Estimation of age effect with change-points on survival of cancer patients

There is a global trend that the average onset age of many human complex diseases is decreasing, and the age of cancer patients becomes more spread out. The age effect on survival is nonlinear in practice and may have one or more important change-points at which the trend of the effect can be very different before and after these threshold ages. Identification of these change-points allows clinical researchers to understand the biologic basis for the complex relation between age and prognosis for optimal prognostic decision. This paper considers estimation of the potentially nonlinear age effect for general partly linear survival models to ensure a valid statistical inference on the treatment effect. A simple and efficient sieve maximum likelihood estimation method that can be implemented easily using standard statistical software is proposed. A data-driven adaptive algorithm to determine the optimal location and the number of knots for the identification of the change-points is suggested. Simulation studies are performed to study the performance of the proposed method. For illustration purpose, the method is applied to a breast cancer data set from the public domain to investigate the effect of onset age on the disease-free survival of the patients. The results revealed that the risk is highest among young patients and young postmenopausal patients, probably because of a change in hormonal environment during a certain phase of menopause.