Direct estimation and inference of higher-level correlations from lower-level measurements with applications in gene-pathway and proteomics studies

TL;DR

This paper introduces a latent factor model that directly estimates higher-level correlations from lower-level biological measurements, avoiding data aggregation and improving accuracy in gene-pathway and proteomics studies.

Contribution

A novel latent factor approach for direct estimation of higher-level correlations from lower-level data, with a shrinkage estimator and asymptotic normality for inference.

Findings

Accurate estimation of higher-level correlations demonstrated in simulations.

Effective application to proteomics and gene expression datasets.

R package highcor implemented for practical use.

Abstract

This paper tackles the challenge of estimating correlations between higher-level biological variables (e.g., proteins and gene pathways) when only lower-level measurements are directly observed (e.g., peptides and individual genes). Existing methods typically aggregate lower-level data into higher-level variables and then estimate correlations based on the aggregated data. However, different data aggregation methods can yield varying correlation estimates as they target different higher-level quantities. Our solution is a latent factor model that directly estimates these higher-level correlations from lower-level data without the need for data aggregation. We further introduce a shrinkage estimator to ensure the positive definiteness and improve the accuracy of the estimated correlation matrix. Furthermore, we establish the asymptotic normality of our estimator, enabling efficient computation of p-values for the identification of significant correlations. The effectiveness of our approach is demonstrated through comprehensive simulations and the analysis of proteomics and gene expression datasets. We develop the R package highcor for implementing our method.