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RAREMETAL METHOD

292 bytes added, 13:28, 20 May 2019
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<math> S </math> is the number of studies
<math> f_{i} </math> is the pooled allele frequency of <math>i^{th} </math> variant
<math> f_{i,k} </math> is the allele frequency of <math>i^{th} </math> variant in <math>k^{th} </math> study
<math> {\delta_{k}} </math> is the deviation of trait value of <math>k^{th} </math> study
<math> \mathbf{w^T} = (w_1,w_2,...,w_m)^T</math> is the vector of weights for <math>m</math> rare variants in a gene.
<math>T_{meta_i}=U_{meta_i}\bigg/\sqrt{V_{meta_i}}=\sum_{k=1}^S {U_{i,k}}\bigg/\sqrt{\sum_{k=1}^S{V_{ii,k}}} \sim\mathbf{N}(0,1)</math>.
Optimized method for unbalanced studies:
'''Optimized method for unbalanced studies (--useExact)''': <math>U_{meta_i}=\sum_{k=1}^S {U_{i,k}/\hat{\Omega_{k}}}-\sum_{k=1}^S{2n_{k}{\delta_{k}^{2}(f_{i}-f_{i,k})}}</math> <math>V_{meta_i}={\sigma^{2}}\sum_{k=1}^S{(V_{ii,k}{\Omega_{k}}-4n_{k}(ff'-f_{k}f_{k}'))}</math> <math>{\sigma^{2}}=\sum_{k=1}^S{((n_{k}-1){\Omega_{k}}+n_{k}{\delta_{k}^{2}})}/(n-1)</math>
===BURDEN META ANALYSIS===
<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.
 
 
[[Category:RAREMETAL]]
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