A frequentist test of proportional colocalization after selecting relevant genetic variants

• Objective: This paper introduced prop-coloc-cond, a novel frequentist test of proportional colocalization designed to assess whether two traits share the same causal genetic variants in a specific genomic region.
• Methodological Advance: The key innovation is that the test formally accounts for the uncertainty introduced by selecting the relevant genetic variants (e.g., through fine-mapping) before testing for proportionality, which ensures accurate Type I error control.
• Role in Research: This test provides a valuable complement to existing Bayesian colocalization methods, offering robust evidence based on different statistical assumptions, particularly useful when Bayesian results are inconclusive or sensitive to prior choices.

arXiv: 2402.12171 Overview generated by: Gemini 2.5 Flash, 28/11/2025

Key Findings: Proportional Colocalization Test

This paper proposes a novel frequentist test of proportional colocalization, named prop-coloc-cond, designed to assess whether two traits are affected by the same causal genetic variants in a specific genomic region. This method serves as a crucial complement to the widely-used Bayesian colocalization tests.

• Novel Frequentist Approach: The test is based on the concept of proportional colocalization, which posits that if two traits share the same causal variant(s), the vector of genetic associations for the first trait should be proportional to the vector of associations for the second trait in that region.
• Addressing Selection Uncertainty: A key methodological contribution is that the prop-coloc-cond test explicitly accounts for the uncertainty introduced by selecting the relevant genetic variants (e.g., fine-mapping or selecting the top SNPs) that are included in the test. By conditioning on the selection, the test achieves accurate Type I error control, ensuring reliable results in real-world applications.
• Complementary to Bayesian Methods: The prop-coloc-cond approach uses assumptions markedly different from those of Bayesian colocalization methods (like coloc). This offers a valuable alternative for obtaining complementary evidence, especially when Bayesian results are ambiguous, sensitive to prior distributions, or when the underlying assumptions of the Bayesian test are questionable.
• Simulations and Empirical Validation: Simulation studies demonstrated that the new method correctly controls the Type I error rate. The empirical investigation into the GLP1R gene expression locus confirmed the utility of the test in providing robust evidence of colocalization.
• Simplicity of Implementation: The test requires only summary data on genetic associations for the two traits, making it straightforward to implement using existing Genome-Wide Association Study (GWAS) results.

Study Design and Methods

Methodology

The study focuses on developing a new frequentist statistical test for colocalization, which contrasts with established Bayesian methods.

1. Proportional Colocalization Model: The core assumption is that the genetic association vector for trait 1 (\(\hat{\beta}_1\)) is proportional to the genetic association vector for trait 2 (\(\hat{\beta}_2\)), plus noise (\(\epsilon\)): \[\hat{\beta}_2 = \alpha \hat{\beta}_1 + \epsilon\] where \(\alpha\) is the proportionality constant, and the null hypothesis for colocalization is defined as \(\alpha \neq 0\).
2. Variant Selection: The authors first perform a step to select the relevant genetic variants in the region (e.g., using a conditional association approach or fine-mapping) to focus the analysis on the most likely causal SNPs.
3. Conditional Test (prop-coloc-cond): The innovation lies in deriving a test statistic (a modified F-statistic or Wald test) that is conditioned on the selection procedure. This conditioning step is crucial because performing a standard proportional test after selecting variants based on the data violates statistical assumptions and leads to inflated Type I error rates. The conditional test corrects for this selection bias.
4. Comparison: The performance of the prop-coloc-cond test was compared to a non-conditional proportional colocalization test and Bayesian colocalization methods using simulations under various genetic architectures (e.g., single causal variant, multiple causal variants).

Data Application

• Empirical Example: The method was applied to investigate the colocalization between gene expression of the GLP1R gene (Glucagon-like peptide 1 receptor) and Type 2 Diabetes (T2D) risk, demonstrating its ability to provide clear statistical evidence in a locus highly relevant to drug development.

Conclusions and Recommendations

The paper concludes that the prop-coloc-cond test provides a robust and valuable tool for colocalization analysis, enhancing the ability of researchers to distinguish between shared and distinct genetic etiology of traits.

• Enhancing Causal Inference: The test is recommended for use in conjunction with Bayesian methods to provide a more comprehensive and statistically rigorous assessment of colocalization, particularly in critical applications like drug target prioritization where mechanistic certainty is paramount.
• Future Directions: The authors suggest that the principle of conditional testing used in this work can be extended to develop frequentist approaches for other complex genetic association analyses, such as assessing heterogeneity or pleiotropy, where variant selection is a prerequisite.