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LDSC (Yengo et al 2022, Height)

I applied Linkage Disequilibrium Score Regression1 to the non-23-and-me European subset of the adult height GWAS of Yengo et al.2 to estimate heritability and look for signs of population stratification or confounding.

The results are below:

Parameter Value
h2_liab 0.4314
h2_liab_se 0.02148
Lambda_gc 5.191
Mean_chi2 15.38
Intercept 2.429
Intercept_se 0.05703
Ratio 0.09943
Ratio_se 0.003967

A SNP heritability of approximately 43% is consistent with estimates from other sources.

An LD-score regression intercept of 2.429 and a genomic control \(\lambda\) of 5.191 may seem high. Note however, that height is a highly polygenic trait, and the Yengo GWAS has a very large sample size. This is reflected in the very large mean \(\chi^2\) (15.38). In such a circumstances, the best measure of degree of potential stratification/ confounding is the attenuation ratio, which is calculated as

\[ \frac{\text{intercept} -1}{\chi^2_{\text{mean}} -1}. \]

Here the attenuation ratio is 0.09943, which suggests an acceptably low level of stratification.

To investigate the fit of the LDSC model, I also generated the LDSC diagnostic plot below

LDSC diagnostic plot. Genetic variants are binned by LD Score. For each bin, we plot the mean LD score of variants in the bin (x axis) against Wald chi squared statistic (y axis 1) and scaled Wald chi squared statistic (y axis 2). Each plotted bin includes error bars indicating the standard error of bin chi squared mean. We also plot the LDSC regression line (solid) and the line corresponding to chi squared =1 (dashed). If the LDSC model fits the data perfectly, we should expect that the intercept of the regression line is at chi squared=1

As would be expected of GWAS of a highly polygenic quantitative trait, the Yengo et al. GWAS appears to fit the LDSC model well: most of the binned \(\chi^2\) values lie close to the regression line

  1. Brendan K Bulik-Sullivan, Po-Ru Loh, Hilary K Finucane, Stephan Ripke, Jian Yang, Nick Patterson, Mark J Daly, Alkes L Price, and Benjamin M Neale. LD Score regression distinguishes confounding from polygenicity in genome-wide association studies. Nature Genetics, 47(3):291–295, 2015. URL: https://pmc.ncbi.nlm.nih.gov/articles/PMC4495769/. ↩

  2. Loïc Yengo, Sailaja Vedantam, Eirini Marouli, Julia Sidorenko, Eric Bartell, Saori Sakaue, Marielisa Graff, Anders U Eliasen, Yunxuan Jiang, Sridharan Raghavan, and others. A saturated map of common genetic variants associated with human height. Nature, 610(7933):704–712, 2022. URL: https://www.nature.com/articles/s41586-022-05275-y. ↩