Table 8 Table of allele counts for SNP i (\(i=1\ldots M\)) in the \(\ell \) -th GWAS (\(\ell =1\ldots L\)).

From: Reconstructing SNP allele and genotype frequencies from GWAS summary statistics

 

\(A_1\) (effective allele)

\(A_2\) (non-effective allele)

Number of alleles

Cases

\(a_{i\ell }^{\text {cse}}\)

\(u_{i\ell }^{\text {cse}}\)

\(2N^{\text {cse}}_{\ell }\)

Controls

\(a_{i\ell }^{\text {cnt}}\)

\(u_{i\ell }^{\text {cnt}}\)

\(2N^{\text {cnt}}_{\ell }\)

  1. The total number of cases for the \(\ell \)-th study is \(N_{\ell }^{{\texttt {cse}}}\) and the total number of controls for the \(\ell \)-th study is \(N_{\ell }^{{\texttt {cnt}}}\). Clearly, the total number of cases and controls in a study is the same for all SNPs, which is why the variable N does not depend on i. The total number of alleles in cases and controls is equal to twice the number of cases and controls, respectively.