Hierarchical mixed effects cubic spline modeling of methylation-based tumor fraction dynamics for pan-cancer assessment of treatment response and outcomes in immunotherapy patients

Background: Methylation-based tumor fraction (TF) dynamics are a promising surrogate marker for monitoring disease, but their evolution varies widely across patients and cancer types. To characterize these patterns, we developed a hierarchical mixed-effects cubic spline model that captures non-linear longitudinal TF trends while accounting for patient-level heterogeneity and clinical covariates. Compared with traditional approaches, this framework supports multiple cancer types, baseline factors, and generates outcome-stratified trajectories (e.g., disease progression and survival). By enabling trajectory bifurcation by outcome, the model simultaneously reflects treatment response and prognosis, improving our understanding of how TF dynamics relate to therapeutic efficacy across diverse cancer types. Methods: We analyzed 519 patients from the RADIOHEAD study consisting of 1,070 immunotherapy-naive patients receiving standard-of-care immune checkpoint inhibitor (ICI) regimens. Included patients had ≥2 plasma samples beyond baseline. TF was measured using Guardant Reveal, a clinically validated methylation-based assay. Model selection using Akaike information criterion compared linear, non-linear, and spline models; a natural cubic spline with five knots best fit the data. Covariates included age, smoking status, stage (III vs IV), and gender. Cancer types analyzed were lung, bladder, melanoma, renal cell carcinoma, and head and neck carcinoma. Binary outcomes were 15-month survival (alive/deceased) and disease progression (yes/no). Results: Because spline coefficients are not interpretable, findings were presented graphically. After adjusting for covariates, TF trajectories diverged beyond 95% confidence bands and exhibited distinct patterns by cancer type and outcome. An interactive R Shiny application was developed to display these trajectories, along with velocity plots providing the instantaneous rate of TF change to aid interpretation. Conclusions: This analysis provides a framework for characterizing TF evolution during immunotherapy and how these dynamics differentiate clinical outcomes across cancer types. Outcome-stratified trajectories and TF velocity may help identify early indicators of treatment response, supporting more informed therapeutic decisions. Additionally, since TF dynamics vary by disease indication, future studies could integrate TF dynamics with genomic and other clinical indicators to better understand response mechanisms, resistance factors, and other biological drivers that may underly a heterogeneous response to ICIs.