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.

Preparing the simulation…