Background Joint models of longitudinal and time-to-event data are essential for dynamic prediction in chronic disease research, but standard formulations typically assume linear biomarker–hazard associations and unidirectional influence from biomarkers to events. These assumptions are often violated in multimorbidity and oncology, where clinical events alter subsequent biomarker trajectories and where biomarker–risk relationships are non-linear or threshold-like. Methods that relax both assumptions simultaneously, and that are accessible to applied researchers, are currently lacking. Methods We extend the joint modeling framework through the <Emphasis FontCategory="NonProportional">JMbdirect</Emphasis> package by introducing semi-parametric association structures based on penalized splines and neural additive components, and by embedding explicit bidirectional feedback between events and biomarkers via post-event level shifts and slope changes in the longitudinal trajectory. Estimation is supported via penalized maximum likelihood with Laplace approximation and a Bayesian alternative using Hamiltonian Monte Carlo. Performance was assessed in simulation studies crossing four design factors (form of the association function, presence and magnitude of feedback, single versus competing events, and baseline hazard specification) at sample sizes <InlineEquation ID="IEq1"><EquationSource Format="TEX">\(n \in \{200, 500, 1000\}\)</EquationSource></InlineEquation>, and in an applied analysis of the primary biliary cirrhosis (PBC) cohort. Results Incorporating feedback and flexible links improved discrimination and calibration relative to classical linear specifications, particularly under non-linear risk mechanisms. In the representative competing-risks scenario (<InlineEquation ID="IEq2"><EquationSource Format="TEX">\(n=500\)</EquationSource></InlineEquation>), the spline-with-feedback estimator attained AUC@5 of 0.85 and an integrated Brier score of 0.134 with near-nominal 95% coverage, compared with AUC@5 of 0.72, an integrated Brier score of 0.168 and 88% coverage for the linear model without feedback; calibration slopes were 0.99 and 0.74, respectively. Feedback parameters were recovered with negligible bias at moderate and strong magnitudes. In the PBC application, the spline-based model identified a threshold effect at approximately 3 mg/dL of serum bilirubin and improved cross-validated discrimination (AUC@5 0.78 versus 0.71 for the linear specification). Conclusions Flexible association structures and explicit bidirectional feedback yield more accurate and more interpretable dynamic predictions than classical joint models, with manageable computational cost. By combining these methodological advances with an open-source R package and a publicly available dashboard interface, this work supports the translation of joint modeling into personalized risk prediction and clinical decision support in multimorbid populations.

JMbdirect: joint modeling with semi-parametric link functions for bidirectional feedback in longitudinal-survival data

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2026年8月1日

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Atanu Bhattacharjee

摘要

Background

Joint models of longitudinal and time-to-event data are essential for dynamic prediction in chronic disease research, but standard formulations typically assume linear biomarker–hazard associations and unidirectional influence from biomarkers to events. These assumptions are often violated in multimorbidity and oncology, where clinical events alter subsequent biomarker trajectories and where biomarker–risk relationships are non-linear or threshold-like. Methods that relax both assumptions simultaneously, and that are accessible to applied researchers, are currently lacking.

Methods

We extend the joint modeling framework through the JMbdirect package by introducing semi-parametric association structures based on penalized splines and neural additive components, and by embedding explicit bidirectional feedback between events and biomarkers via post-event level shifts and slope changes in the longitudinal trajectory. Estimation is supported via penalized maximum likelihood with Laplace approximation and a Bayesian alternative using Hamiltonian Monte Carlo. Performance was assessed in simulation studies crossing four design factors (form of the association function, presence and magnitude of feedback, single versus competing events, and baseline hazard specification) at sample sizes \(n \in \{200, 500, 1000\}\), and in an applied analysis of the primary biliary cirrhosis (PBC) cohort.

Results

Incorporating feedback and flexible links improved discrimination and calibration relative to classical linear specifications, particularly under non-linear risk mechanisms. In the representative competing-risks scenario (\(n=500\)), the spline-with-feedback estimator attained AUC@5 of 0.85 and an integrated Brier score of 0.134 with near-nominal 95% coverage, compared with AUC@5 of 0.72, an integrated Brier score of 0.168 and 88% coverage for the linear model without feedback; calibration slopes were 0.99 and 0.74, respectively. Feedback parameters were recovered with negligible bias at moderate and strong magnitudes. In the PBC application, the spline-based model identified a threshold effect at approximately 3 mg/dL of serum bilirubin and improved cross-validated discrimination (AUC@5 0.78 versus 0.71 for the linear specification).

Conclusions

Flexible association structures and explicit bidirectional feedback yield more accurate and more interpretable dynamic predictions than classical joint models, with manageable computational cost. By combining these methodological advances with an open-source R package and a publicly available dashboard interface, this work supports the translation of joint modeling into personalized risk prediction and clinical decision support in multimorbid populations.