A two-stage approach for Bayesian joint models: reducing complexity while maintaining accuracy

Danilo Alvares

University of Cambridge (UK)

Ciências, ULisboa, Room 6.4.30 & ZOOM

22nd September 2023 (Friday) – 14h:30m                                                  


Several joint models for longitudinal and survival data have been proposed in recent years. In particular, many authors have preferred to employ the Bayesian approach to model more complex structures, make dynamic predictions, or use model averaging. However, Markov chain Monte Carlo methods are computationally very demanding and may suffer convergence problems, especially for complex models with random effects, which is the case for most joint models. These issues can be overcome by estimating the parameters of each submodel separately, leading to a natural reduction in the complexity of the joint modeling, but often producing biased estimates. Hence, we propose a novel two-stage approach that uses the estimations from the longitudinal submodel to specify an informative prior distribution for the random effects when estimating them within the survival submodel. In addition, as a bias correction mechanism, we incorporate the longitudinal likelihood function in the second stage, where its fixed effects are set according to the estimation using only the longitudinal submodel. Based on simulation studies and real applications, we empirically compare our proposal with joint specification and standard two-stage approaches considering different types of longitudinal responses (continuous, count, and binary) that share information with a Weibull proportional hazard model. The results show that our estimator is more accurate than its two-stage competitor and as good as jointly estimating all parameters. Moreover, the novel two-stage approach significantly reduces the computational time compared to the joint specification.

Short bio:

Danilo Alvares is a Research Associate in the MRC Biostatistics Unit at the University of Cambridge (UK), and his research topics are Bayesian methods, longitudinal data, survival analysis, and statistical modeling in public health and educational studies. Previously, Dr. Alvares was an Assistant Professor in the Department of Statistics at the Pontificia Universidad Católica de Chile (Chile) and a Postdoctoral Research Fellow in the Department of Biostatistics at Harvard University (USA). He holds a B.Sc. in Applied Mathematics and Scientific Computing, an M.Sc. in Computer Science and Computational Mathematics from the University of São Paulo (Brazil), and an M.Sc. in Biostatistics and a Ph.D. in Statistics from the Universitat de València (Spain).


Project UIDB/00006/2020