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Open Access Methodology article

Testing allele homogeneity: the problem of nested hypotheses

Rafael Izbicki1*, Victor Fossaluza2, Ana Gabriela Hounie3, Eduardo Yoshio Nakano4 and Carlos Alberto de Bragança Pereira5*

Author Affiliations

1 Department of Statistics, Carnegie Mellon University, Pittsburgh, USA

2 Department of Statistics, Universidade Federal de São Carlos, São Carlos, Brazil

3 Department of Psychiatry, University of São Paulo, São Paulo, Brazil

4 Department of Statistics, University of Braslia, Brasília, Brazil

5 Department of Statistics, University of São Paulo, São Paulo, Brazil

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BMC Genetics 2012, 13:103  doi:10.1186/1471-2156-13-103

Published: 23 November 2012



The evaluation of associations between genotypes and diseases in a case-control framework plays an important role in genetic epidemiology. This paper focuses on the evaluation of the homogeneity of both genotypic and allelic frequencies. The traditional test that is used to check allelic homogeneity is known to be valid only under Hardy-Weinberg equilibrium, a property that may not hold in practice.


We first describe the flaws of the traditional (chi-squared) tests for both allelic and genotypic homogeneity. Besides the known problem of the allelic procedure, we show that whenever these tests are used, an incoherence may arise: sometimes the genotypic homogeneity hypothesis is not rejected, but the allelic hypothesis is. As we argue, this is logically impossible. Some methods that were recently proposed implicitly rely on the idea that this does not happen. In an attempt to correct this incoherence, we describe an alternative frequentist approach that is appropriate even when Hardy-Weinberg equilibrium does not hold. It is then shown that the problem remains and is intrinsic of frequentist procedures. Finally, we introduce the Full Bayesian Significance Test to test both hypotheses and prove that the incoherence cannot happen with these new tests. To illustrate this, all five tests are applied to real and simulated datasets. Using the celebrated power analysis, we show that the Bayesian method is comparable to the frequentist one and has the advantage of being coherent.


Contrary to more traditional approaches, the Full Bayesian Significance Test for association studies provides a simple, coherent and powerful tool for detecting associations.

Allelic homogeneity test; Bayesian methods; Chi-squared test; Hardy-Weinberg equilibrium; FBST; Monotonicity