Fine-mapping from Summary Data with SuSiE

Posted on Jan 22, 2024

Tags: Variable Selection, Linear Regression, Genetic Fine Mapping

This post is for Zou, Y., Carbonetto, P., Wang, G., & Stephens, M. (2022). Fine-mapping from summary data with the “Sum of Single Effects” model. PLOS Genetics, 18(7), e1010299.

Summary data for fine-mapping

1. vectors $\hat b=(\hat b_1,\ldots, \hat b_J)^\top$ and $\hat s=(\hat s_1,\ldots, \hat s_J)^\top$ containing estimates of marginal association for each SNP $j$, and corresponding standard errors, from a simple linear regression:

\[\hat b_j = \frac{x_j^\top y}{x_j^\top x_j}\] \[\hat s_j = \sqrt{\frac{(y-x_j\hat b_j)^\top(y-x_j\hat b_j)}{Nx_j^\top x_j}}\]

An alternative to $\hat b, \hat s$ is the vector $\hat z=(\hat z_1,\ldots, z_J)^\top$ of $z$-scores,

\[\hat z_j = \frac{\hat b_j}{\hat s_j}\]

1. An estimate $\hat R$ of the in-sample LD matrix $R$, where $R$ is the $J\times J$ SNP-by-SNP sample correlation matrix

\[R = D_{xx}^{-1/2}X^TXD_{xx}^{-1/2}\]

where $D_{xx}=\diag(X^TX)$ is a diagonal matrix that ensures the diagonal entries of $R$ are all 1.

Often, the estimate $\hat R$ is taken to be out of sample LD matrix