Joint modelling
A biomarker, a score or a repeated measurement that changes over time often says something about the risk of an event. A joint model links the two, so the trajectory and the event are analysed together instead of one after the other. We design, fit and interpret joint models for clinical-trial data, electronic health records and registers, and explain what they show.
Built by the people who wrote the methods and the software. merlin, our own framework, fits joint models in R and Stata.
Four kinds of question
The model has to follow the question, not the other way round. These are the questions we are asked most.
A biomarker that predicts survival
Joint models link a repeatedly measured outcome, such as a biomarker tracked over time, with a survival outcome, through shared random effects or functions of them.
Measurement error and visit patterns
A biomarker measured with error, or recorded only when a patient is seen, can mislead a standard survival analysis. A joint model can allow for both.
Dropout and competing events
Patients drop out, die or have another event that changes the picture. Joint models can allow for non-ignorable dropout and for competing risks.
An answer a clinician can use
Predicted survival from the whole trajectory of a biomarker, and quality-adjusted life years after a joint model, rather than coefficients alone.
One patient’s biomarker: measured (dots), then predicted ahead (dashed)
and the chance of staying event-free for the next 3 years, updated at each visit
From the model to what it means
Most engagements are one of these, or a few of them together.
Design the model around the question
Which longitudinal process, which link to the risk of the event, and how the model will be checked: chosen from the clinical question and the data you have.
Fit it with the software we wrote
Joint models with one or several biomarkers, with time-dependent effects, competing risks or recurrent events, fitted in the merlin family, in R and Stata.
Predict and explain
Predictions of survival from a patient's whole trajectory, with the uncertainty around them, and what a biomarker response means for outcomes.
Quality-adjusted life years
QALYs after a joint model, with jmqaly: quality of life weighted by the probability of being alive to experience it, up to a horizon you choose.
Trial, record and register data
Applied to clinical-trial data and electronic health records, and to Swedish register data. See also our real-world evidence work.
Teaching your team
The methods taught hands-on, in our open course on joint modelling of longitudinal and survival data, or as bespoke in-house training.
Joint-model methods we have developed
Ten peer-reviewed papers on joint models, each with Michael Crowther as an author, published between 2012 and 2026. Where a method became software, the software paper is listed too.
- 2026A Framework for the Estimation of Quality-Adjusted Life-Years Using Joint Models of Longitudinal and Survival Data. Medical Decision Making 2026. View → Worked example → jmqaly →
- 2025
- 2020Faster Monte Carlo estimation of semiparametric joint models for time-to-event and multivariate longitudinal data. Computational Statistics and Data Analysis 2020;151:107010. View →
- 2020Mixed effects models for healthcare longitudinal data with an informative visiting process: a Monte Carlo simulation study. Statistica Neerlandica 2020;74(1):5-23. View →
- 2018Joint longitudinal and time-to-event models for multilevel hierarchical data. Statistical Methods in Medical Research 2018;28(12):3502-3515. View →
- 2016Joint longitudinal hurdle and time-to-event models: an application related to viral load and duration of the first treatment regimen in patients with HIV initiating therapy. Statistics in Medicine 2016;35(20):3583–3594. View →
- 2016Joint modelling of longitudinal and survival data: Incorporating delayed entry and an assessment of model misspecification. Statistics in Medicine 2016;35(7)1193-1209. View →
- 2015Joint modelling of survival and longitudinal non-survival data: current methods and issues. Report of the DIA Bayesian joint modelling working group. Statistics in Medicine 2015;34(14):2181-2195. View →
- 2013Adjusting for measurement error in baseline prognostic biomarkers included in a time-to-event analysis: A joint modelling approach. BMC Medical Research Methodology 2013;13:146. View →
- 2012Flexible parametric joint modelling of longitudinal and survival data. Statistics in Medicine 2012;31(30):4456-4471. View →
The software papers
- 2020
- 2013
Published work
The question, the approach, and what it showed.
The people who wrote the methods and the software
The expertise behind this work is published and open to inspection.
merlin
Our framework for survival, joint, multi-state and competing-risks models, maintained in R and Stata.
jmqaly
Quality-adjusted life years after a joint longitudinal–survival model fitted with merlin, in Stata. It accompanies the 2026 paper below.
Courses
An open course on joint modelling of longitudinal and survival data, and a week-long summer school with real applications to clinical-trial data and electronic health records.
Specialises in survival analysis and joint longitudinal–survival models, is the author of the merlin framework, and teaches advanced courses with an emphasis on joint modelling and multi-state survival analysis.
View profile →
Research focused on cancer survival and survivorship, and a co-author of the joint model of PSA response in metastatic prostate cancer (European Urology Oncology, 2026).
View profile →Engagements that fit the problem
Expert advisory
Hours to days. A focused conversation or short review: a second opinion on a model, a sanity check on an approach, or direction before you commit to an analysis.
Project engagement
Weeks to months. Scoped to a defined deliverable, such as the joint model for a study or a paper, with a named expert team, an agreed scope and milestones, and reproducible code and documentation.
Ongoing support
Continuous access across several studies a year, where the relationship compounds.
The method, in the open
Primers and worked examples on the problems above. Nothing needs an account.
An introduction to joint modelling
When you need a joint model, and how shared random effects link a repeatedly measured biomarker to survival, with worked code.
Joint longitudinal and competing risks models
Extending joint longitudinal–survival models to incorporate competing risks: simulation, estimation, and prediction.
Joint models with time-dependent effects
Modelling time-dependent (non-proportional hazards) effects within a joint longitudinal–survival framework.
Multivariate joint models
Extending joint models to handle multiple continuous longitudinal outcomes modelled jointly with a survival outcome.
Time-dependent covariates in the Cox model
How the data are laid out, how it avoids immortal time bias, and the pitfalls of covariates measured on the patient.
Joint frailty models
Joint frailty models for analysing recurrent events alongside a terminal event, with interpretation guidance using merlin.