In this paper, we study a particular aspect of this relationship both analytically and empirically. We consider case-control studies that genotype SNPs and disease models with either a single SNP or a pair of interacting SNPs. We ask two related questions. First, how do the disease model parameters (“effects”) change as the LD between the causal and tag SNPs diminishes? Second, how does the power to detect departure from the multiplicative model change? We show that as the LD between causal and marker loci decreases, nonmultiplicative and interaction effects decay faster than multiplicative effects, quadratically rather than linearly. This makes the former harder to detect; stated in terms of power, the decay is quartic rather than quadratic. Furthermore, compared to the true disease model, the apparent disease effect as observed at marker SNPs will be distorted to look more like a multiplicative one.
