Bayesian semiparametric modelling of biomarker variability in joint models

Summary: There is growing interest in the role of within-individual variability (WIV) in biomarker trajectories for assessing disease risk and progression. A trajectory-based definition that has attracted recent attention characterises WIV as the curvature-based roughness of the latent biomarker trajectory (TB-WIV). To evaluate TB-WIV associa tions with clinical outcomes and perform dynamic risk prediction, joint models for longitudinal and time-to-event data (JM) are necessary. However, specifying the longitudinal trajectory is critical and poses methodological challenges. In this work, we investigate three Bayesian semiparametric approaches for longitudinal modelling and TB-WIV estimation. We propose two new approaches based on Bayesian penalised splines (P-splines) and functional principal component analysis (FPCA), and adapt an existing semiparametric approach to the Bayesian JM setting. Through simulation studies, we evaluate parameter estimation, detection of TB-WIV associations, estimation of their raw and standardized magnitudes, and survival prediction, providing insights for method choice and highlighting the need for caution when interpreting raw TB-WIV association magnitudes. We apply the approaches to UK Cystic Fibrosis Registry data, where we identify significant positive associations between lung function TB-WIV and mortality risk in patients with cystic fibrosis, after adjustment for the underlying lung function level, and provide evidence that TB-WIV adds information for survival prediction.