Some doubts in the simulation

[JHahaWang]

Hi, I have recently been trying to repeat the simulation process in the supplement note of your article, and there is some confusion that I can't understand. When I get the matrix of sigma(LD) ,I will estmate Sigma use the Sigma(LD) and inverse matrix of C(the diagonal matrix with the elements of the diagonal is 1/sqrt(chi-square - 1)). I can't understand how to get the chi-square statistic for the trait t , we only have the vector of trait (βt) ， do you mean to calculate the chi-squart test use the βt and βt hat ? Hope this makes sense and thank you very much for the response.

[paturley]

Hello,

I'm not 100% sure I understand your question, but I believe you are asking where the chi2 statistic comes from. In these simulations, the expected chi2 statistic is chosen as an input parameter of the simulation. We wanted to be able to assess MTAG's performance for different levels of the expected chi2 stat, and the way we vary that parameter is through the matrix C.

Does that help?

Best, Patrick

On Sun, Sep 18, 2022 at 9:29 PM Destiny041 @.***> wrote:

Hi, I have recently been trying to repeat the simulation process in the supplement note of your article, and there is some confusion that I can't understand. When I get the matrix of sigma(LD) ,I will estmate Sigma use the Sigma(LD) and inverse matrix of C(the diagonal matrix with the elements of the diagonal is 1/sqrt(chi-square - 1)). I can't understand how to get the chi-square statistic for the trait t , we only have the vector of trait (βt) ， do you mean to calculate the chi-squart test use the βt and βt hat ? Hope this makes sense and thank you very much for the response.

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[JHahaWang]

Hi patrick , Thanks for your reply ,that helps a lot . And I have a few other puzzles . When we use MTAG with the real data ,the chi2 statistic was used only in the process of LDSC , we don't use it in the estimate of Σ and Ω .The matrix of C just adds some variance to the normalized matrix during the simulation to get closer to the actual situation . We use the LD score regression intercept to build the Σ(ie , the ΣLD is the estimation of Σ in the real data.) and then to estimate the Ω and the β of MTAG with the GWAS summary data. I wonder if I'm right about that. Wish you all the best！

[paturley]

I'm sorry, I'm a bit confused about your question. The parameters using the simulation described in the SI of the MTAG paper are not based on real data. They are meant to generate simulated data that can then be used to test the MTAG method. How are you using real data?

On Tue, Sep 20, 2022 at 9:37 PM Destiny041 @.***> wrote:

Hi patrick , Thanks for your reply ,that helps a lot . And I have a few other puzzles . When we use MTAG with the real data ,the chi2 statistic was used only in the process of LDSC , we don't use it in the estimate of Σ and Ω .The matrix of C just adds some variance to the normalized matrix during the simulation to get closer to the actual situation . We use the LD score regression intercept to build the Σ(ie , the ΣLD is the estimation of Σ in the real data.) and then to estimate the Ω and the β of MTAG with the GWAS summary data. I wonder if I'm right about that. Wish you all the best！

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