Syntax for other multivariate GWAS methods

[Michael Levin]

Several multivariate GWAS methods have been described (eg. MTAG, N-GWAMA, etc). In this video overview of the Genomic SEM method (https://youtu.be/ECwQS5UD3YM?t=2768), a Genomic SEM implementation of the MTAG method is mentioned. Is there example lavaan syntax for implementing this method (eg. for 2+ traits)? 

Similarly, how does the common factor approach compare with the N-weighted multivariate GWAMA method reported here: https://www.nature.com/articles/s41588-018-0320-8 - if different, can this model be specified within Genomic SEM?

Thanks,

-Mike

[Elliot Tucker-Drob]

Hi Mike,

The supplement to the original Grotzinger 2019 paper provides a formal treatment of how a model equivalent to the MTAG model can be specified within Genomic SEM. In practice, there are a few ways to do this. One way is to regress the target phenotype on the SNP (T ~ SNP) and regress the supporting phenotypes on the target phenotype (Y1 + Y2 +Y3 ~ T). The supporting phenotypes can be allowed to have residual covariances with one another (Y1~~Y2, Y1~~Y3, Y2~~Y3). A second way is to specify a common factor GWAS, forcing the residual variance of the target phenotype to 0, such that the factor is isomorphic with the target phenotype (F ~ SNP, F =~ 1*T + Y1 + Y2 + Y3, T ~~ 0*T). Again, the supporting phenotypes can be allowed to have residual covariances with one another (Y1~~Y2, Y1~~Y3, Y2~~Y3).

With respect to N-weighted multivariate GWAMA, the key assumption is that the contributing GWAS each represent the same phenotype (in practice different genetically correlated GWAS phenotypes can be used, but this is not taken into account), but that they may be differentially precise (hence the N-weighting) and differentially heritable (e.g. due to differences in reliability of the measures used). Note that, like MTAG and Genomic SEM, N-weighted multivariate GWAMA takes (potentially unknown) sample overlap into account. A Genomic SEM model similar to N-weighted multivariate GWAMA would be to create a common factor GWAS with all residual variances of the factor indicators fixed to 0 (F~SNP, F=~ Y1+Y2+Y3, Y1~~0*Y1, Y2~~0*Y2, Y3~~0*Y3). Note that the weighted least squares estimator in Genomic SEM optimizes parameter estimates by weighting by the inverse square of the standard errors of the SNP effects (and genetic covariances) which is similar to N-weighting. To represent a model similar to a standard GWAS meta-analysis that assumes the same phenotype and equal heritabilities, you would further fix all factor loadings to be equal.  This can be done by making them all 1.0 (F =~ 1*Y1 + 1*Y2 + 1*Y3).

Finally, you may be interested in what we have referred to in the Grotzinger et al. (2020) preprint as an unstructured GWAS meta-analysis, which imposes no structure on the expected pattern of associations between the SNPs and the individual GWAS phenotypes. This is similar to the ASSET-based method used for meta-analysis in Lee et al. (2019). To conduct an unstructured GWAS meta-analysis, you compare a model in which all phenotypes are regressed onto the SNP (Y1 + Y2 + Y3 ~ SNP) with one in which all of these regressions are fixed to 0 (Y1 + Y2 + Y3 ~ 0*SNP). Residual covariances among the phenotypes can be freely estimated in both models. In other words, you run 2 models per SNP. The difference in chi square statistics between the two models is itself a chi squared distributed test statistic with df equal to the number of GWAS phenotypes. This test statistic quantifies the evidence for an overall effect of the SNP on any subset of the phenotypes, irrespective of the patterning or directionality of the effects.

Best Regards,

Elliot

--
You received this message because you are subscribed to the Google Groups "Genomic SEM Users" group.
To unsubscribe from this group and stop receiving emails from it, send an email to genomic-sem-us...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/genomic-sem-users/f1f4b944-f9e8-49db-9c1e-40d593cf6ebdn%40googlegroups.com.

[Michael Levin]

This is great - thanks for the help!

-Mike