The confidence interval of allelic odds ratios under the Hardy-Weinberg disequilibrium

In single nucleotide polymorphism (SNP) data analysis, the allelic odds ratio and its confidence interval (CI) are usually used to evaluate the association between disease and alleles at each SNP. The usual formula for calculating the CI of the allelic odds ratio based on the Hardy-Weinberg equilibrium (HWE) may, however, lead to errors beyond the control assured by the nominal confidence level if HWE is not true. We therefore present a generalized formula for CI that does not assume HWE. CIs calculated by this generalized formula are likely to be wider than those by the usual method if the Hardy-Weinberg disequilibrium (HWD) is toward a relative deficiency of the heterozygotes (fixation index greater than 0), whereas they are likely to be narrower if HWD is toward a relative excess of the heterozygotes (fixation index less than 0). A simulation experiment to examine the influence of the generalization was performed for the case where 2% of SNPs had a fixation index greater than 0. The result revealed that the generalized method slightly decreased the mean number of falsely detected SNPs.