Confusing results with genomic SEM - higher-order p factor models

[Liliana Garcia]

Hi everyone!

I have specified two models in genomic SEM: a p-factor and a higher order p-factor model (both include the same internalizing and externalizing traits). I obtained summary statistics for the p factors and for internalizing and externalizing components with the userGWAS function, and I used these sumstats to compute PRS for the p-factors.

Unfortunately, my p factor PRS have very low or negative correlations with the PRS for the externalizing and internalizing traits (many correlations are ~0.005). This does not make sense, as I used the same summary statistics for the genomic SEM analyses and for calculating the trait PRS. These correlations also contradict the genetic (LDSC) correlations I obtained between my p-factor summary statistics and the trait summary statistics.

If you would have any ideas on what might have gone wrong in the process, or on checks I could do to better understand my results, I would appreciate it so much!

A few more details on the analyses: to avoid negative residual variances, I placed constraints on some of the trait residuals. My model fit was decent for both the simple p factor and the higher order model (CFI > 0.9, SRMR < .10), and the standardized estimates made sense. I calculated the PRS in a genetic dataset that has no sample overlap with the GWAS used for the genomic SEM analyses. 

I am also attaching images for the model specification and fit, the genetic (LDSC) correlations and the correlations between the PRS, in case this can be helpful.

Thank you for your attention!

Liliana

Genetic (LDSC) correlations:

Correlations between PRS in unrelated sample:

[Michel Nivard]

Hi,

sorry for the slow response, summer break etc. 

so this is a difficult question to fully work trough. first let me say I dont discount the fact that something may have gone wrong, either on our end or on your end during the GenomicSEM steps. That being said, even with pretty big samples PRS correlations can be fairly low due to the fact that there is a lot of noise in PRS (this is also why the explain far less variance then the heritability.) To asses whether the correlatiosn really are too low can you share with us the correlations between the PRS for the psychiatric disorders themselfs?

also note that the EXT, INT and P PRS are highly correlated, possibly because the loadings from P -> INT and EXT are set to 1 (you can prob free one of these doubt it will matter much). 

Best,

Michel

[Liliana Garcia]

Hi Michel!

Thank you very much for your answer! I am attaching the correlations between the PRS. The correlations of internalizing traits are moderate, and the correlations of externalizing traits and between externalizing and internalizing traits are indeed weak, although not as weak as the correlations I between my p-factor PRS and the psychiatric traits.

I have tried to free loadings from the higher-order model (P =~ 1*INT + 1*EXT), but if I try to make any changes to this section, the model is either not identifiable (I get negative CFI estimates) or the model estimates remain the same as in the original model specification.

I have also received feedback from Andrew by email, and he also thought that the issue might come from the calculation of the PRS, as the LDSC correlations seem to make more sense. He suggested to check whether the PRS software I am using aligns alleles as part of its QC, as misaligned alleles could be a source of PRS miscalculation. I am using PRSice, and from what I understand, the software takes care of alligning alleles between the base and the target data. I did some checks, and although it still seems to me that it is not necessary to flip alleles or the direction of the effect in the summary statistics, what I did find was that if I restricted the SNPs from my p factor summary statistics to SNPs available in the Hapmap 3 SNPs, and calculated new PRS based on these reduced summary statistics files, the correlations between the PRS make much more sense.

I am including a table that shows the correlations between the updated pfactor PRS and the psychiatric traits (the "old_pfactor" column contains the PRS from my original p factor, for comparison). With the updated p factor PRS, the correlations with internalizing traits have increased dramatically, and although the correlations with externalizing traits remain low, they have also increased quite a bit compared with the original p factor PRS.

 

I was wondering if you might have an idea why it would make such a big difference in the PRS calculation if I restrict my summary statistics to SNPs available in Hapmap 3? Andrew mentioned he doesn't see a reason why restricting the SNPs would be necessary. I am wondering if there has been anyone that has faced a similar issue when trying to compute PRS from summary statistics generated by genomic SEM. As a test suggested by Andrew, I have also restricted the SNPs of two of my psychiatric trait summary statistics to SNPs available in Hapmap 3, and I recalculated the PRS based on these restricted summary statistics files. However, the correlations between the PRS remained quite similar (e.g. the correlation between the original depression PRS and the hapmap-restricted depression PRS is 0.8, as opposed to what I see in the p factor and the hapmap-restricted p factor PRS, which have a correlation of 0.01).

If you would have any suggestions on further checks I could make to better understand my results, I would appreciate it so much!

Thank you very much for your attention!

Best wishes,

Liliana