Using Importance Sampling to Estimate $p$-values in All-Subset Meta-Analysis, with Applications to Single-Cell eQTL Mapping

TL;DR

This paper introduces an importance-sampling algorithm to accurately estimate p-values in all-subset meta-analysis, especially for very small p-values, improving over traditional methods in genetic association studies.

Contribution

It develops a computationally efficient importance-sampling method that enhances p-value estimation accuracy in meta-analyses, particularly when normality assumptions are violated.

Findings

IS method provides accurate p-value estimates for small p-values.

ASSET's analytic approximation is accurate under normality.

The method is applied to single-cell eQTL mapping in diverse cohorts.

Abstract

Pooling genome-wide association studies of multiple related traits can substantially increase power for detecting genetic variants with pleiotropic effects. ASSET, which exhaustively searches all subsets of studies for association signals, has been widely used to detect modest effects and improve interpretability. Under a normality assumption, ASSET computes p-values via an analytic approximation that accounts for multiple testing. However, this approximation has been evaluated only in limited scenarios and for p-values no smaller than $10^{-3}$. A systematic assessment in the extreme tail is therefore needed, yet na\"ive Monte Carlo methods would require prohibitively many simulations. We develop a computationally efficient importance-sampling (IS) algorithm that provides accurate ASSET p-value estimates for both independent and overlapping studies, achieving substantial efficiency gains over na\"ive Monte Carlo, particularly for very small p-values. Using IS, we show that ASSET's analytic approximation is highly accurate across nearly the entire p-value range when normality holds. In contrast, when normality is violated (due to small sample sizes, low-frequency variants, or non-normal traits), ASSET p-values can be inflated or deflated by orders of magnitude, whereas our IS approach remains accurate. We illustrate the method through applications to single-cell eQTL mapping using peripheral blood mononuclear cells from the OneK1K cohort and lung cells from a Korean population.