MTAG fails to produce summary for LDL × AD pair; is low LDSC rg a potential cause?

[zhuochang863-ai]

Hello,

I encountered an issue when running MTAG on LDL and AD GWAS summary statistics. The MTAG run terminates with an error during the summary output:

cannot convert float NaN to integer

Relevant portions of the log are attached (LDL_vs_AD.log, mtag.o730124).

Some details from my run:

• Trait 1 (LDL): Mean Chi^2 = 3.215
• Trait 2 (AD): Mean Chi^2 = 1.161
• LDSC genetic correlation: rg = -0.126, p = 0.465 (non-significant)
• Both traits have been QCed; MAF and allele harmonization done
• No missing or NaN values in either GWAS input

My question is whether MTAG instability in this case could be related to the very low or non-significant genome-wide genetic correlation between LDL and AD. The error occurs after the Omega/Sigma estimation, which may become non-positive-definite when the covariance between traits is weak or heterogeneous.

LDL_vs_AD.log

mtag.log

Thank you for your help!

[zhuochang863-ai]

Hello again. I wanted to provide a follow-up on the LDL × AD MTAG analysis.

The original issue that MTAG could not complete has now been resolved. The key fix was to restore MTAG’s internal sample-size filtering (i.e. removing --n_min 0.0) and to handle extreme p-values in the AD input (for example, replacing P<=0 with a very small positive value such as 1e-300). After this, the analysis runs successfully.

However, I found another issue that makes me uncertain about how reliable the trait-specific MTAG estimates are for AD.

From the successful LDL × AD run, the cross-trait correlation appears to be quite small:

Sigma hat:
[[2.305 0.131]
[0.131 1.081]]

(Correlation):
[[1. 0.083]
[0.083 1. ]]

Estimated Omega:
[[ 6.277e-07 -2.642e-07]
[-2.642e-07 5.748e-07]]

(Correlation):
[[ 1. -0.44]
[-0.44 1. ]]

MTAG weight factors: (average across SNPs)
[ 0.851 -0.494]

I then checked the APOE-region SNPs rs429358 and rs7412 by comparing the original QCed GWAS with the MTAG outputs:

==================== LDL_QC ====================
SNP CHR POS A2 A1 N BETA SE P FRQ MAF VARBETA
rs429358 19 45411941 T C 1226340 0.22074 0.00194052 1e-300 0.152 0.152 3.7656178704e-06
rs7412 19 45412079 C T 1226343 -0.515782 0.0026212 1e-300 0.075 0.075 6.870689440000001e-06

==================== AD_QC ====================
SNP CHR POS A1 A2 BETA SE FRQ P N NEFFECTIVE MAF VARBETA
rs429358 19 45411941 T C -1.1275 0.0132 0.818714660020412 1e-300 397685 113573.3632692 0.18128533997958796 0.00017423999999999999
rs7412 19 45412079 T C -0.4776 0.0214 0.0633472826905748 1.6500000000000002e-110 397842 113673.6154785 0.0633472826905748 0.00045795999999999993

==================== MTAG_trait1 ====================
SNP A1 A2 Z N FRQ mtag_beta mtag_se mtag_z mtag_pval
rs429358 C T 113.75301465586544 1226340.0 0.152 0.12249017141076067 0.0025816833704781516 47.44585366720411 0.0
rs7412 T C -196.77323363345033 1226343.0 0.075 -0.4203684197900612 0.003518907650808539 -119.45991810653888 0.0

==================== MTAG_trait2 ====================
SNP A1 A2 Z N FRQ mtag_beta mtag_se mtag_z mtag_pval
rs429358 C T 85.41666666666666 113573.3632692 0.18128533997958796 -0.027973827065534983 0.002991339025195213 -9.35160703281014 8.632597016339983e-21
rs7412 T C -22.317757009345797 113673.6154785 0.0633472826905748 0.41623892562303816 0.004730416632329911 87.99202226253473 0.0

For rs7412, the original AD GWAS beta is negative, but the MTAG trait2 beta becomes positive. More broadly, when I compared the original GWAS direction with MTAG direction genome-wide, I found:

• For LDL (trait1):

  • Overall concordance: 0.879
  • Concordance for strong AD SNPs (P < 1e-20): 0.9997

• For AD (trait2):

  • Overall concordance: 0.737
  • Concordance for strong AD SNPs (P < 1e-20): 0.639

So the direction inconsistency seems to be much more substantial for trait2 than for trait1.

My question is: should these trait2-specific MTAG estimates be considered unreliable in this setting? In particular, could this direction reversal be a consequence of the very small cross-trait sigma correlation (and weak global shared signal), rather than a meaningful biological result?

At this point, I am inclined to trust the original GWAS / CPASSOC / coloc results more for interpreting direction at APOE-region SNPs, and use MTAG mainly for locus discovery. But I would be very grateful for any guidance on whether this interpretation is correct.

