# PROLONG: penalized regression for outcome guided longitudinal omics analysis with network and group constraints

## TL;DR

PROLONG is a new statistical method for analyzing longitudinal omics data to identify biomarkers that change over time with a clinical outcome.

## Contribution

PROLONG introduces a penalized regression approach combining group lasso and Laplacian penalties for longitudinal omics data analysis.

## Key findings

- PROLONG achieves high specificity and sensitivity in selecting target metabolites across various scenarios.
- The method successfully identifies interesting metabolite targets from real tuberculosis data.
- PROLONG improves power by leveraging first differences and incorporating variable dependencies.

## Abstract

There is a growing interest in longitudinal omics data paired with some longitudinal clinical outcome. Given a large set of continuous omics variables and some continuous clinical outcome, each measured for a few subjects at only a few time points, we seek to identify those variables that co-vary over time with the outcome. To motivate this problem we study a dataset with hundreds of urinary metabolites along with Tuberculosis mycobacterial load as our clinical outcome, with the objective of identifying potential biomarkers for disease progression. For such data clinicians usually apply simple linear mixed effects models which often lack power given the low number of replicates and time points. We propose a penalized regression approach on the first differences of the data that extends the lasso + Laplacian method [Li and Li (Network-constrained regularization and variable selection for analysis of genomic data. Bioinformatics 2008;24:1175–82.)] to a longitudinal group lasso + Laplacian approach. Our method, PROLONG, leverages the first differences of the data to increase power by pairing the consecutive time points. The Laplacian penalty incorporates the dependence structure of the variables, and the group lasso penalty induces sparsity while grouping together all contemporaneous and lag terms for each omic variable in the model.

With an automated selection of model hyper-parameters, PROLONG correctly selects target metabolites with high specificity and sensitivity across a wide range of scenarios. PROLONG selects a set of metabolites from the real data that includes interesting targets identified during EDA.

An R package implementing described methods called “prolong” is available at https://github.com/stevebroll/prolong. Code snapshot available at 10.5281/zenodo.14804245.