Polygenic risk score

Summary of polygenic risk score estimation method

Method	$\mathit{\beta }$ assumption	$\mathit{\beta }$ estimation	PRS estimation
P + T
SBLUP	$\beta \sim \mathcal{N}(0,\frac{h_g^2}{m})$
LDpred, LDpred2	${\beta }_j\sim \{\begin{array}{lr}\mathcal{N}(0,\frac{h_g^2}{Mp}),& p\\ 0,& 1-p\end{array}$	$\mathbb{E}(\beta |\tilde{\beta },D)\approx (\frac{1}{1-h_l^2}D+\frac{M}{N{h}^2}I{)}^{-1}\tilde{\beta }$
LDpred-funct	${\beta }_j\sim \mathcal{N}(0,c\ast {\sigma }_j^2)$	$\mathbb{E}(\beta |\tilde{\beta },D,{\sigma }_1^2,\dots ,{\sigma }_M^2)=[N\ast D+\frac{1}{c}(\left[\begin{array}{ccc}\frac{1}{{\sigma }_1^2}& \dots & 0\\ ⋮& \ddots & ⋮\\ 0& \dots & \frac{1}{{\sigma }_{M_{+}}^2}\end{array}\right])+D{]}^{-1}N\times \tilde{\beta }$