Bayesian model and variable selection for survival data

Project ID: 2228cd1423 (You will need this ID for your application)

UCL Lead department: Statistical Science

Lead Supervisor: Jim Griffin

Project Summary:

Description.

Survival models are of great interest in a number of scientific areas, including medicine, epidemiology, biology and engineering. This sort of models are typically formulated at the level of the hazard function.
The most popular survival models are the Proportional Hazards (PH) model and the Accelerated Failure Time (AFT) model. PH and AFT models make different assumptions on the role of the covariates in the hazard function. A more general type of survival model is the general hazard (GH) model, which contains the PH and the AFT models as particular cases. An appealing feature of the GH structure is that selecting the relevant variables as well as the hazard structure can be seen as a variable selection problem.

The aim of this project is to develop theory, methods, and software to conduct Bayesian variable selection in the GH model, which allows for a simultaneous selection of the relevant covariates as well as their role in the model. Different types of priors will be compared, and their effect on the asymptotic Bayes factor rates will be studied. The implementation of the proposed variable selection methods requires the use of numerical methods to approximate the marginal likelihood, as well as MCMC methods to perform model-space exploration. These methods will be implemented in an R package, and will be made publicly available. Applications in the context of medical statistics, using real data, will be studied.

Desired profile.

This project requires a combination of statistical theory (Bayesian inference, Statistical Inference, Asymptotic theory, and Survival analysis), numerical methods (MCMC, Laplace approximation, optimisation), and programming (R and/or C++).

Supervisors.

The candidate will work with Dr. F. Javier Rubio and Prof. Jim Griffin.