An entropy-based statistic for genomewide association studies

Abstract

Efficient genotyping methods and the availability of a large collection of single-nucleotide polymorphisms provide valuable tools for genetic studies of human disease. The standard chi2 statistic for case-control studies, which uses a linear function of allele frequencies, has limited power when the number of marker loci is large. We introduce a novel test statistic for genetic association studies that uses Shannon entropy and a nonlinear function of allele frequencies to amplify the differences in allele and haplotype frequencies to maintain statistical power with large numbers of marker loci. We investigate the relationship between the entropy-based test statistic and the standard chi2 statistic and show that, in most cases, the power of the entropy-based statistic is greater than that of the standard chi2 statistic. The distribution of the entropy-based statistic and the type I error rates are validated using simulation studies. Finally, we apply the new entropy-based test statistic to two real data sets, one for the COMT gene and schizophrenia and one for the MMP-2 gene and esophageal carcinoma, to evaluate the performance of the new method for genetic association studies. The results show that the entropy-based statistic obtained smaller P values than did the standard chi2 statistic.

Figure 1

Distribution of the test statistic T_PE with the use of two-SNP haplotypes (A) and six-SNP haplotypes (B). χ²₍₃₎ and χ²₍₇₎ indicate χ² distribution with 3 df and 7 df, respectively.

Figure 2

A, Power of the entropy-based test statistic and the standard χ² test statistic with a significance level of α=0.001, as a function of the genetic distance between the marker and disease loci, for a recessive disease (A) and a dominant disease (B) under the assumption that N=100, t=100 generations, the frequencies of the minor alleles at both of the marker loci are equal to 0.1, and P_D=0.1. C, Power of the entropy-based test statistic and the standard χ² test statistic with a significance level of α=0.001 for a disease with genotype relative risk r=4, as a function of the genetic distance between the marker and disease loci, under the assumption that N=200, t=100 generations, the frequencies of the minor alleles at the first and second marker loci are equal to 0.4 and 0.1, respectively, and P_D=0.2.