An application of changepoint methods in studying the effect of age on survival in breast cancer

Abstract

The role of age in prognostic studies in breast cancer remains to be clearly established. There is reasonable agreement that younger patients have higher risk of an unfavorable outcome but there is little agreement on the precise nature of the relationship between age and prognosis. A first step in studying any such relationship can be based on the division of patients into two groups: a high risk and a low risk group. A simple and popular classification rule consists in determining a cutoff value of the continuous variable age. How to choose the actual cutoff however is not a straightforward problem (Lausen and Schumacher Biometrics 48 (1992) 73–75; Comput. Statist. Data Anal. 21 (1996) 307–326; Altman et al., J. Natl. Cancer Institute 86 (1994) 829–835). We address this problem in a way similar to that of Lausen and Schumacher by showing that the asymptotic distribution of a re-scaled rank statistic is the same as the distribution of the Brownian bridge. Our approach avoids arbitrarily eliminating potential cutpoints near the extremities. The maximisation of the proposed statistic enables estimation of a cutpoint and the calculation of its significance. The statistical problem is presented in the general case and is detailed in the case of survival analysis with censored data. Simulations suggest our approach to have smaller bias and greater power in certain situations than that of Lausen and Schumacher. We present a Monte-Carlo study and an illustration of the approach in a study on the effect of age at diagnosis and subsequent survival in breast cancer.