Improved Statistics for Genome-Wide Interaction Analysis

Recently, Wu and colleagues [1] proposed two novel statistics for genome-wide interaction analysis using case/control or case-only data. In computer simulations, their proposed case/control statistic outperformed competing approaches, including the fast-epistasis option in PLINK and logistic regression analysis under the correct model; however, reasons for its superior performance were not fully explored. Here we investigate the theoretical properties and performance of Wu et al.'s proposed statistics and explain why, in some circumstances, they outperform competing approaches. Unfortunately, we find minor errors in the formulae for their statistics, resulting in tests that have higher than nominal type 1 error. We also find minor errors in PLINK's fast-epistasis and case-only statistics, although theory and simulations suggest that these errors have only negligible effect on type 1 error. We propose adjusted versions of all four statistics that, both theoretically and in computer simulations, maintain correct type 1 error rates under the null hypothesis. We also investigate statistics based on correlation coefficients that maintain similar control of type 1 error. Although designed to test specifically for interaction, we show that some of these previously-proposed statistics can, in fact, be sensitive to main effects at one or both loci, particularly in the presence of linkage disequilibrium. We propose two new “joint effects” statistics that, provided the disease is rare, are sensitive only to genuine interaction effects. In computer simulations we find, in most situations considered, that highest power is achieved by analysis under the correct genetic model. Such an analysis is unachievable in practice, as we do not know this model. However, generally high power over a wide range of scenarios is exhibited by our joint effects and adjusted Wu statistics. We recommend use of these alternative or adjusted statistics and urge caution when using Wu et al.'s originally-proposed statistics, on account of the inflated error rate that can result. Author Summary: Gene–gene interactions are a topic of great interest to geneticists carrying out studies of how genetic factors influence the development of common, complex diseases. Genes that interact may not only make important biological contributions to underlying disease processes, but also be more difficult to detect when using standard statistical methods in which we examine the effects of genetic factors one at a time. Recently a method was proposed by Wu and colleagues [1] for detecting pairwise interactions when carrying out genome-wide association studies (in which a large number of genetic variants across the genome are examined). Wu and colleagues carried out theoretical work and computer simulations that suggested their method outperformed other previously proposed approaches for detecting interactions. Here we show that, in fact, the method proposed by Wu and colleagues can result in an over-preponderence of false postive findings. We propose an adjusted version of their method that reduces the false positive rate while maintaining high power. We also propose a new method for detecting pairs of genetic effects that shows similarly high power but has some conceptual advantages over both Wu's method and also other previously proposed approaches.