several questions while using MTAG

[zwang2333]

Dear authors and users,

Here are three quick questions: 1, What is the relationship between the Omega matrix and the genetic covariance matrix? 2, According to the MTAG paper, the Sigma_j matrix is different for different SNP. But there is only one Sigma matrix reported in MTAG result. What does it stand for? 3, How does MTAG program estimate beta only using z statistics as input? Why is my MTAG result using z statistics different from the result using beta and se?

Many thanks,

[paturley]

Hello!

1. They should be closely related. Genetic covariance is generally defined as either the covariance between the genetic components for a pair of traits or as the covariance of the causal effect sizes. In MTAG, the Omega matrix is the covariance of the marginal effect sizes when genotypes and phenotypes are standardized.
2. The Sigma matrix reported by MTAG I believe is just the intercepts from LD score regression. (We call that Sigma_LD in the paper, I think.) This matrix is rescaled for each SNP relative to the sample size for that SNP. So if there is heterogeneity in the sample size across SNPs, MTAG will use a different Sigma matrix for each SNP.
3. In general, Z/sqrt(N) is a good approximation of the marginal effect size for a SNP in standard deviation units for the genotype and phenotype. MTAG uses this approximation to obtain marginal effect sizes. The beta-SE specification of MTAG tries to keep things in the original units of the GWAS. For example, using MTAG on height and your phenotype is measured in cm, then using the Z-N option, the units of MTAGs beta coefficients would be "standard deviations of height per allele." If you use the beta-SE option, it should be "cm per allele". Theoretically, the p-values should be more or less the same for each approach (though not exact since they rely on different approximations). If they are very different, I imagine the Z-N option is more reliable since that's the version that we thoroughly tested for publication. Let me know if there appears to be big discrepancies.

On Tue, Jun 16, 2020 at 1:12 AM zhwang [email protected] wrote:

Dear authors and users,

Here are three quick questions: 1, What is the relationship between the Omega matrix and the genetic covariance matrix? 2, According to the MTAG paper, the Sigma_j matrix is different for different SNP. But there is only one Sigma matrix reported in MTAG result. What does it stand for? 3, How does MTAG program estimate beta only using z statistics as input? Why is my MTAG result using z statistics different from the result using beta and se?

Many thanks,

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[zwang2333]

Hi Patrick,

Thank you so much for your timely and detailed reply.

1, If one of my traits is a case/control study( e.g. one is a quantitative trait, another is case/control), can I just use the commands "--beta_name" and "--se_name" to specify the log(OR) and corresponding standard error?

2, What if there is no sample size column in my GWAS sumstats? Is it fine to use the known overall sample size (same for every SNP)? And does there exit commands which allow users to specify the overall sample size (just like "--N 11810 " command in the munge step of LDSC)?

3, I picked one SNP(rs2060465) in the NEUR and SWB sumstats provided here as an example to do the calculation manually. Using Omega matrix and Sigma matrix reported by MTAG, the MTAG beta estimator and standard error for NEUR are 0.02675958 and 0.003683382. However, the results reported by MTAG package are 0.03897124 and 0.005364285. I'm really confused about why there is a difference.

Many thanks

[paturley]

Hello,

1. I think that should work fine. Ideally, you would use the betas and standard errors directly from the logistic regression, but using log(OR) should give you approximately the same thing.
2. If you know the known overall sample size, just using that value for every SNP should be fine. I don't think we added an option to just add that as an option, so you may need to add that column to the summary statistics that you are using manually.
3. Not totally sure what the difference is, but note that your estimates are just constant multiples of the estimates of those produced by MTAG, so perhaps it has to do with how the betas are scaled to account for the allele frequencies. Did you get these with the beta-SE flag or the Z-N flag?

On Tue, Jun 16, 2020 at 6:51 PM zhwang [email protected] wrote:

Hi Patrick,

Thank you so much for your timely and detailed reply.

1, If one of my traits is a case/control study( e.g. one is a quantitative trait, another is case/control), can I just use the commands "--beta_name" and "--se_name" to specify the log(OR) and corresponding standard error?

2, What if there is no sample size column in my GWAS sumstats? Is it fine to use the known overall sample size (same for every SNP)? And does there exit commands which allow users to specify the overall sample size (just like "--N 11810 " command in the munge step of LDSC)?

3, I picked one SNP(rs2060465) in the NEUR and SWB sumstats provided here as an example to do the calculation manually. Using Omega matrix and Sigma matrix reported by MTAG, the MTAG beta estimator and standard error for NEUR are 0.02675958 and 0.003683382. However, the results reported by MTAG package are 0.03897124 and 0.005364285. I'm really confused about why there is a difference.

Many thanks

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[zwang2333]

Hi,

Thank you for your reply.

For 3), I just use the GWAS sumstats provided in the Wiki of MTAG, i.e. the neuroticism and subjective well-being data summary statistics. Since there is no beta and se in the original GWAS sumstats, I use the Z-N flag and the code is exactly the same as the example in Wiki. Attached is a summary of my calculation. I want to make sure I correctly understand how MTAG works. Could you help me check where I went wrong? test.docx

Many thanks

[zwang2333]

Hi Paturley,

I'm still confused about the definition of the Omega matrix. For example, if I calculate the genetic covariance matrix by using LDSC, how can I get the Omega matrix then?

Thank you.

[paturley]

Hello,

Apologies for the slow responses here. I've been swamped by other projects so I haven't had time to dig deeply into your particular case. The genetic correlation matrix and Omega are related, but not the same. In the meantime, you can read in more detail about how Omega is constructed in the "Estimation of Omega" section of the MTAG paper and in the Supplement to the paper.

I'll try to get to this when I can.

Best, Patrick

[zwang2333]

No worries. Thanks

[zwang2333]

Hi Patrick,

Hope everything goes well. Do you have any comments on the difference between my manual calculation and MTAG program result mentioned in test.docx in my previous question?

Best, Stephen

[paturley]

Hi Stephen,

Sorry about the delay here. This fell off my radar.

I think part of the problem may be the units of the genotype. Since you are using beta=Z/sqrt(N) to get estimates of beta, your beta is in standardized genotype and phenotype units. MTAG does all of it's analysis in these units as well, but it transforms the output into genotype counts units in the last step. If you divide the estimate that you produced by hand by sqrt(2maf(1-maf)), you get estimates that are pretty close to what MTAG reports, right?

On Tue, Aug 25, 2020 at 1:16 PM zhwang [email protected] wrote:

Hi Patrick,

Hope everything goes well. Do you have any comments on the difference between my manual calculation and MTAG program result mentioned in test.docx in my previous question?

Best, Stephen

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