A fast and powerful W-test for pairwise epistasis testing

Abstract

Epistasis plays an essential role in the development of complex diseases. Interaction methods face common challenge of seeking a balance between persistent power, model complexity, computation efficiency, and validity of identified bio-markers. We introduce a novel W-test to identify pairwise epistasis effect, which measures the distributional difference between cases and controls through a combined log odds ratio. The test is model-free, fast, and inherits a Chi-squared distribution with data adaptive degrees of freedom. No permutation is needed to obtain the P-values. Simulation studies demonstrated that the W-test is more powerful in low frequency variants environment than alternative methods, which are the Chi-squared test, logistic regression and multifactor-dimensionality reduction (MDR). In two independent real bipolar disorder genome-wide associations (GWAS) datasets, the W-test identified significant interactions pairs that can be replicated, including SLIT3-CENPN, SLIT3-TMEM132D, CNTNAP2-NDST4 and CNTCAP2-RTN4R The genes in the pairs play central roles in neurotransmission and synapse formation. A majority of the identified loci are undiscoverable by main effect and are low frequency variants. The proposed method offers a powerful alternative tool for mapping the genetic puzzle underlying complex disorders.

Diagram 1.

Decomposition of the W-test. The W-test measures the distributional differences between cases and controls using a combined log odds ratio. The dependency among the cells is handled by the data-dependent scalars h and f, estimated from the null hypothesis. The overall test statistic follows a Chi-squared distribution with f degrees of freedom.

Figure 1.

Power of alternative methods in low frequency variant environment. In the low frequency variant environment (1% < MAF < 5%),the W-test outperforms alternative methods for both linear and non-linear models.

Figure 2.

Power comparison of alternative methods at different sample sizes. As the sample size reduces, the W-test shows a robust power compared to alternative methods. The power is calculated under the genetic environment of 1% < MAF < 5% and LD 20% < r²< 80%, using a non-linear model.

Figure 3.

Q–Q Plot of W-test on real genome-wide data. The W-test is computed on real genome-wide data with permuted phenotype for SNP–SNP interactions. No inflation of spurious association is observed.

Figure 4.

Gene-gene Interaction Networks. The solid lines represent significant epistasis effect. Blue color indicates pairs found in the GAIN dataset and red color indicates that they are identified in the WTCCC dataset. Purple circles represent genes replicated by the two independent data; all of which play important roles in brain and neuronal function.