Heritability conversion

GWASLab provides functions to convert heritability estimates between observed-scale and liability-scale, which is essential for comparing heritability estimates across studies with different case-control ratios or for binary traits.

When to use liability-scale conversion

For binary (case-control) traits, heritability estimates depend on the case-control ratio in the sample. To compare heritability estimates across studies or to estimate population-level heritability, conversion to the liability scale is necessary. The liability scale assumes an underlying continuous liability distribution with a threshold model for disease.

gl.h2_obs_to_liab()

Converts heritability on the observed scale in an ascertained sample to heritability on the liability scale in the population.

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 (proportion of cases).
• K : float in (0,1)
  • Prevalence of the phenotype in the population (proportion in general population).
• se_obs : float, optional
  • Standard error of h2_obs. If provided, the function will also return the standard error on the liability scale.

Returns

• If se_obs is None: Returns a single float value h2_liab (heritability on liability scale).
• If se_obs is provided: Returns a tuple (h2_liab, se_liab) where:
  • h2_liab : float - Heritability on the liability scale.
  • se_liab : float - Standard error of heritability on the liability scale.

Examples

Basic conversion without standard error:

import gwaslab as gl

# Example: Type 2 diabetes
# Observed-scale heritability from LDSC
h2_obs = 0.15

# Sample prevalence (50% cases in the study)
P = 0.5

# Population prevalence (estimated 10% in general population)
K = 0.10

# Convert to liability scale
h2_liab = gl.h2_obs_to_liab(h2_obs, P, K)
print(f"Liability-scale heritability: {h2_liab:.4f}")

Conversion with standard error:

# With standard error
h2_obs = 0.15
se_obs = 0.02
P = 0.5
K = 0.10

h2_liab, se_liab = gl.h2_obs_to_liab(h2_obs, P, K, se_obs=se_obs)
print(f"Liability-scale heritability: {h2_liab:.4f} ± {se_liab:.4f}")

Handling missing prevalence values:

If both P and K are NaN, the function returns h2_obs unchanged (no conversion applied).

gl.h2_se_to_p()

Converts a heritability estimate and its standard error to a p-value using a one-sided test.

gl.h2_se_to_p(h2, se)

Parameters

• h2 : float
  • Heritability estimate (can be on observed or liability scale).
• se : float
  • Standard error of the heritability estimate.

Returns

• p_value : float
  • One-sided p-value testing whether the heritability is significantly greater than zero.

Example

import gwaslab as gl

# Heritability estimate and standard error
h2 = 0.15
se = 0.02

# Calculate p-value
p_value = gl.h2_se_to_p(h2, se)
print(f"P-value: {p_value:.4e}")