Multivariate regression with missing response data for modelling regional DNA methylation QTLs

TL;DR

This paper introduces issoNet, a new convex estimation framework that accurately models regional DNA methylation QTLs with missing response data, avoiding bias from imputation and improving prediction and variable selection.

Contribution

The paper presents issoNet, a novel method for multivariate regression with missing responses, combining unbiased surrogate estimators with theoretical guarantees, outperforming existing methods.

Findings

issoNet outperforms existing methods in simulations.

It achieves superior predictive accuracy in real mQTL data.

It effectively identifies known and novel genetic associations.

Abstract

Identifying genetic regulators of DNA methylation (mQTLs) with multivariate models enhances statistical power, but is challenged by missing data from bisulfite sequencing. Standard imputation-based methods can introduce bias, limiting reliable inference. We propose \texttt{missoNet}, a novel convex estimation framework that jointly estimates regression coefficients and the precision matrix from data with missing responses. By using unbiased surrogate estimators, our three-stage procedure avoids imputation while simultaneously performing variable selection and learning the conditional dependence structure among responses. We establish theoretical error bounds, and our simulations demonstrate that \texttt{missoNet} consistently outperforms existing methods in both prediction and sparsity recovery. In a real-world mQTL analysis of the CARTaGENE cohort, \texttt{missoNet} achieved superior predictive accuracy and false-discovery control on a held-out validation set, identifying known and credible novel genetic associations. The method offers a robust, efficient, and theoretically grounded tool for genomic analyses, and is available as an R package.