SOLVE: A structured orthogonal latent variable framework for disentangling confounding in matrix data.

Area of Science:

• Bioinformatics
• Computational Biology
• Genomics

Background:

• Latent factor models are crucial in bioinformatics for handling unmeasured variation alongside observed covariates.
• Existing methods often struggle to differentiate known effects from latent structures and manage complex loss functions.
• There is a need for robust models that can jointly analyze measured effects and residual variation for improved biological insights.

Purpose of the Study:

• To present a unified framework for latent factor modeling that augments predictors with a low-rank latent component.
• To ensure identifiability and interpretability by imposing orthogonality constraints on coefficient and latent factor matrices.
• To develop an efficient algorithm capable of handling general non-quadratic losses and provide valid statistical inference.

Main Methods:

• A unified framework incorporating a low-rank latent component with row and column predictors.
• Orthogonality constraints on coefficient and latent factor matrices for identifiability and interpretability.
• An efficient algorithm using monotone descent, truncated singular value decomposition, and projections for parameter updates.
• Selection of the number of latent factors using a degrees-of-freedom-adjusted information criterion and an elbow rule.
• Parametric bootstrap for valid inference on feature-outcome associations.

Main Results:

• The framework successfully separates measured effects from residual variation, capturing unexplained variance.
• Application to pharmacogenomic data identified biologically coherent gene-drug associations, including EGFR-inhibitor links.
• Novel candidate biomarkers and gene programs related to drug sensitivity and resistance mechanisms were revealed.
• The model demonstrated improved interpretability and identified a latent unfolded-protein-response module influencing drug sensitivity.

Conclusions:

• The proposed framework offers a powerful tool for analyzing complex biological data, particularly in pharmacogenomics.
• It enhances the discovery of biomarkers for patient stratification and provides deeper insights into drug resistance.
• The method's ability to handle non-quadratic losses and ensure identifiability makes it broadly applicable in precision oncology.