A fast and powerfulW-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.

Further investigations of the W-test for pairwise epistasis testing

“…Interestingly, all formulations result in a χ 2 test statistic on k − 1 = 8 df (provided all cells are represented in the data), reflecting the fact that there are k − 1 additional independent parameters to be estimated under the alternative hypothesis (where the row and column variables are allowed to be associated) compared to the null hypothesis (where there is no association between the row and column variables). This contrasts with the W -test proposed by Wang et al 1 , in which k = 9 non-independent (log odds ratio) quantities are combined, resulting in the necessity for a scaled χ 2 test statistic (with parameters h and f estimated using bootstrapping) in order to account for the non-independence between the k = 9 normalized log odds ratios.…”

“…In a paper recently published in the journal Nucleic Acids Research , Wang and colleagues 1 proposed a novel W -test for pairwise epistasis testing. The thrust of the proposed method was to compare the distributions of the k observed genotype combinations at L = 2 diallelic genetic loci such as single nucleotide polymorphisms (SNPs), between cases and controls (see Table 1 ).…”

“…These cell-specific quantities are then combined to construct a scaled χ 2 test statistic whose value and (possibly non-integer) degrees of freedom (df) can be calculated as a function of two parameters ( h and f ) that are estimated using a bootstrapping approach. Although in principle applicable to other orders of SNP combinations, including single SNPs (where k = 3) and combinations of more than two SNPs (where k = 3 L ), the main focus of the published paper 1 and accompanying software was on the pairwise test.…”

A W‐test collapsing method for rare‐variant association testing in exome sequencing data

“…The W-test is a model-free statistic that measures the distributional differences of categorical variables between the affected and unaffected groups through a combined log of odds ratio (Wang et al, 2016). It can be used to test the main effect of a single-nucleotide polymorphism (SNP) or epistasis of an SNP-pair.…”

“…Empirical studies give h ≈ (k−1)/k and f ≈ k−1. Because the parameters are estimated from the data, they could reduce bias in testing probability distribution arose from complex data structures (Wang et al, 2016).…”