The cure model and time confounded risk in the analysis of survival and other timed events

The use of the Kaplan-Meier estimator for the analysis and testing of cure model data is discussed and results are compared with the more commonly used logrank test. The Kaplan-Meier estimator is particularly appropriate for describing the shape of the underlying survival distribution of data from bone marrow transplantation but is also relevant for different types of timed events data from other chronic diseases. The estimate of the event-free fraction by the product limit, may have a bias depending on the extent of follow-up, the parameters of the model, and confounding by competing risk events. The test based on the product limit has appropriate size and is more powerful as long as follow-up is sufficient to minimize the bias. On the other hand, the logrank test, which is optimal for testing differences in time-to-event curves under proportional hazard assumptions, may be inappropriate and misleading for evaluating the difference in event-free fractions under the cure model.