Utilizing mutual information for detecting rare and common variants associated with a categorical trait

Background. Genome-wide association studies have succeeded in detecting novel common variants which associate with complex diseases. As a result of the fast changes in next generation sequencing technology, a large number of sequencing data are generated, which offers great opportunities to identify rare variants that could explain a larger proportion of missing heritability. Many effective and powerful methods are proposed, although they are usually limited to continuous, dichotomous or ordinal traits. Notice that traits having nominal categorical features are commonly observed in complex diseases, especially in mental disorders, which motivates the incorporation of the characteristics of the categorical trait into association studies with rare and common variants. Methods. We construct two simple and intuitive nonparametric tests, MIT and aMIT, based on mutual information for detecting association between genetic variants in a gene or region and a categorical trait. MIT and aMIT can gauge the difference among the distributions of rare and common variants across a region given every categorical trait value. If there is little association between variants and a categorical trait, MIT or aMIT approximately equals zero. The larger the difference in distributions, the greater values MIT and aMIT have. Therefore, MIT and aMIT have the potential for detecting functional variants. Results.We checked the validity of proposed statistics and compared them to the existing ones through extensive simulation studies with varied combinations of the numbers of variants of rare causal, rare non-causal, common causal, and common non-causal, deleterious and protective, various minor allele frequencies and different levels of linkage disequilibrium. The results show our methods have higher statistical power than conventional ones, including the likelihood based score test, in most cases: (1) there are multiple genetic variants in a gene or region; (2) both protective and deleterious variants are present; (3) there exist rare and common variants; and (4) more than half of the variants are neutral. The proposed tests are applied to the data from Collaborative Studies on Genetics of Alcoholism, and a competent performance is exhibited therein. Discussion. As a complementary to the existing methods mainly focusing on quantitative traits, this study provides the nonparametric tests MIT and aMIT for detecting variants associated with categorical trait. Furthermore, we plan to investigate the association between rare variants and multiple categorical traits.