Classification and regression trees (CART) used for the exploration of prognostic factors measured on different scales

The modelling of the relationship of some response to factors measured on different scales is a common problem in various fields of application. We discuss the regression tree model in the context of general regression models and present the idea od the regression tree algorithm. In this approach all factors under consideration have to be split to binary variables, leading to a high probability of wrongly identifying as influential a variable with many splits. We propose a strategy to adjust for such an undesirable Finally, we illustrate our modification of the classification and regression tree method with data from a multicenter randomized clinical trial in patients with brain tumors.

[1]  P. McCullagh,et al.  Generalized Linear Models , 1972, Predictive Analytics.

[2]  David R. Cox,et al.  Regression models and life tables (with discussion , 1972 .

[3]  G. Hommel.  A comparison of two modified Bonferroni procedures , 1989 .

[4]  Brian D. Ripley,et al.  Statistical aspects of neural networks , 1993 .

[5]  G. Hommel.  A stagewise rejective multiple test procedure based on a modified Bonferroni test , 1988 .

[6]  Berthold Lausen,et al.  Maximally selected rank statistics , 1992 .

[7]  Leo Breiman,et al.  Classification and Regression Trees , 1984 .

[8]  Antonio Ciampi,et al.  Tree-Growing for the Multivariate Model: The RECPAM Approach , 1992 .

[9]  M. Segal.  Tree-Structured Methods for Longitudinal Data , 1992 .

[10]  Mark R. Segal,et al.  Regression Trees for Censored Data , 1988 .

[11]  W. Loh,et al.  Tree-Structured Classification via Generalized Discriminant Analysis. , 1988 .

[12]  A. Schauer,et al.  The prognostic effect of histological tumor grade in node-negative breast cancer patients , 1993, Breast Cancer Research and Treatment.

[13]  R. Tibshirani,et al.  A Strategy for Binary Description and Classification , 1992 .

[14]  K. Worsley.  Testing for a Two-Phase Multiple Regression , 1983 .

[15]  D. Siegmund,et al.  Maximally Selected Chi Square Statistics , 1982 .

[16]  A. Zaiß,et al.  Evaluierung Prognostisch Homogener Subpopulationen mit Hilfe der Methode Der Klassifikationsbäume , 1991 .

[17]  K. Worsley.  An improved Bonferroni inequality and applications , 1982 .

[18]  M Schumacher,et al.  Comparison of the Cox model and the regression tree procedure in analysing a randomized clinical trial. , 1993, Statistics in medicine.

[19]  D. Nelson,et al.  Recursive partitioning analysis of prognostic factors in three Radiation Therapy Oncology Group malignant glioma trials. , 1993, Journal of the National Cancer Institute.