Mixture model-based association analysis with case-control data in genome wide association studies

Abstract

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.

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

“…Testing the number of components to determine the exact structure of the mixture model was a vital tool to deal with the above problem [10,11]. In much the same direction, the most used way of handling the above issues is adding a latent variable that results in a complete data log likelihood rather than using the incomplete one [12,13], and then estimating the model parameters by the expectation maximization(EM) algorithm [14][15][16].…”

Estimation of Parameters of Finite Mixture of Rayleigh Distribution by the Expectation‐Maximization Algorithm

“…Terefore, determining the exact number of components by performing a relevant test is considered an important starting point in applying the mixture model [12,13]. In the same manner, the most common way of handling the above issues is by using a latent variable that leads to a complete-data log likelihood rather than using the incomplete one [14], and then, the expectation-maximization (EM) algorithm is employed to estimate model parameters [15][16][17].…”