Polygenic risk score#
Method |
\(\boldsymbol{\beta}\) assumption |
\(\boldsymbol{\beta}\) estimation |
PRS estimation |
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P + T |
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SBLUP |
\(\beta \sim \mathcal{N}(0,\frac{h^2_g}{m})\) |
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\(\beta_j \sim \left\{\begin{array}{@{}% no padding l@{\quad}% some padding r@{}% no padding >{{}}r@{}% no padding >{{}}l@{}% no padding } \mathcal{N}(0,\frac{h^2_g}{Mp}) , & p \\ 0 , & 1 - p \end{array} \right.\) |
\(\mathbb{E}(\beta|\tilde{\beta},D)\approx \bigg (\frac{1}{1-h^2_l} D + \frac{M}{Nh^2}I \bigg )^{-1}\tilde{\beta}\) |
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\(\beta_j \sim \mathcal{N}(0,c* \sigma^2_j)\) |
\(\mathbb{E}(\beta|\tilde{\beta},D,\sigma^2_1,\dots,\sigma^2_M) = \Bigg [ N * D + \frac{1}{c}\bigg (\begin{bmatrix} \frac{1}{\sigma^2_1} & \dots & 0 \\\vdots & \ddots & \vdots \\ 0 & \dots & \frac{1}{\sigma^2_{M_{+}}} \end{bmatrix} \bigg ) + D \Bigg ]^{-1}N \times \tilde{\beta}\) |
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