Changes

| un-weighted Burden      || <math>T_b=\sum_{i=1}^n{\mathbf{U_i}}\Big/\sqrt{\sum_{i=1}^n{\mathbf{V_i}}}</math> || <math>T_b\sim\mathbf{N}(0,1)</math> ||<math> \mathbf{U_i}\text{ is the vector of score statistics from study }i, or </math> <math> \mathbf{U_i}=\{U_{i1},...,U_{im}\};</math> <math>\mathbf{V_i} \text{ is the covariance of } \mathbf{U_i}.</math>

| un-weighted Burden      || <math>T_b=\sum_{i=1}^n{\mathbf{U_i}}\Big/\sqrt{\sum_{i=1}^n{\mathbf{V_i}}}</math> || <math>T_b\sim\mathbf{N}(0,1)</math> ||<math> \mathbf{U_i}\text{ is the vector of score statistics from study }i, or </math> <math> \mathbf{U_i}=\{U_{i1},...,U_{im}\};</math> <math>\mathbf{V_i} \text{ is the covariance of } \mathbf{U_i}.</math>

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| Weighted Burden || <math>T_{wb}=\mathbf{w^T}\sum_{i=1}^n{\mathbf{U_i}}\bigg/\sqrt{\mathbf{w^T}\left(\sum_{i=1}^n{\mathbf{V_i}}\right)\mathbf{w}}</math>  || <math>T_{wb}\sim\mathbf{N}(0,1)</math> || <math> \mathbf{w^T}=\{w_1,w_2,...,w_m\} \text{ is the weight vector.}</math>

| Weighted Burden || <math>T_{wb}=\mathbf{w^T}\sum_{i=1}^n{\mathbf{U_i}}\bigg/\sqrt{\mathbf{w^T}\left(\sum_{i=1}^n{\mathbf{V_i}}\right)\mathbf{w}}</math>  || <math>T_{wb}\sim\mathbf{N}(0,1)</math> || <math> \mathbf{w^T}=\{w_1,w_2,...,w_m\}^T \text{ is the weight vector.}</math>

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| VT || <math>T_{VT}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}),\text{ where}</math><math>T_{b\left(f_i\right)}=\boldsymbol{\nu}_{f_i}^\mathbf{T}\sum_{i=1}^n{\mathbf{U_i}}\bigg/\sqrt{\boldsymbol{\nu}_{f_i}^\mathbf{T}\left(\sum_{i=1}^n{\mathbf{V_i}}\right)\boldsymbol{\nu}_{f_i}}\text{, where}</math> <math> \boldsymbol{\nu}_{f_i}\text{ is a vector of indicators.} </math> ||<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Phi}^\mathbf{T}\sum_{i=1}^n{\mathbf{V_i}}\boldsymbol{\Phi}\right)</math>

| VT || <math>T_{VT}=\max(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}),\text{ where}</math><math>T_{b\left(f_i\right)}=\boldsymbol{\nu}_{f_i}^\mathbf{T}\sum_{i=1}^n{\mathbf{U_i}}\bigg/\sqrt{\boldsymbol{\nu}_{f_i}^\mathbf{T}\left(\sum_{i=1}^n{\mathbf{V_i}}\right)\boldsymbol{\nu}_{f_i}}\text{, where}</math> <math> \boldsymbol{\nu}_{f_i}\text{ is a vector of indicators.} </math> ||<math> \left(T_{b\left(f_1\right)},T_{b\left(f_2\right)},\dots,T_{b\left(f_m\right)}\right)</math><math>\sim\mathbf{MVN}\left(\mathbf{0},\boldsymbol{\Phi}^\mathbf{T}\sum_{i=1}^n{\mathbf{V_i}}\boldsymbol{\Phi}\right)</math>