Open Conference Systems, 50th Scientific meeting of the Italian Statistical Society

Font Size: 
A multivariate extension of the joint models
Marcella Mazzoleni, Mariangela Zenga

Last modified: 2018-05-10


The joint models analyse the effect of longitudinal covariates onto the risk of an event. They are composed of two sub-models, the longitudinal and the survival sub-model. For the longitudinal sub-model a multivariate mixed model can be proposed. Whereas for the survival sub-model, a Cox proportional hazards model is proposed, considering jointly the influence of more than one longitudinal covariate onto the risk of the event. The purpose of the work is to extend an estimation method based on a joint likelihood formulation to the case in which the longitudinal submodel is multivariate through the implementation of an Expectation-Maximisation (EM) algorithm.


1. P. Albert and J. Shih. An approach for jointly modeling multivariate longitudinal measurements and discrete time-to-event data. The Annals of Applied Statistics, 4:1517–1532, 2010.

2. C. Faucett and D. Thomas. Simultaneously modelling censored survival data and repeatedly measured covariates: a Gibbs sampling approach. Statistics in Medicine, 15:1663–1685, 1996.

3. A. Henderson, V. De Gruttola, and M. Wulfsohn. Joint modelling of longitudinal measurements and event time data. Biostatistics, 1:465–480, 2000.

4. G. Hickey, P. Philipson, A. Jorgensen, R. Kolamunnage-Dona, P.Williamson, and D. Rizopoulos. joineRML: Joint Modelling of Multivariate Longitudinal Data and Time-to-Event Outcomes, 2017. version 0.4.1.

5. G. L. Hickey, P. Philipson, A. Jorgensen, and R. Kolamunnage-Dona. Joint modelling of time-to-event and multivariate longitudinal outcomes: recent developments and issues. BMC Medical Research Methodology, 16:117–131, 2016.

6. D. Rizopoulos. Joint model for Longitudinal and Time-to-Event Data with applications in R. CRC Press, Boca Raton, 2012.

7. A. Scott. Maximum likelihood estimation using the empirical fisher information matrix. Journal of Statistical Computation and Simulation, 72(8):599–611, 2002.

8. T. Therneau and P. Grambsch. Modeling Survival Data: extending the Cox Model. Springer-Verlang, New York, 2000.

9. T. Therneau and T. Lumley. survival: Survival Analysis, 2015. version 2.41-3.

10. J. Xu and S. Zeger. The evaluation of multiple surrogate endpoints. Biometrics, 57:81–87, 2001.

11. J. Xu and S. Zeger. Joint analysis of longitudinal data comprising repeated measures and times to events. Applies Statistics, 50:375–387, 2001.

Full Text: PDF