Methodology and software for joint modelling


Methodology and software for joint modelling of time-to-event data and longitudinal outcomes across multiple studies

Project Overview

Joint models for longitudinal and time-to-event data are commonly applied to single studies in cases where a longitudinally outcome measured with error is thought to influence the time to an event (e.g. death), where longitudinal studies are affected by informative dropout or where the link or association between a longitudinal and a time-to-event outcome are of equal interest.  However little research has been done in the use of joint models when pooling data from multiple studies, as in a meta-analysis.  This research project aims to review and propose methods for aggregate data (AD) and individual participant data (IPD ) meta-analyses of joint longitudinal and time-to-event data.  Methods will be implemented in the R software.

Start: October 2014

End: September 2017

Funded by: University of Liverpool contribution to HeRC

Disease Area Impacted


Data Source

The INDANA dataset will be used to demonstrate the methods proposed (see  Gueyffier, F., et al., INDANA: a meta-analysis on individual patient data in hypertension. Protocol and preliminary results. Therapie, 1995. 50: p. 353-362.) This dataset contains information on time of death, time to stroke, and time to myocardial infarction, and longitudinally measured systolic and diastolic blood pressures. Data was supplied from 7 of the trials included in the INDANA dataset.


Methods used in this project expand the methodspresented in the papers Wulfsohn, M.S. and A.A. Tsiatis, A Joint Model for Survival and Longitudinal Data Measured with Error. 1997, International Biometric Society. p. 330. and Henderson, R., P. Diggle, and A. Dobson, Joint modelling of longitudinal measurements and event time data. Biostatistics (Oxford, England), 2000. 1(4): p. 465-480. from the single study to the multiple study case.  Apart from this, standard methods for meta-analysis are used, as well as cox proportional hazards models and linear mixed models to model the time-to-event and longitudinal data separately, in order to compare separate or standalone methods to joint modelling methods.


Researchers aiming to examine longitudinal and time-to-event data resulting from multiple studies simultaneously will have access to new methods that allow the heterogeneity between the included studies to be accounted for. They will also have the programmes available to implement these methods in the freely available statistical software R. By having access to these methods and programmes, researchers in a wide area of medicine (for example HIV linking time to death or time to progression to AIDS to CD4+ cell count, or linking biomarkers in cancer research to time to progression or death) will be able to analyse larger meta-datasets, rather than relying on data from one study.

Intended Outcomes

To provide methods and programmes for researchers to use when performing analysis of joint longitudinal and time-to-event data sourced from multiple studies such as a meta analysis.

Early Findings

Early indications from a simulation investigation indicate benefits of conducting two stage meta-analyses using joint models over seperate longitudinal or time-to-event models in cases where association exists between the longitudinal and time-to-event outcome. A publication to discuss these results is being prepared.

Researchers Involved

Maria Sudell

Dr Catrin Tudur-Smith

Dr Ruwanthi Kolamunnage-Dona