Estimating longitudinal biomarker effects using a Lasso-network constrained time-Varying mixed effects model.

The relationship between covariates and outcomes can change over time, regardless of whether these covariates are time-varying or static. For instance, the influence of circulating biomarkers like white blood cell counts on the efficacy of standard chemotherapy in cancer patients may shift throughout the treatment duration. Traditional models with constant coefficients may fail to capture these dynamic interactions. Additionally, when multiple covariates are present, their interactions within and across time periods can become complex. To address these issues, we introduce a Lasso-Network constrained time-varying linear mixed-effects model (TVLMM) accompanied by an efficient two-stage parameter estimation algorithm that tracks the evolution of fixed-effect coefficients over time. We validate our approach through extensive simulations that highlight its effectiveness and computational efficiency in high-dimensional settings. Our method is further applied to real data from a randomized clinical trial of patients with metastatic colorectal cancer (mCRC), treated with standard chemotherapy with or without panitumumab. This case study demonstrates how our approach adeptly captures the time-varying impacts of critical circulating biomarkers on treatment outcomes, specifically tumor size reduction.