Entropy based genetic association tests and gene-gene interaction tests

Abstract

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, Rényi entropy, where Shannon entropy is a special case of order 1. The order λ (>0) of Rényi 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.

Figure 1:

Power and sample size for the likelihood ratio (LR) test and entropy-based test for λ values of 0.9, 1.0, and 2.0 under different marginal effects.

Figure 2:

Type I error rate of likelihood ratio (LR) test and entropy-based test with λ values of 0.9, 1.0 and 2.0

Figure 3:

Power of the entropy-based test with sample size 100, 300 and 500 for different λ values under strong dominant and multiplicative marginal effects

Figure 4:

Six models with different marginal and interaction effects under case-only design. Power of χ²-test and entropy-based tests with λ = 0.9, 1 and 2 are plotted against the sample size

Figure 5:

The changing pattern of entropy-based association test p-values of SNPs rs2038024, rs9332627 and rs2176473

Figure 6:

Distribution of p-values of entropy-based association tests for SNP pairs. Upper panel: SNP pairs of strong, moderate or no marginal effect. Lower panel: SNP pairs of moderate or no marginal effect.