title: Weibull regression with Bayesian variable selection to identify prognostic tumour markers of breast cancer survival.
abstract: 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.
authors.affiliation: 1 MRC Biostatistics Unit, Cambridge, UK.
authors.forename: P J
authors.initials: PJ
authors.lastname: Newcombe
authors.affiliation: 2 Cancer Research UK Cambridge Institute, Cambridge, UK.|3 Department of Pathology, University of Cambridge, Cambridge, UK.|4 Cambridge Experimental Cancer Medicine Centre and NIHR Cambridge Biomedical Research Centre, Cambridge, UK.
authors.forename: H
authors.initials: H
authors.lastname: Raza Ali
authors.affiliation: 5 Department of Oncology, University of Cambridge, Cambridge, UK.
authors.forename: F M
authors.initials: FM
authors.lastname: Blows
authors.affiliation: 6 NIH Cambridge Biomedical Research Centre, Cambridge, UK.
authors.forename: E
authors.initials: E
authors.lastname: Provenzano
authors.affiliation: 4 Cambridge Experimental Cancer Medicine Centre and NIHR Cambridge Biomedical Research Centre, Cambridge, UK.|5 Department of Oncology, University of Cambridge, Cambridge, UK.|7 Strangeways Research Laboratory, Cambridge, UK.
authors.forename: P D
authors.initials: PD
authors.lastname: Pharoah
authors.affiliation: 2 Cancer Research UK Cambridge Institute, Cambridge, UK.|4 Cambridge Experimental Cancer Medicine Centre and NIHR Cambridge Biomedical Research Centre, Cambridge, UK.|5 Department of Oncology, University of Cambridge, Cambridge, UK.
authors.forename: C
authors.initials: C
authors.lastname: Caldas
authors.affiliation: 1 MRC Biostatistics Unit, Cambridge, UK.
authors.forename: S
authors.initials: S
authors.lastname: Richardson
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D014408:Biomarkers, Tumor / Q000032:analysis*; D001943:Breast Neoplasms / Q000378:metabolism / Q000401:mortality*; D005260:Female; D006801:Humans; D011379:Prognosis; D011960:Receptors, Estrogen / Q000378:metabolism; D012044:Regression Analysis; D016019:Survival Analysis
chemical_list: D014408:Biomarkers, Tumor; D011960:Receptors, Estrogen
keywords: Bayesian variable selection; MCMC; breast cancer; gene expression; penalised regression; reversible jump; stability selection; survival analysis