Comparison of statistical power between 2×2 allele frequency and allele positivity tables in case-control studies of complex disease genes

In case-control studies of complex disease genes, allele frequencies or allele positivities at candidate loci or markers are compared between cases and controls. Although 2 x 2 contingency tables based on allele frequency and allele positivity are generally used to perform simple statistical tests (e.g. a comparison of two proportions and a chi2 test), little is known about the difference in power between the two tables. In this study, we investigated the number of subjects required to obtain a power of 1-beta with a significance level of alpha for the allele frequency and allele positivity tables. A large difference in the required number of subjects was found between the two tables. Allele positivity tables were suitable for the detection of susceptibility alleles showing a dominant mode of inheritance (MOI). On the other hand, allele frequency tables were suitable for the identification of susceptibility alleles showing a recessive MOI or a multiplicative MOI. In the case of an additive MOI, a suitable table was determined by combining the frequency of the susceptibility allele and the penetrance. These results imply that there are cases in which true association is detected based on one contingency table and is not detected based on another. A simulation analysis revealed that the type I error rate was not much inflated under the null hypothesis of no association, even when a statistical test was performed twice using both allele frequency and allele positivity tables. In contrast, under the alternative hypothesis, the loss of power was marked when a test was performed once using an unsuitable table. In conclusion, statistical tests should be performed using both tables, without adjustment of multiplicity, in case-control studies of complex disease genes when the study objective is exploratory.