Stable variable selection for right censored data: comparison of methods

The instability in the selection of models is a major concern with data sets containing a large number of covariates. This paper deals with variable selection methodology in the case of high-dimensional problems where the response variable can be right censored. We focuse on new stable variable selection methods based on bootstrap for two methodologies: the Cox proportional hazard model and survival trees. As far as the Cox model is concerned, we investigate the bootstrapping applied to two variable selection techniques: the stepwise algorithm based on the AIC criterion and the L1-penalization of Lasso. Regarding survival trees, we review two methodologies: the bootstrap node-level stabilization and random survival forests. We apply these different approaches to two real data sets. We compare the methods on the prediction error rate based on the Harrell concordance index and the relevance of the interpretation of the corresponding selected models. The aim is to find a compromise between a good prediction performance and ease to interpretation for clinicians. Results suggest that in the case of a small number of individuals, a bootstrapping adapted to L1-penalization in the Cox model or a bootstrap node-level stabilization in survival trees give a good alternative to the random survival forest methodology, known to give the smallest prediction error rate but difficult to interprete by non-statisticians. In a clinical perspective, the complementarity between the methods based on the Cox model and those based on survival trees would permit to built reliable models easy to interprete by the clinician.Comment: nombre de pages : 29 nombre de tableaux : 2 nombre de figures :

Two Survival Tree Models for Myocardial Infarction Patients

In the search of a better prognostic survival model for post-acute myocardial infarction patients, the scientists at the Technical University of Munich's "Klinikum rechts der Isar" and the German Heart Center in Munich have developed some new parameters using 24-hour ECG (Schmidt et al 1999). A series of investigations were done using these parameters on different data sets and the Cox-PH model (Schmidt et al 1999, Ulm et al 2000). This paper is a response to the discussion paper by Ulm et al (2000), which suggests a Cox model for calculating the risk stratification of the MPIP data set patients including the predictors ejection fraction and heart rate turbulence. The current paper suggests the use of the classification and regression trees technique for survival data in order to deduct a survival stratification model for the NIRVPIP data set. Two models are compared: one contains the variables suggested by Ulm et al (2000) the other model has two additional variables, namely presence of couplets and number of extra systolic beats in the longest salvo of the patient's 24-hour ECG. The second model is shown to be an improvement on the first one