Adaptive Regression Splines in the Cox Model
- 1 March 1999
- journal article
- Published by Oxford University Press (OUP) in Biometrics
- Vol. 55 (1) , 204-213
- https://doi.org/10.1111/j.0006-341x.1999.00204.x
Abstract
Summary.We develop a method for constructing adaptive regression spline models for the exploration of survival data. The method combines Cox's (1972,Journal of the Royal Statistical Society, Series B34, 187–200) regression model with a weighted least‐squares version of the multivariate adaptive regression spline (MARS) technique of Friedman (1991,Annals of Statistics19, 1–141) to adaptively select the knots and covariates. The new technique can automatically fit models with terms that represent nonlinear effects and interactions among covariates. Applications based on simulated data and data from a clinical trial for myeloma are presented. Results from the myeloma application identified several important prognostic variables, including a possible nonmonotone relationship with survival in one laboratory variable. Results are compared to those from the adaptive hazard regression (HARE) method of Kooperberg, Stone, and Truong (1995,Journal of the American Statistical Association90, 78–94).Keywords
This publication has 22 references indexed in Scilit:
- Hazard RegressionJournal of the American Statistical Association, 1995
- Proportional hazards tests and diagnostics based on weighted residualsBiometrika, 1994
- Flexible Methods for Analyzing Survival Data Using Splines, with Applications to Breast Cancer PrognosisJournal of the American Statistical Association, 1992
- Multivariate Adaptive Regression SplinesThe Annals of Statistics, 1991
- Discussion: Multivariate Adaptive Regression SplinesThe Annals of Statistics, 1991
- Discussion: Multivariate Adaptive Regression SplinesThe Annals of Statistics, 1991
- Regression Splines in the Cox Model with Application to Covariate Effects in Liver DiseaseJournal of the American Statistical Association, 1990
- Martingale-based residuals for survival modelsBiometrika, 1990
- Partial residuals for the proportional hazards regression modelBiometrika, 1982