[paturley]

Sorry for the delay. MTAG is best behaved when there are not outliers for effect sizes (especially if the SNP is an outlier for one trait and not the other) since having different parts of the genome where the correlation of the effect sizes is very different that other other sections is a violation of the "homogeneous Omega" assumption that we describe in the paper. Since APOE behaves quite differently that the rest of the genome for AD, I can imagine that the MTAG estimates in that region might act a little funny. If I were you, I'd probably omit that region from the MTAG analysis and see how it works. I'd expect the betas to have a reasonable level of concordance given the size of the standard errors in that case.

…

On Mon, Mar 30, 2026 at 7:39 AM Zhuochang Bi ***@***.***> wrote: *zhuochang863-ai* left a comment (JonJala/mtag#253) <#253 (comment)> Hello again. I wanted to provide a follow-up on the LDL × AD MTAG analysis. The original issue that MTAG could not complete has now been resolved. The key fix was to restore MTAG’s internal sample-size filtering (i.e. removing --n_min 0.0) and to handle extreme p-values in the AD input (for example, replacing P<=0 with a very small positive value such as 1e-300). After this, the analysis runs successfully. However, I found another issue that makes me uncertain about how reliable the trait-specific MTAG estimates are for AD. From the successful LDL × AD run, the cross-trait correlation appears to be quite small: Sigma hat: [[2.305 0.131] [0.131 1.081]] (Correlation): [[1. 0.083] [0.083 1. ]] Estimated Omega: [[ 6.277e-07 -2.642e-07] [-2.642e-07 5.748e-07]] (Correlation): [[ 1. -0.44] [-0.44 1. ]] MTAG weight factors: (average across SNPs) [ 0.851 -0.494] I then checked the APOE-region SNPs rs429358 and rs7412 by comparing the original QCed GWAS with the MTAG outputs: ==================== LDL_QC ==================== SNP CHR POS A2 A1 N BETA SE P FRQ MAF VARBETA rs429358 19 45411941 T C 1226340 0.22074 0.00194052 1e-300 0.152 0.152 3.7656178704e-06 rs7412 19 45412079 C T 1226343 -0.515782 0.0026212 1e-300 0.075 0.075 6.870689440000001e-06 ==================== AD_QC ==================== SNP CHR POS A1 A2 BETA SE FRQ P N NEFFECTIVE MAF VARBETA rs429358 19 45411941 T C -1.1275 0.0132 0.818714660020412 1e-300 397685 113573.3632692 0.18128533997958796 0.00017423999999999999 rs7412 19 45412079 T C -0.4776 0.0214 0.0633472826905748 1.6500000000000002e-110 397842 113673.6154785 0.0633472826905748 0.00045795999999999993 ==================== MTAG_trait1 ==================== SNP A1 A2 Z N FRQ mtag_beta mtag_se mtag_z mtag_pval rs429358 C T 113.75301465586544 1226340.0 0.152 0.12249017141076067 0.0025816833704781516 47.44585366720411 0.0 rs7412 T C -196.77323363345033 1226343.0 0.075 -0.4203684197900612 0.003518907650808539 -119.45991810653888 0.0 ==================== MTAG_trait2 ==================== SNP A1 A2 Z N FRQ mtag_beta mtag_se mtag_z mtag_pval rs429358 C T 85.41666666666666 113573.3632692 0.18128533997958796 -0.027973827065534983 0.002991339025195213 -9.35160703281014 8.632597016339983e-21 rs7412 T C -22.317757009345797 113673.6154785 0.0633472826905748 0.41623892562303816 0.004730416632329911 87.99202226253473 0.0 For rs7412, the original AD GWAS beta is negative, but the MTAG trait2 beta becomes positive. More broadly, when I compared the original GWAS direction with MTAG direction genome-wide, I found: - For LDL (trait1): - Overall concordance: 0.879 - Concordance for strong AD SNPs (P < 1e-20): 0.9997 - For AD (trait2): - Overall concordance: 0.737 - Concordance for strong AD SNPs (P < 1e-20): 0.639 So the direction inconsistency seems to be much more substantial for trait2 than for trait1. My question is: should these trait2-specific MTAG estimates be considered unreliable in this setting? In particular, could this direction reversal be a consequence of the very small cross-trait sigma correlation (and weak global shared signal), rather than a meaningful biological result? At this point, I am inclined to trust the original GWAS / CPASSOC / coloc results more for interpreting direction at APOE-region SNPs, and use MTAG mainly for locus discovery. But I would be very grateful for any guidance on whether this interpretation is correct. — Reply to this email directly, view it on GitHub <#253?email_source=notifications&email_token=AFBUB5L35H36PDY34BMUGMD4TJMGNA5CNFSNUABFM5UWIORPF5TWS5BNNB2WEL2JONZXKZKDN5WW2ZLOOQXTIMJVGQZTONZVG43KM4TFMFZW63VKON2WE43DOJUWEZLEUVSXMZLOOSWGM33PORSXEX3DNRUWG2Y#issuecomment-4154377576>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AFBUB5LMUHDAI75PFKIVFID4TJMGNAVCNFSM6AAAAACXE33FZ2VHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHM2DCNJUGM3TONJXGY> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>