Regression splines for threshold selection in survival data analysis

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.