A Note on Exact Conditional and Unconditional Tests for Hardy-Weinberg Equilibrium

Abstract

The exact conditional approach is frequently used for testing Hardy-Weinberg equilibrium in population genetics. This approach respects the test size as compared to the traditionally used asymptotic approaches. It is a full-enumeration method and very computational. Many efficient algorithms have been successfully developed to implement this exact approach. An alternative to the conditional approach is the unconditional approach, which relaxes the restriction of the fixed number of allelic counts as in the conditional approach. The first unconditional test considered in this study is the one based on maximization, which has been shown to be more powerful than the conditional test to loci with two alleles for small sample sizes. By using the p value of the conditional approach as a test statistic in the following maximization step, the second unconditional test is uniformly more powerful than the conditional approach. We compared these exact tests based on three commonly used test statistics with regards to type I error rate and power. It is recommended to use the second unconditional approach in practice due to the power gain in the case with two alleles.

Sample size determination for a matched‐pairs study with incomplete data using exact approach

“…As compared to the exact approach for sample size calculation, (Lloyd, 2007, 2014, 2008a; Shan, 2013; Shan, Ma, Hutson, & Wilding, 2012; Shan & Ma, 2016; Shan, 2015; Shan, Wilding, Hutson, & Gerstenberger, 2016; Shan, Moonie, & Shen, 2016; Shan, 2015), the existing GEE approach does not guarantee type I and II error rates although it is computationally easy with a closed form. With the wide availability of powerful computers or supercomputers, exact sample size computation is practical and feasible.…”

Lack of association between CARD10/CARMA3 tag SNPs and psoriasis vulgaris in the southern Chinese population

“…For allele and genotype comparisons, the statistical significance of differences between groups was calculated by either the chi-square test or the Fisher exact test. Deviation from HardyWeinberg equilibrium was assessed according to the method described by Shan (2013). All tests were two-sided, and the threshold for statistical significance was set as P < 0.05.…”

Association of matrix metalloproteinase‐10 polymorphisms with susceptibility to pelvic organ prolapse

“…Continuous variables with normal distribution are expressed as the mean ± standard deviation (SD), skewed distributed continuous variables are expressed as the median value (interquartile range), and categorical data are presented with frequency counts. Gene counting was applied to estimate the genotype/allele frequencies of MMP‐10 rs17435959 and rs17293607, and departure from Hardy–Weinberg equilibrium was detected among the healthy controls and the POP patients separately . Comparison of the genotype distribution and allele frequencies between the POP patients and the controls was performed by χ 2 ‐test.…”