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Per SNP Heritability

GWASLab provides a function to calculate the variance explained by each SNP (per-SNP heritability or R²), which is useful for Mendelian randomization, polygenic risk scores, and understanding the contribution of individual variants to trait variance.

Available since v3.4.20

.get_per_snp_r2()

Calculates the proportion of variance explained by each SNP and optionally computes F-statistics for instrument strength assessment.

mysumstats.get_per_snp_r2(**kwargs)

Required Columns

  • For quantitative traits (mode="q"): BETA and EAF (effect allele frequency)
  • For binary traits (mode="b"): BETA, EAF, plus ncase, ncontrol, and prevalence parameters
  • For F-statistics: N (sample size) column

Parameters

General Parameters

Parameter DataType Description Default
mode str Trait type: "q" for quantitative, "b" for binary "q"
beta str Column name for effect size (beta coefficient) "BETA"
af str Column name for effect allele frequency "EAF"
n str Column name for sample size "N"
se str Column name for standard error (used when vary="se") "SE"
adjuested bool If True, calculate adjusted R² False
verbose bool Print progress messages True

Parameters for Quantitative Traits (mode="q")

Parameter DataType Description Default
vary float or "se" Variance of the phenotype Y. If "se", Var(Y) is estimated from SE, N, and MAF 1
k int or "all" Number of parameters for F-statistic calculation. Use "all" to set k = number of SNPs 1

Parameters for Binary Traits (mode="b")

Parameter DataType Description Default
ncase int Number of cases in the study Required
ncontrol int Number of controls in the study Required
prevalence float Disease prevalence in the general population (0-1) Required

Output Columns

The function adds the following columns to the sumstats:

  • SNPR2: Proportion of variance explained by each SNP (R²)
  • ADJUESTED_SNPR2: Adjusted R² (only if adjuested=True)
  • F: F-statistic for instrument strength (only if N column is available)
  • _VAR(BETAX): Variance of BETA × X (intermediate calculation for quantitative traits)
  • _SIGMA2: Error variance (intermediate calculation when vary="se")
  • _POPAF: Population allele frequency (intermediate calculation for binary traits)
  • _VG: Genetic variance (intermediate calculation for binary traits)

Quantitative Traits (mode="q")

For quantitative traits, the variance explained by SNP \(i\) is calculated as:

\[ R^2_i = \frac{Var(\beta_i \times X_i)}{Var(Y)} \]

Where:

  • \(Var(\beta_i \times X_i) = 2 \times \beta_i^2 \times **EAF**_i \times (1 - **EAF**_i)\)

  • \(Var(Y)\) depends on the vary parameter:

  • If vary is a number: \(Var(Y) = \text{vary}\)

  • If vary="se": \(Var(Y) = Var(\beta_i \times X_i) + **SE**_i^2 \times 2 \times **N** \times **EAF**_i \times (1 - **EAF**_i)\)

F-statistic (when N is available):

\[ F_i = \frac{R^2_i \times (N - k - 1)}{(1 - R^2_i) \times k} \]

Where \(k\) is the number of parameters (default: 1).

When vary=1 and k=1

The simplified formulas are:

\[ R^2_i = 2 \times \beta_i^2 \times EAF_i \times (1 - EAF_i) \]
\[ F_i = \frac{R^2_i \times (N - 2)}{1 - R^2_i} \]

Reference for quantitative traits

Shim, H., Chasman, D. I., Smith, J. D., Mora, S., Ridker, P. M., Nickerson, D. A., ... & Stephens, M. (2015). A multivariate genome-wide association analysis of 10 LDL subfractions, and their response to statin treatment, in 1868 Caucasians. PloS one, 10(4), e0120758.

Binary Traits (mode="b")

For binary traits, the function estimates the variance of liability explained by each variant using a liability threshold model.

The calculation involves:

  1. Estimating population allele frequency from sample allele frequency, case-control ratio, odds ratio, and population prevalence
  2. Calculating genetic variance: \(V_G = \beta^2 \times p \times (1-p)\) where \(p\) is the population allele frequency
  3. Calculating R²: \(R^2 = \frac{V_G}{V_G + V_E}\) where \(V_E = \frac{\pi^2}{3} \approx 3.29\) (error variance for logistic regression)

Reference for binary traits

Equation 10 in Lee, S. H., Goddard, M. E., Wray, N. R., & Visscher, P. M. (2012). A better coefficient of determination for genetic profile analysis. Genetic epidemiology, 36(3), 214-224.

Implementation adopted from TwoSampleMR.

Examples

Basic usage for quantitative trait:

import gwaslab as gl

# Load sumstats
mysumstats = gl.Sumstats("t2d_bbj.txt.gz", 
                         snpid="SNP",
                         chrom="CHR",
                         pos="POS",
                         ea="ALT",
                         nea="REF",
                         neaf="Frq",
                         beta="BETA",
                         se="SE",
                         n=170000)

# Calculate per-SNP R² with default settings (vary=1)
mysumstats.get_per_snp_r2()

# View results
print(mysumstats.data[["SNP", "BETA", "EAF", "SNPR2", "F"]].head())

Quantitative trait with estimated Var(Y):

# Estimate Var(Y) from SE, N, and MAF
mysumstats.get_per_snp_r2(vary="se")

Quantitative trait with custom Var(Y):

# Provide known variance of the phenotype
mysumstats.get_per_snp_r2(vary=2.5)

Binary trait:

# For binary traits, provide case/control counts and prevalence
mysumstats.get_per_snp_r2(mode="b",
                          ncase=8500,
                          ncontrol=161500,
                          prevalence=0.10)

With adjusted R²:

# Calculate adjusted R²
mysumstats.get_per_snp_r2(adjuested=True)

Custom k for F-statistic:

# Use k=10 for F-statistic calculation
mysumstats.get_per_snp_r2(k=10)

# Or use all SNPs as k
mysumstats.get_per_snp_r2(k="all")

Use Cases

  • Mendelian Randomization: F-statistics > 10 indicate strong instruments
  • Polygenic Risk Scores: R² values help assess individual variant contributions
  • Power Analysis: Understanding variance explained by each variant
  • Quality Control: Identifying variants with unexpectedly high or low R² values