Comparison of objective Bayes factors for variable selection in parametric regression models for survival analysis. (7th July 2014)

• Record Type: Journal Article
• Authors: Cabras, Stefano; Castellanos, Maria Eugenia; Perra, Silvia
• Is Part Of: Statistics in medicine. Volume 33:Number 26(2014)
• Page Start: 4637
• Page End: 4654
• Publication Date: 2014-07-07
• Subjects: Medical statistics -- Periodicals; Statistique médicale -- Périodiques; Statistiques médicales -- Périodiques; 610.727
• DOI: 10.1002/sim.6249
• Languages: English
• ISSNs: 0277-6715

Abstract

<abstract abstract-type="main" id="sim6249-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p id="sim6249-para-0001">This paper considers the problem of selecting a set of regressors when the response variable is distributed according to a specified parametric model and observations are censored. Under a Bayesian perspective, the most widely used tools are Bayes factors (BFs), which are undefined when improper priors are used. In order to overcome this issue, fractional (<italic>FBF</italic>) and intrinsic (<italic>IBF</italic>) BFs have become common tools for model selection. Both depend on the size, <italic>N</italic><sub><italic>t</italic></sub>, of a minimal training sample (MTS), while the <italic>IBF</italic> also depends on the specific MTS used. In the case of regression with censored data, the definition of an MTS is problematic because only uncensored data allow to turn the improper prior into a proper posterior and also because full exploration of the space of the MTSs, which includes also censored observations, is needed to avoid bias in model selection. To address this concern, a sequential MTS was proposed, but it has the drawback of an increase of the number of possible MTSs as <italic>N</italic><sub><italic>t</italic></sub> becomes random. For this reason, we explore the behaviour of the <italic>FBF</italic>, contextualizing its definition to censored data. We show that these are consistent, providing also the corresponding fractional prior. Finally, a large simulation study and an application to real data are used to compare <italic>IBF</italic>, <italic>FBF</italic> and the well‐known Bayesian information criterion. Copyright © 2014 John Wiley & Sons, Ltd.</p> </abstract>