title: Comparison of Cox Model Methods in A Low-dimensional Setting with Few Events.
abstract: Prognostic models based on survival data frequently make use of the Cox proportional hazards model. Developing reliable Cox models with few events relative to the number of predictors can be challenging, even in low-dimensional datasets, with a much larger number of observations than variables. In such a setting we examined the performance of methods used to estimate a Cox model, including (i) full model using all available predictors and estimated by standard techniques, (ii) backward elimination (BE), (iii) ridge regression, (iv) least absolute shrinkage and selection operator (lasso), and (v) elastic net. Based on a prospective cohort of patients with manifest coronary artery disease (CAD), we performed a simulation study to compare the predictive accuracy, calibration, and discrimination of these approaches. Candidate predictors for incident cardiovascular events we used included clinical variables, biomarkers, and a selection of genetic variants associated with CAD. The penalized methods, i.e., ridge, lasso, and elastic net, showed a comparable performance, in terms of predictive accuracy, calibration, and discrimination, and outperformed BE and the full model. Excessive shrinkage was observed in some cases for the penalized methods, mostly on the simulation scenarios having the lowest ratio of a number of events to the number of variables. We conclude that in similar settings, these three penalized methods can be used interchangeably. The full model and backward elimination are not recommended in rare event scenarios.
authors.affiliation: Department of General and Interventional Cardiology, University Heart Center Hamburg-Eppendorf, 20246 Hamburg, Germany. Electronic address: f.ojeda-echevarria@uke.de.
authors.forename: Francisco M
authors.initials: FM
authors.lastname: Ojeda
authors.affiliation: Department of General and Interventional Cardiology, University Heart Center Hamburg-Eppendorf, 20246 Hamburg, Germany; German Center for Cardiovascular Research (DZHK), Hamburg/Kiel/Luebeck, Germany.
authors.forename: Christian
authors.initials: C
authors.lastname: Müller
authors.affiliation: Department of General and Interventional Cardiology, University Heart Center Hamburg-Eppendorf, 20246 Hamburg, Germany; German Center for Cardiovascular Research (DZHK), Hamburg/Kiel/Luebeck, Germany.
authors.forename: Daniela
authors.initials: D
authors.lastname: Börnigen
authors.affiliation: Sorbonne Universités, Université Pierre et Marie Curie Paris 06, Institut National pour la Santé et la Recherche Médicale (INSERM), Unité Mixte de Recherche en Santé (UMR_S) 1166, F-75013 Paris, France; Institute for Cardiometabolism and Nutrition (ICAN), F-75013 Paris, France.
authors.forename: David-Alexandre
authors.initials: DA
authors.lastname: Trégouët
authors.affiliation: Institut für Medizinische Biometrie und Statistik, Universität zu Lübeck, Universitätsklinikum Schleswig-Holstein, Campus Lübeck, 23562 Lübeck, Germany; German Center for Cardiovascular Research (DZHK), Hamburg/Kiel/Luebeck, Germany.
authors.forename: Arne
authors.initials: A
authors.lastname: Schillert
authors.affiliation: Institute of Computational Biology, German Research Center for Environmental Health, Helmholtz Zentrum München, 85764 Neuherberg, Germany.
authors.forename: Matthias
authors.initials: M
authors.lastname: Heinig
authors.affiliation: Department of General and Interventional Cardiology, University Heart Center Hamburg-Eppendorf, 20246 Hamburg, Germany; German Center for Cardiovascular Research (DZHK), Hamburg/Kiel/Luebeck, Germany.
authors.forename: Tanja
authors.initials: T
authors.lastname: Zeller
authors.affiliation: Department of General and Interventional Cardiology, University Heart Center Hamburg-Eppendorf, 20246 Hamburg, Germany; German Center for Cardiovascular Research (DZHK), Hamburg/Kiel/Luebeck, Germany.
authors.forename: Renate B
authors.initials: RB
authors.lastname: Schnabel
mesh_terms: D015415:Biomarkers / Q000097:blood / Q000378:metabolism; D003324:Coronary Artery Disease / Q000175:diagnosis* / Q000235:genetics; D014644:Genetic Variation; D006801:Humans; D011379:Prognosis; D016016:Proportional Hazards Models; D011446:Prospective Studies
chemical_list: D015415:Biomarkers
keywords: Coronary artery disease; Events per variable; Penalized regression; Proportional hazards regression