Entropy based genetic association tests and gene-gene interaction tests

In the past few years, several entropy-based tests have been proposed for testing either single SNP association or gene-gene interaction. These tests are mainly based on Shannon entropy and have higher statistical power when compared to standard χ² tests. In this paper, we extend some of these tests using a more generalized entropy definition, Renyi entropy, where Shannon entropy is a special case of order 1. The order λ (>0) of Renyi entropy weights the events (genotype/haplotype) according to their probabilities (frequencies). Higher λ places more emphasis on higher probability events while smaller λ (close to 0) tends to assign weights more equally. Thus, by properly choosing the λ, one can potentially increase the power of the tests or the p-value level of significance. We conducted simulation as well as real data analyses to assess the impact of the order λ and the performance of these generalized tests. The results showed that for dominant model the order 2 test was more powerful and for multiplicative model the order 1 or 2 had similar power. The analyses indicate that the choice of λ depends on the underlying genetic model and Shannon entropy is not necessarily the most powerful entropy measure for constructing genetic association or interaction tests.