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Credible Set Purity

Summary

Credible Set Purity is a metric used in statistical fine-mapping to assess the correlation (linkage disequilibrium, or LD) among genetic variants contained within an estimated credible set (CS). High purity indicates that the variants in the CS are highly correlated, meaning they represent a single, clear association signal. Credible sets with low purity are typically discarded because they represent diffuse or unreliable signals.

Mathematical Formulation

Single-Ancestry Purity

In a single-population analysis (e.g., standard SuSiE), the purity of a credible set $CS$ is defined as the minimum absolute correlation among all pairwise combinations of SNPs within that set: $$\text{Purity}(CS) = \min_{j, j' \in CS} |r_{j,j'}|$$ where $r_{j,j'}$ is the Pearson correlation coefficient (measuring linkage disequilibrium) between variant $j$ and variant $j'$ in the sample.

Multi-Ancestry Purity (SuShiE)

In a multi-ancestry or multi-population context (e.g., SuShiE), where a credible set may span multiple populations with different LD patterns, the overall purity is calculated as a sample-size-weighted average of ancestry-specific purities: $$\phi = \frac{1}{n} \sum_{i=1}^k n_i \phi_i$$ where: - $k$ is the number of ancestries. - $\phi_i$ is the purity of the credible set in ancestry $i$, calculated using the ancestry-specific LD matrix. - $n_i$ is the sample size for ancestry $i$. - $n$ is the total sample size across all ancestries ($n = \sum_{i=1}^k n_i$).

Typically, a threshold of $\phi \ge 0.5$ is applied to retain credible sets.

Citations

  • Wang, G., Sarkar, A., Carbonetto, P., & Stephens, M. (2020). A simple new approach to variable selection in regression, with application to genetic fine mapping. Journal of the Royal Statistical Society: Series B.
  • Lu, Z., Wang, X., Carr, M., Kim, A., Gazal, S., Mohammadi, P., Wu, L., Pirruccello, J., Kachuri, L., Gusev, A., & Mancuso, N. (2025). Improved multiancestry fine-mapping identifies cis-regulatory variants underlying molecular traits and disease risk. Nature Genetics.