Bias in genome-wide association test statistics due to omitted interactions

Over the past two decades, genome-wide association studies (GWAS) enabled the discovery of thousands of variants associated with many complex human traits. However, conventional GWAS are still widely performed with linear models with the assumption that the genetic effects are predominantly additive. In this work, we investigate the test statistic behavior when linear models are used to obtain significant genotype-phenotype associations without accounting for epistasis. We first algebraically derive mean and variance shift in the null statistic due to the omitted interaction term, and define the boundary between conservative (i.e., deflated statistic tail) and anti-conservative (i.e., inflated statistic tail) regimes for the common GWAS significance threshold. We then perform phenotype simulation analyses using the Estonian Biobank genotypes and validate the mathematical model. We demonstrate that the anti-conservative regime is plausible under realistic parameter settings and models omitting interaction terms can produce spurious significance. Our findings suggest caution when interpreting statistically significant signals reported in the literature based on linear models, especially for large-scale GWAS.