Table 1. Summary of calculations for regression estimates.

Study design	Regression model	Regression coefficient	R 2
Between family	Y~PGSmix	1	$\frac{{\sigma }_{dir}^2+{\sigma }_{ind}^2+2{\rho }_g}{{\sigma }_{dir}^2+2{\sigma }_{ind}^2+2{\rho }_g+{\sigma }_e^2}$
Sibling difference	ΔY~ΔPGSmix	$\frac{{\sigma }_{dir}^2+{\rho }_g}{{\sigma }_{dir}^2+{\sigma }_{ind}^2+2{\rho }_g}$	$\frac{{\left({\sigma }_{dir}^2+{\rho }_g\right)}^2}{\left({\sigma }_{dir}^2+{\sigma }_{ind}^2+2{\rho }_g\right)\left[{\sigma }_{dir}^2+2{\sigma }_e^2\left(1-r_e\right)\right]}$
Sibling difference	ΔY~ΔPGSdir	1	$\frac{{\sigma }_{dir}^2}{{\sigma }_{dir}^2+2{\sigma }_e^2\left(1-r_e\right)}$

PGS regression coefficients and R² in different study designs. Different study designs can be used for PGS regression analysis. In a “between family” analysis, phenotype Y is regressed on PGS. In a sibling difference design, the phenotype difference between siblings is regressed on their PGS difference. PGS can be calculated using either a mixture of direct and indirect SNP effects (PGS_mix) or using only the direct effect (PGS_dir).