Posterior Inclusion Probability (PIP)

Summary

The Posterior Inclusion Probability (PIP) is a Bayesian statistical metric used extensively in genetic fine-mapping. It quantifies the probability that a specific genetic variant is causally associated with a trait of interest, given the observed data and prior assumptions. PIP is a core output of methods like the Sum of Single Effects (SuSiE) model and its multi-ancestry/multi-trait extensions.

Mathematical Formulation

Single-Trait/Single-Population SuSiE PIP

In the Sum of Single Effects (SuSiE) model, which decomposes the regression into $L$ single-effect components (where each component contains exactly one causal variant), the PIP for variant $j$ is the probability that it is the causal variant in at least one of the $L$ components: $$\text{PIP}j = 1 - \prod\right)$$ where $\alpha_j^{(l)}$ is the posterior probability that variant $j$ is the causal variant in the $l$-th single-effect regression component.}^L \left(1 - \alpha_j^{(l)

Multi-Ancestry Post Hoc PIP (PIPmeta)

In a multi-ancestry post hoc analysis (e.g., PIPmeta), where single-ancestry fine-mapping has been performed independently in $K$ cohorts, the joint PIP for variant $i$ is calculated under the assumption that causality is independent across ancestries: $$\text{PIP}i = 1 - \prod}^K \left(1 - \text{PIP{i,k}\right)$$ where $\text{PIP}$ is the PIP of variant $i$ estimated using SuSiE in ancestry $k$.

Marginal Posterior Probability Terminology

flashfmZero reports a variant's marginal posterior probability (MPP) of causal association with a latent factor. Operationally, this is the same type of marginal causal probability commonly called PIP: posterior support for models containing the variant, summed across compatible causal configurations. The package also reports MPPg, which aggregates posterior probability across a high-LD SNP group whose variants remain statistically interchangeable.[1]

An MPP or PIP above 0.90 is a common high-confidence reporting threshold, but it is not a universal decision rule. Its calibration depends on the fine-mapping model, priors, LD accuracy and whether the causal variants are represented in the analyzed data.

Citations

[1] Astle, Butterworth and Asimit (2025), flashfmZero protocol - 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. - Rossen, J., Shi, H., Strober, B. J., Zhang, M. J., Kanai, M., McCaw, Z. R., Liang, L., Weissbrod, O., & Price, A. L. (2026). MultiSuSiE improves multi-ancestry fine-mapping in All of Us whole-genome sequencing data. Nature Genetics.