This lecture:
the LDSC genetic correlation estimator
Making sure the LD score you use, are appropriate for the cohort/GWAS you have,
The Practical!
Lets start grabbing the data, its a bit more data then some of the other practicals.
Code is in the forum (“ISG Workshop logisitcs”), and in the shared files
Univariate LDSC:
\[Z_{j}^2 = \frac{ N * h^2_{snp} }{M}*l_j + 1 + Na\]
Bivariate LDSC:
\[Z_{1j} *Z_{2j} = \frac{ \sqrt{N_{1} N_{2}} * cov_g }{M}*l_j + \frac{cor_p * N_s}{\sqrt{N_{1} N_{2}}} + \sqrt{N_{1} N_{2}}*cor(a_1,a_2)\]
Bulik-Sullivan, B., Finucane, H. K., Anttila, V., Gusev, A., Day, F. R., Loh, P. R., … & Neale, B. M. (2015). An atlas of genetic correlations across human diseases and traits. Nature genetics, 47(11), 1236-1241.
Bivariate LDSC:
\[Z_{1j} *Z_{2j} = \frac{ \sqrt{N_{1} N_{2}} * cov_g }{M}*l_j + \frac{cor_p * N_s}{\sqrt{N_{1} N_{2}}} + \sqrt{N_{1} N_{2}}*cor(a_1,a_2)\]
It’s just a regression:
\[y_j = b*l_j + a\]
GWAS sumstats for traits 1 and 2 for SNP j:
\[Z_{1j} *Z_{2j}\]
Audience Q: “What is this Z?”
The LD score, a per SNP measure of the size of the part of the genome tagged by SNP j:
\[l_i\]
\[ b = \frac{\sqrt{N_{1} N_{2}} * cov_g}{M} = slope\]
\[ a = \frac{cor_p * N_s}{\sqrt{N_{1} N_{2}}} + a = intercept\]
Its a regression where the “outcome” (GWAS results) and the “predictor” (LD score) come form different sources…
That’s really weird… and it puts a little bit of responsibility on the user to ensure the variables are from a common population…
Salehi Nowbandegani, P., Wohns, A. W., Ballard, J. L., Lander, E. S., Bloemendal, A., Neale, B. M., & O’Connor, L. J. (2023). Extremely sparse models of linkage disequilibrium in ancestrally diverse association studies. Nature Genetics, 55(9), 1494-1502.
Use ancestry specific LD scores, for example:
What if I still don’t really think their appropriate for my sample?
Use “covariate adjusted” LD scores in admixed samples.
cov-LDSC software: https://github.com/immunogenomics/cov-ldsc
BUT it obviously also pulls in all cultural, cohort, measurement differences between your GWASs!
Solutions: compute rg between traits, within an admixed person correlating the genetic effects betwene their two ancestries.
Acessible explanation: https://www.nature.com/articles/s41588-023-01325-x
Original paper: https://www.nature.com/articles/s41588-023-01338-6
Software: https://github.com/KangchengHou/admix-kit
we have GWAS data and LD scores of MDD and BMI for people of European and east-Asian ancestry
What is YOUR estimand? (what do YOU want to know?)
We estimate the rg’s using LDSC (estimator)
We see if we can learn about your estimand using our estimates?