The practical utility of incorporating model selection uncertainty into prognostic models for survival data

N Augustin, W Sauerbrei, M Schumacher

Research output: Contribution to journalArticlepeer-review


Predictions of disease outcome in prognostic factor models are usually based on one selectedmodel. However, often several models fit the data equally well, but these models might differ substantiallyin terms of included explanatory variables and might lead to different predictions for individual patients.For survival data, we discuss two approaches to account for model selection uncertainty in two dataexamples, with the main emphasis on variable selection in a proportional hazard Cox model. The main aim of our investigation is to establish the ways in which either of the two approaches is useful in suchprognostic models. The first approach is Bayesian model averaging (BMA) adapted for the proportionalhazard model, termed ‘approx. BMA’ here. As a new approach, we propose a method which averages overa set of possible models using weights estimated from bootstrap resampling as proposed by Bucklandet al.,but in addition, we perform an initial screening of variables based on the inclusion frequency of eachvariable to reduce the set of variables and corresponding models. For some necessary parameters of the procedure, investigations concerning sensible choices are still required. The main objective of prognosticmodels is prediction, but the interpretation of single effects is also important and models should be generalenough to ensure transportability to other clinical centres. In the data examples, we compare predictions ofour new approach with approx. BMA, with ‘conventional’ predictions from one selected model and withpredictions from the full model. Confidence intervals are compared in one example. Comparisons are basedon the partial predictive score and the Brier score. We conclude that the two model averaging methods yieldsimilar results and are especially useful when there is a high number of potential prognostic factors, mostlikely some of them without influence in a multivariable context. Although the method based on bootstrap resampling lacks formal justification and requires some ad hoc decisions, it has the additional positiveeffect of achieving model parsimony by reducing the number of explanatory variables and dealing with correlated variables in an automatic fashion.
Original languageEnglish
Pages (from-to)95-118
Number of pages24
JournalStatistical modelling
Issue number2
Publication statusPublished - Jul 2005


  • survival analysis
  • prognostic
  • bootstrap
  • model selection uncertainty
  • model averaging
  • factor models


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