We assumed a liability threshold model, where an underlying continuous risk trait captures all genetic and environmental contributions to risk and resistance. Under this model and for this work, this is operationalized as: Zi=β1X1+β2X2+β3X3+β4X4+ε where Zi is the liability trait, β1 is the correlation between polygenic risk X1 and outcome (assuming standardized coefficients), β2 is the correlation between family environment X2 and outcome, β3 is the correlation between a specific SNP genotype X3 and outcome, β4 is the correlation between a specific protective environment X4 and outcome, and ε is the residual variance. Outcomes were dichotomized to a disease outcome (Yi) by: Prob(Yi)=eZi1+eZi
