A Bayesian hierarchical model for detecting haplotype-haplotype and haplotype-environment interactions in genetic association studies

Abstract

Objective: Genetic association studies based on haplotypes are powerful in the discovery and characterization of the genetic basis of complex human diseases. However, statistical methods for detecting haplotype-haplotype and haplotype-environment interactions have not yet been fully developed owing to the difficulties encountered: large numbers of potential haplotypes and unknown haplotype pairs. Furthermore, methods for detecting the association between rare haplotypes and disease have not kept pace with their counterpart of common haplotypes.

Methods/results: We herein propose an efficient and robust method to tackle these problems based on a Bayesian hierarchical generalized linear model. Our model simultaneously fits environmental effects, main effects of numerous common and rare haplotypes, and haplotype-haplotype and haplotype-environment interactions. The key to the approach is the use of a continuous prior distribution on coefficients that favors sparseness in the fitted model and facilitates computation. We develop a fast expectation-maximization algorithm to fit models by estimating posterior modes of coefficients. We incorporate our algorithm into the iteratively weighted least squares for classical generalized linear models as implemented in the R package glm. We evaluate the proposed method and compare its performance to existing methods on extensive simulated data.

Conclusion: The results show that the proposed method performs well under all situations and is more powerful than existing approaches.

Fig. 1

Main effect model: estimated 68 and 95% coverages of the ‘true’ values (indicated by bold and thin horizontal lines in the left column, respectively) and empirical powers or type I error rates [empirical powers or type I error rates for α = 0.001 (×), α = 0.01 (o), and α = 0.05 (+)] for each of 4 haplotypes based on the four methods with sample sizes of 250 (top), 500 (middle), and 1,000 (bottom). B = BayesGLM; C = GLM; R = rGLM; S = ScoreGLM.

Fig. 2

Main and interacting effect model: estimated 68 and 95% coverages of the ‘true’ values (indicated by bold and thin horizontal lines in the left column, respectively) and empirical powers or type I error rates [empirical powers or type I error rates for α = 0.001 (×), α = 0.01 (o), and α = 0.05 (+)] for each of 8 predictors based on the four methods with sample sizes of 250 (top), 500 (middle), and 1,000 (bottom). B = BayesGLM; C = GLM; R = rGLM; S = ScoreGLM.

Fig. 3

Full model: estimated 68 and 95% coverages of the ‘true’ values (indicated by bold and thin horizontal lines in the 1st, 3rd, and 5th columns, respectively) and empirical powers or type I error rates [empirical powers or type I error rates for α = 0.001 (×), α = 0.01 (o), and α = 0.05 (+)] for each of 81 predictors based on BayesGLM with sample sizes of 250 (first 2 columns), 500 (3rd and 4th columns), and 1,000 (last 2 columns). The black labels on the vertical axis stand for the disease-associated predictors, while the gray labels stand for the non-disease-associated predictors.