---
title: "genetic-correlations-in-ldsc"
author: "Michel Nivard"
format: 
  revealjs:
    smaller: true
    transition: slide
    navigation-mode: vertical
    fig-align: center
    theme: sky
highlight-style: "nord"
---

## Genetic correlation in LD score regression

This lecture:

-   the LDSC genetic correlation **estimator**

-   Making sure the LD score you use, are appropriate for the cohort/GWAS you have,

-   The Practical!

## Get the data for 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

![](images/clipboard-3995278007.png)

``` r
system("mkdir $HOME/michel")
system("cp -R /faculty/michel/2024/practical* $HOME/michel")
setwd("~/michel/practical")
```

## Genetic correlation in LD score regression

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.

## LDSC as a regression

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:

$$y_j = b*l_j + a$$

## Data

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:

$$l_i$$

## Parameters

$$ b = \frac{\sqrt{N_{1} N_{2}} * cov_g}{M} = slope$$

$$ a = \frac{cor_p * N_s}{\sqrt{N_{1} N_{2}}} + a = intercept$$

## Works for GWAS that do not overlap!

![](images/clipboard-491799321.gif)

## BUT!

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...

## A look at variation in the LD map

![](images/clipboard-3762975377.png)

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.

## So we want to match ancestry in the LDscore to the GWAS sample

Use ancestry specific LD scores, for example:

-   GNOMAD: https://gnomad.broadinstitute.org/downloads#v2-linkage-disequilibrium
-   UKBiobank Pan ancestry: https://pan-dev.ukbb.broadinstitute.org/downloads

What if I still don't really think their appropriate for my sample?

-   Make your won LD scores: https://github.com/bulik/ldsc/wiki/LD-Score-Estimation-Tutorial
-   (You need sequencing data!)

## Can we use LDSC in admixed samples?

-   Many people have multiple ancestries

![](images/clipboard-3888322111.png)

## How can we use cov-LDSC in admixed samples?

-   Use "covariate adjusted" LD scores in admixed samples.

-   cov-LDSC software: https://github.com/immunogenomics/cov-ldsc

## What if you want to compute the rg between GWASs in different ancestries?

-   There is a tool called popcorn that models the differences in LD and AF and rg at the same time
-   https://github.com/brielin/Popcorn

## What if you want to compute the rg between GWASs in different ancestries?

-   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

## Popcorn vs Admix-kit

![](images/clipboard-2146785733.png)

## Let's look at the practical for today!

-   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?