Tree-augmented Cox proportional hazards models.

We study a hybrid model that combines Cox proportional hazards regression with tree-structured modeling. The main idea is to use step functions, provided by a tree structure, to 'augment' Cox (1972) proportional hazards models. The proposed model not only provides a natural assessment of the adequacy of the Cox proportional hazards model but also improves its model fitting without loss of interpretability. Both simulations and an empirical example are provided to illustrate the use of the proposed method.

[1]  David A. Schoenfeld,et al.  Partial residuals for the proportional hazards regression model , 1982 .

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

[3]  Sudeshna Adak,et al.  Survival Analysis with Time‐Varying Regression Effects Using a Tree‐Based Approach , 2002, Biometrics.

[4]  R. Brand,et al.  Coronary heart disease in Western Collaborative Group Study. Final follow-up experience of 8 1/2 years. , 1975, JAMA.

[5]  D R Ragland,et al.  Coronary heart disease mortality in the Western Collaborative Group Study. Follow-up experience of 22 years. , 1988, American journal of epidemiology.

[6]  Ørnulf Borgan,et al.  A method for checking regression models in survival analysis based on the risk score , 1996, Lifetime data analysis.

[7]  L. J. Wei,et al.  The Robust Inference for the Cox Proportional Hazards Model , 1989 .

[8]  A. Raftery,et al.  Bayesian Information Criterion for Censored Survival Models , 2000, Biometrics.

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

[10]  Burton H. Singer,et al.  Recursive partitioning in the health sciences , 1999 .

[11]  S. Keleş,et al.  Residual‐based tree‐structured survival analysis , 2002, Statistics in medicine.

[12]  Eric V. Slud,et al.  Robust covariate-adjusted logrank tests , 1997 .

[13]  Anastasios A. Tsiatis,et al.  Group sequential tests with censored survival data adjusting for covariates , 1985 .

[14]  M. LeBlanc,et al.  Survival Trees by Goodness of Split , 1993 .

[15]  C. R. Rao,et al.  Linear Statistical Inference and its Applications , 1968 .

[16]  A. Ciampi,et al.  Stratification by stepwise regression, correspondence analysis and recursive partition: A comparison of three methods of analysis for survival data with covaria , 1986 .

[17]  D. Carmelli,et al.  Obesity and 33‐Year Follow‐up for Coronary Heart Disease and Cancer Mortality , 1997, Epidemiology.

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

[19]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[20]  J. Morgan,et al.  Problems in the Analysis of Survey Data, and a Proposal , 1963 .

[21]  D. Ragland,et al.  Coronary Heart Disease Mortality in the Western Collaborative Group Study , 1988 .

[22]  M. LeBlanc,et al.  Relative risk trees for censored survival data. , 1992, Biometrics.

[23]  N. Schneiderman,et al.  Biobehavioral aspects of cardiovascular disease: progress and prospects. , 1989, Health psychology : official journal of the Division of Health Psychology, American Psychological Association.

[24]  R B Davis,et al.  Exponential survival trees. , 1989, Statistics in medicine.

[25]  Michael LeBlanc,et al.  Step‐function covariate effects in the proportional‐hazards model , 1995 .

[26]  R. Olshen,et al.  Tree-structured survival analysis. , 1985, Cancer treatment reports.

[27]  P. Grambsch,et al.  Martingale-based residuals for survival models , 1990 .

[28]  W. Loh,et al.  Tree-structured proportional hazards regression modeling. , 1994, Biometrics.

[29]  D. Hosmer,et al.  A Simplified Method of Calculating an Overall Goodness-of-Fit Test for the Cox Proportional Hazards Model , 1998, Lifetime data analysis.

[30]  M. Kupperman.  Linear Statistical Inference and Its Applications 2nd Edition (C. Radhakrishna Rao) , 1975 .