We see that the dominance effect at the marker SNP decreases quadratically with r as the LD becomes weaker. Analogous to Equation (4), this is a key result and in this formulation it appears to be novel. Sham et al. [2000] derive a similar result relating variance components in models of quantitative traits; our derivation here relates parameters in models of case-control data. The formula gives an intuitive and convenient relationship between the parameters of interest, and the relationship later derived for the effect of LD on power follows directly from it. Crucially, this result contrasts with that for the additive parameter, with the dependence on LD being through r2 rather than r.
