A new approach to testing for sufficient follow-up in cure-rate analysis

The problem of sufficient follow-up arises naturally in the context of cure rate estimation. This problem was brought to the fore by Maller and Zhou [1992. Estimating the proportion of immunes in a censored sample. Biometrika 79, 731–739; 1994. Testing for sufficient follow-up and outliers in survival data. J. Amer. Statist. Assoc. 89, 1499–1506] in an effort to develop nonparametric statistical inference based on a binary mixture model. The authors proposed a statistical test to help practitioners decide whether or not the period of observation has been long enough to detect the presence of cured (immune) individuals in the study population. The test is inextricably entwined with estimation of the cure probability by the Kaplan–Meier estimator at the point of last observation. While intuitively appealing, the test by Maller and Zhou does not provide a satisfactory solution to the problem because of its unstable and nonmonotonic behavior when the duration of follow-up increases. The present paper introduces an alternative concept of sufficient follow-up allowing derivation of a lower bound for the expected proportion of immune subjects in a wide class of cure models. By building on the proposed bound, a new statistical test is designed to address the issue of the presence of immunes in the study population. The usefulness of the proposed approach is illustrated with an application to survival data on breast cancer patients identified through the NCI Surveillance, Epidemiology and End Results Database.