A permutation test for a weighted Kaplan-Meier estimator with application to the nutritional prevention of cancer trial

The phenomenon of losing statistical significance with increasing follow-up can arise when a proportional hazard model is applied in a clinical trial where the impact of the intervention results in delaying a negative event such as cancer diagnosis, progression or death. Often parametric methods can be employed in such a setting, however, in studies where only a small percentage of subjects have an event, these methods are often inappropriate. We present an alternative method based on a weighted Kaplan-Meier estimator and a permutation test, and demonstrate its utility in the setting of the Nutritional Prevention of Cancer study where increasing follow-up resulted in loss of statistical significance for the ability of selenized yeast to prevent lung cancer.