Local False Sign Rate (lfsr)

Summary

The Local False Sign Rate (lfsr) is a statistical metric used to assess the significance and direction of an estimated genetic effect on a specific trait. Used extensively in multitrait fine-mapping (e.g., mvSuSiE) and multivariate sharing analysis (e.g., mash), lfsr measures the probability that the estimated sign (positive or negative) of a variant's effect is incorrect. It serves as a more conservative and informative alternative to traditional local false discovery rates (lfdr).

Mathematical Formulation

For a genetic variant $j$ and a trait $r$, let $b_{jr}$ be the true effect size. The local false sign rate is defined as: $$\text{lfsr}{jr} = 1 - \max \left( P(b) \right)$$ where: - $P(b_{jr} > 0 \mid \text{data})$ is the posterior probability that the effect is strictly positive. - $P(b_{jr} < 0 \mid \text{data})$ is the posterior probability that the effect is strictly negative.} > 0 \mid \text{data}), P(b_{jr} < 0 \mid \text{data

CS-Level Average lfsr

In mvSuSiE, because variants in a credible set (CS) are in high linkage disequilibrium and share similar properties, a trait-wise significance measure is computed by averaging the lfsr of the variants in the CS: $$\text{Average lfsr}(CS, r) = \sum_{j \in CS} \alpha_j \text{lfsr}_{jr}$$ where $\alpha_j$ is the posterior probability of variant $j$ being the causal variant. A CS is considered significantly associated with trait $r$ if the average lfsr is below a threshold (typically $0.05$ or $0.01$).

Citations

• Urbut, S. M., Wang, G., Carbonetto, P., & Stephens, M. (2019). Flexible statistical methods for estimating and testing effects in genomic studies with multiple conditions. Nature Genetics, 51(1), 187–195.
• Zou, Y., Carbonetto, P., Xie, D., Wang, G., & Stephens, M. (2026). Fast and flexible joint fine-mapping of multiple traits via the Sum of Single Effects model. Nature Genetics.