Multiplicative diallelic penetrance
= Multiplicative diallelic penetrance
{title2=$q_G=p\theta^G,\quad G\sim\operatorname{Bin}(2,\phi)$}
With <Hardy-Weinberg equilibrium>, let $G$ count copies of the risk <allele>. The <penetrance> $p\theta^G$ must lie in $[0,1]$ for every possible <genotype>. Writing $\alpha=1-\phi+\phi\theta$ and $\beta=1-\phi+\phi\theta^2$ gives $\mathbb E(q_G)=p\alpha^2$ and $\mathbb E(q_G^2)=p^2\beta^2$.