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Colocalization Posterior Probability (CLPP)

Summary

Colocalization Posterior Probability (CLPP) is a Bayesian metric used to evaluate whether two distinct traits share a common causal genetic variant in a genomic region. Originally defined in the context of the eCAVIAR framework, CLPP calculates the probability of shared causality by summing the product of the posterior inclusion probabilities (PIPs) of individual variants across the locus.

Mathematical Formulation

CLPP is calculated across a genomic locus containing $M$ variants as: $$\text{CLPP} = \sum_{j=1}^M \text{PIP}{j, \text{Trait 1}} \times \text{PIP}$$ where: - $\text{PIP}}{j, \text{Trait 1}}$ is the posterior inclusion probability (PIP) of variant $j$ being causal for Trait 1. - $\text{PIP}$ is the posterior inclusion probability (PIP) of variant $j$ being causal for Trait 2.}

In studies of genetic colocalization, a CLPP threshold is used to prioritize high-confidence colocalized signals (e.g., CLPP $> 0.04$ or CLPP $> 0.01$). When single causal variant assumptions are enforced, colocalization models like coloc report the posterior probability of hypothesis 4 ($PP.H4$), representing the probability of a shared causal variant, which is sometimes also referred to as a colocalization posterior probability (with thresholds typically set at $PP.H4 > 0.9$).

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