Mixed-Effects & Joint Model Explorer
Simulate patient-specific longitudinal biomarker trajectories linked to a survival hazard, and see how the association parameter α couples the two submodels.
- mixed-effects models
- joint models
- longitudinal data
- random effects
Individual trajectories with random effects
Mean biomarker vs. event/censor time
Crosses = event; circles = censored (color-coded by outcome via position)
Simulation summary
Patients
30.000
Events
16.000
Censored
14.000
Corr(biomarker, event time)
-0.174
One latent trajectory, two submodels, one linkage parameter
The dashed line is the population-average trajectory; the faint solid lines are each patient's true latent trajectory $m_i(t)$; the scattered points are noisy observed measurements. The association parameter α links that latent trajectory to the hazard: with α > 0, patients with higher orange-dot biomarker levels cluster toward shorter event times in the lower panel — exactly the informative-biomarker scenario a joint model is built to exploit, and a baseline-only Cox model would miss.