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Heritability conversion

GWASLab can convert Observed-scale heritability to Liability-scale heritability.

Quote

Conversion formula (Equation 23 from Lee. 2011): $$ h^2_{liability-scale} = h^2_{observed-scale} * {{K(1-K)}\over{Z^2}} * {{K(1-K)}\over{P(1-P)}} $$

  • \(K\) : Population disease prevalence.
  • \(P\) : Sample disease prevalence.
  • \(Z\) : The height of the standard normal probability density function at threshold T. scipy.stats.norm.pdf(T, loc=0, scale=1).
  • \(T\) : The threshold. scipy.stats.norm.ppf(1 - K, loc=0, scale=1) or scipy.stats.norm.isf(K).

Reference: Estimating Missing Heritability for Disease from Genome-wide Association Studies https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3059431/

gl.h2_obs_to_liab()

gl.h2_obs_to_liab(h2_obs, P, K, se_obs=None)

Parameters

  • h2_obs : float. Heritability on the observed scale in an ascertained sample.
  • P : float in (0,1). Prevalence of the phenotype in the sample.
  • K : float in (0,1) . Prevalence of the phenotype in the population.
  • se_obs : float. se of h2_obs.

Quote

Codes were adopted from LDSC.

Reference : Bulik-Sullivan, B. K., Loh, P. R., Finucane, H. K., Ripke, S., Yang, J., Patterson, N., ... & Neale, B. M. (2015). LD Score regression distinguishes confounding from polygenicity in genome-wide association studies. Nature genetics, 47(3), 291-295.