Bayesian Methods for Examining Hardy-Weinberg Equilibrium

• Published in: Biometrics Vol. 66; no. 1; pp. 257 - 265
• Main Author: Wakefield, Jon
• Format: Journal Article
• Language: English
• Published: Malden, USA Blackwell Publishing Inc 01.03.2010; Wiley-Blackwell; Blackwell Publishing Ltd
• Subjects: Algorithms; alleles; Bayes factors; Bayes Theorem; Bayesian analysis; BIOMETRIC PRACTICE; Biometrics; biometry; Biometry - methods; Calibration; Computer Simulation; data collection; Data Interpretation, Statistical; Diabetes; Disease models; Epidemiologic Methods; Exact test; Genetic Markers - genetics; Genetic Predisposition to Disease - epidemiology; Genetic Predisposition to Disease - genetics; Genome-wide association studies; Genotypes; Hardy Weinberg law; Human genetics; Humans; Importance sampling; loci; Markov chain; Medical genetics; Models, Genetic; Monte Carlo simulation; P values; Parametric models; Prior choice; Sample size; Significance level; single nucleotide polymorphism; Statistical analysis
• ISSN: 0006-341X; 1541-0420; 1541-0420
• DOI: 10.1111/j.1541-0420.2009.01267.x

Testing for Hardy-Weinberg equilibrium is ubiquitous and has traditionally been carried out via frequentist approaches. However, the discreteness of the sample space means that uniformity of p-values under the null cannot be assumed, with enumeration of all possible counts, conditional on the minor allele count, offering a computationally expensive way of p-value calibration. In addition, the interpretation of the subsequent p-values, and choice of significance threshold depends critically on sample size, because equilibrium will always be rejected at conventional levels with large sample sizes. We argue for a Bayesian approach using both Bayes factors, and the examination of posterior distributions. We describe simple conjugate approaches, and methods based on importance sampling Monte Carlo. The former are convenient because they yield closed-form expressions for Bayes factors, which allow their application to a large number of single nucleotide polymorphisms (SNPs), in particular in genome-wide contexts. We also describe straightforward direct sampling methods for examining posterior distributions of parameters of interest. For large numbers of alleles at a locus we resort to Markov chain Monte Carlo. We discuss a number of possibilities for prior specification, and apply the suggested methods to a number of real datasets.