian Methods for Estimation the Parameters of Finite Mixture of Inverse Rayleigh Distribution

Methods of estimating statistical distribution have attracted many researchers when it comes to fitting a specific distribution to data. However, when the data belong to more than one component, a popular distribution cannot be fitted to such data. To tackle this issue, mixture models are fitted by choosing the correct number of components that represent the data. This can be obvious in lifetime processes that are involved in a wide range of engineering applications as well as biological systems. In this paper, we introduce an application of estimating a finite mixture of Inverse Rayleigh distribution by the use of the Bayesian framework when considering the model as Markov chain Monte Carlo (MCMC). We employed the Gibbs sampler and Metropolis – Hastings algorithms. The proposed techniques are applied to simulated data following several scenarios. The accuracy of estimation has been examined by the average mean square error (AMSE) and the average classification success rate (ACSR). The results showed that the method was well performed in all simulation scenarios with respect to different sample sizes