Repository logo

Weibull regression with Bayesian variable selection to identify prognostic tumour markers of breast cancer survival.

Accepted version

Repository DOI



Change log


Newcombe, PJ 
Raza Ali, H 
Blows, FM 
Provenzano, E 
Pharoah, PD 


As data-rich medical datasets are becoming routinely collected, there is a growing demand for regression methodology that facilitates variable selection over a large number of predictors. Bayesian variable selection algorithms offer an attractive solution, whereby a sparsity inducing prior allows inclusion of sets of predictors simultaneously, leading to adjusted effect estimates and inference of which covariates are most important. We present a new implementation of Bayesian variable selection, based on a Reversible Jump MCMC algorithm, for survival analysis under the Weibull regression model. A realistic simulation study is presented comparing against an alternative LASSO-based variable selection strategy in datasets of up to 20,000 covariates. Across half the scenarios, our new method achieved identical sensitivity and specificity to the LASSO strategy, and a marginal improvement otherwise. Runtimes were comparable for both approaches, taking approximately a day for 20,000 covariates. Subsequently, we present a real data application in which 119 protein-based markers are explored for association with breast cancer survival in a case cohort of 2287 patients with oestrogen receptor-positive disease. Evidence was found for three independent prognostic tumour markers of survival, one of which is novel. Our new approach demonstrated the best specificity.



Bayesian variable selection, MCMC, breast cancer, gene expression, penalised regression, reversible jump, stability selection, survival analysis, Algorithms, Bayes Theorem, Biomarkers, Tumor, Breast Neoplasms, Female, Humans, Prognosis, Receptors, Estrogen, Regression Analysis, Survival Analysis

Journal Title

Stat Methods Med Res

Conference Name

Journal ISSN


Volume Title


SAGE Publications
Department of Health (via National Institute for Health Research (NIHR)) (NF-SI-0515-10090)
Cancer Research UK (CB4140)
Cancer Research UK (unknown)
Cancer Research UK (60098573)
Cancer Research UK (unknown)
Department of Health (via National Institute for Health Research (NIHR)) (unknown)
European Commission (260791)
Cambridge University Hospitals NHS Foundation Trust (CUH) (RG51913)
Cancer Research Uk (None)
European Commission FP7 Network of Excellence (NoE) (260791)
Cambridge University Hospitals NHS Foundation Trust (CUH) (unknown)
Cancer Research Uk (None)
Academy of Medical Sciences (unknown)
Medical Research Council (MR/M008975/1)
Academy of Medical Sciences (ALI 01/08/14)
Pathological Society of Great Britain & Ireland (CDF 2012/01)
European Commission FP7 Collaborative projects (CP) (258967)
Cancer Research UK (C507/A16278)
European Commission (258967)
Cancer Research UK (20544)
Medical Research Council (MR/P012442/1)
European Commission and European Federation of Pharmaceutical Industries and Associations (EFPIA) FP7 Innovative Medicines Initiative (IMI) (115749)
European Commission (242006)
European Research Council (694620)
Cancer Research UK (A24622)
Cancer Research UK (16942)
PJN and SR were funded by the Medical Research Council. PJN also acknowledges partial support from the NIHR Cambridge Biomedical Research Centre.