Reading the whole PSA trajectory to predict survival
Joint longitudinal–survival modelling links a patient's full PSA trajectory to mortality in metastatic prostate cancer.
The published work
The challenge
PSA is usually summarised at a single time point, but a patient's biomarker trajectory over time carries far more information about how their disease is behaving. Standard analyses also struggle with informative dropout — patients who die stop contributing biomarker measurements, and ignoring that biases the picture.
The approach
Red Door Analytics' Sara Ekberg and Michael Crowther brought joint models of longitudinal and survival data to the problem, linking each patient's entire PSA trajectory to overall survival while accounting for individual variation and informative dropout. The study, in patients with metastatic hormone-sensitive prostate cancer, was published in European Urology Oncology.
What it found
A strong decline in PSA was associated with reduced mortality: each doubling of the rate of decline was linked to a 29% lower risk of death — a relationship that modelling the full trajectory makes visible in a way single-time-point measurements cannot.
Why it matters
Joint modelling applies far beyond prostate cancer — to any biomarker tracked over time, including kidney function, blood glucose, tumour size, and quality-of-life scores.
It is a direct application of the joint longitudinal–survival modelling built into the merlin family — the same methods the team develops, teaches, and ships as software.