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

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.