Regression splines for threshold selection in survival data analysis

• Published in: Statistics in medicine Vol. 20; no. 2; pp. 237 - 247
• Main Authors: Molinari, Nicolas, Daurès, Jean-Pierre, Durand, Jean-François
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 30.01.2001; Wiley
• Subjects: Biological and medical sciences; Carcinoma, Small Cell - drug therapy; Clinical Trials as Topic - methods; Computerized, statistical medical data processing and models in biomedicine; Confidence Intervals; Data Interpretation, Statistical; Female; Heart Transplantation - mortality; Humans; Likelihood Functions; Lung Neoplasms - drug therapy; Male; Medical sciences; Medical statistics; Numerical Analysis, Computer-Assisted; Phosphopyruvate Hydratase - blood; Prognosis; Proportional Hazards Models; Regression Analysis; Survival Analysis; Statistical method; Data analysis; Threshold element; Cox model; Likelihood ratio test; Regression function; Clinical trial; Survival curve; Spline; Confidence interval
• ISSN: 0277-6715; 1097-0258
• DOI: 10.1002/1097-0258(20010130)20:2<237::AID-SIM654>3.0.CO;2-I

The Cox proportional hazards model restricts the hazard ratio to be linear in the covariates. A survival model based on data from a clinical trial is developed using spline functions with variable knots to estimate the log hazard function. Moreover, the main point of the method is that a knot, seen as free parameters for a piecewise linear spline, represents a break point in the log hazard function which may be interpreted as a threshold value. The likelihood ratio test is used to select the final model and to determine the threshold number for a covariate. Confidence intervals for these threshold values are computed by bootstrapping the data. Two examples illustrate the method. Copyright © 2001 John Wiley & Sons, Ltd.