Our analyses showed that if the true model is recessive or dominant, but the locus is nonetheless detected by using the trend test, then a standard test will often also successfully detect deviation from a multiplicative model. Informally, for the relatively small effect sizes typical at GWAS loci, the effect is unlikely to be detected unless the causal variant is relatively common and well tagged by the SNPs on the chip. The high correlation between the causal and hit SNPs then means that there is reasonable power to detect deviation from the multiplicative model, even under model distortion. While encouraging, we note, first, that the dominant and recessive models are extreme, and power to detect nonmultiplicative models, which are “closer” to the multiplicative model, will be lower. Second, as our simulations show, there will be settings where the model distortion is such that under the recessive and dominant models the locus is not detected at all using the trend test.
