A linear spline Cox cure model with its applications

Abstract

A mixture cure model has been increasingly popular in the field of biostatistics, where some individuals may never experience an event of interest during a study. In most cases, effects of continuous covariates are assumed to be linear. However, a traditional linear assumption often fails in practical situations because real-life effects are usually nonlinear. Proposed is a linear spline Cox cure model in which a spline is used to approximate the unknown smooth functional form for the effect of a continuous covariate to identify the nonlinear functional relationship. The justification and estimation procedure starts from Laplace’s approximation of the marginal log-likelihood function and leads to a penalized log-likelihood. The expectation-maximization algorithm is used to estimate the model parameters, and the proposed methodology could then be used to assess the linearity of the continuous covariate effect via the likelihood ratio procedure. An extensive simulation study is conducted to investigate the performance of the proposed lack-of-fit test for the linearity of the continuous covariate effect. The practical use of the methodology is illustrated with fibrous histiocytoma data from the Surveillance, Epidemiology, and End Results (SEER) program database.