Flexible Methods for Analyzing Survival Data Using Splines, With Applications to Breast Cancer Prognosis

Abstract

In this article some flexible methods for modeling censored survival data using splines are applied to the problem of modeling the time to recurrence of breast cancer patients. The basic idea is to use fixed knot splines with a fairly modest number of knots to model aspects of the data, and then to use penalized partial likelihood to estimate the parameters of the model. Test statistics are proposed which are analogs of those used in traditional likelihood analysis, and approximations to the distributions of these statistics are suggested. In an analysis of a large data set taken from clinical trials conducted by the Eastern Cooperative Oncology Group, these methods are seen to give useful insight into how prognosis varies as a function of continuous covariates, and also into how covariate effects change with follow-up time.