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===SKAT META ANALYSIS===
===SKAT META ANALYSIS===
<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>
SKAT has been powerful detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances
<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>.
As shown in Wu et. al, the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as
