Inquiry about MTAG output units for binary and continuous traits

[LouChen-med]

Subject: Inquiry about MTAG output units for binary and continuous traits

Dear Developers,

When running MTAG with Z-scores for Type 2 Diabetes (binary) and Blood Lipids (continuous) as inputs:

1. For T2D_MTAG, are the output mtag_beta and mtag_se on the $log(OR)$ scale or a standardized scale (per 1 SD)?
2. For Lipids_MTAG, is the unit on a standardized scale (per 1 SD)?

OR all the other scale?

Thank you for your assistance.

Best,
Chen Lou

[paturley]

Hello Chen, The scale of MTAG output should be in the standardized scale but relative to the units of the input GWAS. For a continuous trait, this is straightforward to interpret, but for binary traits it's a bit more tricky. If the GWAS was done on the observed scale, then the coefficients are on the scale as if the binary outcomes was standardized and then you did a GWAS on the standardized binary phenotype. If it's based on a logistic regression, it's in the units as if the latent variable underlying the logistic regression had been standardized. It's been a while since I've thought hard about logistic regression, but Google tells me that the implicit latent trait of a logistic model has a variance of (pi^2)/3. Assuming that is true, you'd need to rescale the betas if you want to recover them in log(OR) units. Whether or not you rescale, the p-values should be valid in either case. Sorry this is maybe more complicated than you might have anticipated. Best, Patrick

…

On Tue, Jun 2, 2026 at 10:14 AM Chen Lou ***@***.***> wrote: LouChen-med created an issue (JonJala/mtag#255) Subject: Inquiry about MTAG output units for binary and continuous traits Dear Developers, When running MTAG with Z-scores for Type 2 Diabetes (binary) and Blood Lipids (continuous) as inputs: For T2D_MTAG, are the output mtag_beta and mtag_se on the $log(OR)$ scale or a standardized scale (per 1 SD)? For Lipids_MTAG, is the unit on a standardized scale (per 1 SD)? OR all the other scale? Thank you for your assistance. Best, Chen Lou — Reply to this email directly, view it on GitHub, or unsubscribe. Triage notifications, keep track of coding agent tasks and review pull requests on the go with GitHub Mobile for iOS and Android. Download it today! You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[LouChen-med]

Dear Patrick,

Thank you for your explanation.

What I mean is that I think whether the input GWAS for a binary trait was performed using a linear model on a 0/1 phenotype or logistic regression for disease status should not affect the input binary GWAS Z-scores.

Therefore, if I do not apply any further transformation to the MTAG-GWAS output, because such transformation is difficult to be accurate because the case control can't be estimated after MTAG, is the MTAG beta for a binary trait on a standardized scale, corresponding to a normally distributed liability with SD = 1?I am not sure whether my understanding is correct.

Best,
Chen Lou

[paturley]

I don't think that's true. Logistic regression and OLS on a binary phenotype will give you similar z-statistics but not identical ones. So it really does matter how the input summary statistics were produced. (Though in most cases, the z-stats will be similar so it shouldn't matter very much.)

…

On Tue, Jun 2, 2026 at 9:47 PM Chen Lou ***@***.***> wrote: LouChen-med left a comment (JonJala/mtag#255) Dear Patrick, Thank you for your explanation. What I mean is that I think whether the input GWAS for a binary trait was performed using a linear model on a 0/1 phenotype or logistic regression for disease status should not affect the input binary GWAS Z-scores. Therefore, if I do not apply any further transformation to the MTAG-GWAS output, because such transformation is difficult to be accurate because the case control can't be estimated after MTAG, is the MTAG beta for a binary trait on a standardized scale, corresponding to a normally distributed liability with SD = 1?I am not sure whether my understanding is correct. Best, Chen Lou — Reply to this email directly, view it on GitHub, or unsubscribe. Triage notifications, keep track of coding agent tasks and review pull requests on the go with GitHub Mobile for iOS and Android. Download it today! You are receiving this because you commented.Message ID: ***@***.***>

[LouChen-med]

Thank you, I now understand the difference. To summarize my understanding of the MTAG coefficient scales:

For a binary trait input GWAS using a linear model (observed scale 0/1), the MTAG output coefficients are scaled as if the binary outcome had been standardized, mirroring a standard linear GWAS (i.e., unit is the standard deviation of the observed 0/1 scale).

For a binary trait input GWAS using logistic regression, the MTAG output coefficients are in units of the standardized latent variable underlying the logistic model (i.e., unit is the the standard deviation of the latent variable).

For a continuous trait input GWAS, the MTAG output coefficients are expressed in units of one phenotypic standard deviation (i.e., based on the standard deviation of the continuous trait).

Does all above sound correct?

[paturley]

Yes, that sounds right

…

On Wed, Jun 3, 2026, 7:26 AM Chen Lou ***@***.***> wrote: *LouChen-med* left a comment (JonJala/mtag#255) <#255 (comment)> Thank you, I now understand the difference. To summarize my understanding of the MTAG coefficient scales: For a binary trait input GWAS using a linear model (observed scale 0/1), the MTAG output coefficients are scaled as if the binary outcome had been standardized, mirroring a standard linear GWAS (i.e., unit is the standard deviation of the observed 0/1 scale). For a binary trait input GWAS using logistic regression, the MTAG output coefficients are in units of the standardized latent variable underlying the logistic model (i.e., unit is the the standard deviation of the latent variable). For a continuous trait input GWAS, the MTAG output coefficients are expressed in units of one phenotypic standard deviation (i.e., based on the standard deviation of the continuous trait). Does all above sound correct? — Reply to this email directly, view it on GitHub <#255?email_source=notifications&email_token=AFBUB5JSSR6GBACIPT32PFT46ARP7A5CNFSNUABFM5UWIORPF5TWS5BNNB2WEL2JONZXKZKDN5WW2ZLOOQXTINRRGI4DAMBWGM42M4TFMFZW63VHMNXW23LFNZ2KKZLWMVXHJLDGN5XXIZLSL5RWY2LDNM#issuecomment-4612800639>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AFBUB5JVKDKHFGXJRKQSDMD46ARP7AVCNFSM6AAAAACZXNCVFWVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHM2DMMJSHAYDANRTHE> . Triage notifications, keep track of coding agent tasks and review pull requests on the go with GitHub Mobile for iOS <https://github.com/notifications/mobile/ios/AFBUB5IV3754NIN66AUHOMD46ARP7A5CNFSNUABFM5UWIORPF5TWS5BNNB2WEL2JONZXKZKDN5WW2ZLOOQXTINRRGI4DAMBWGM42M4TFMFZW63VHMNXW23LFNZ2KKZLWMVXHJKTGN5XXIZLSL5UW64Y> and Android <https://github.com/notifications/mobile/android/AFBUB5ODZ63HUSR2JD5NJFT46ARP7A5CNFSNUABFM5UWIORPF5TWS5BNNB2WEL2JONZXKZKDN5WW2ZLOOQXTINRRGI4DAMBWGM42M4TFMFZW63VHMNXW23LFNZ2KKZLWMVXHJLTGN5XXIZLSL5QW4ZDSN5UWI>. Download it today! You are receiving this because you commented.Message ID: ***@***.***>