A comparison of tests of the difference in the proportion of patients who are cured

We compared by simulation the likelihood ratio, Wald, and score tests based on a mixture model similar to that proposed by Farewell (1982, Biometrics 38, 1041-1046), and a simple nonparametric test based on the plateau value of the product-limit estimate, for testing the difference in cured proportions between two groups. The parametric tests obtained their asymptotic properties even in small samples provided that one could assume equal failure rates in the two groups. Otherwise, good agreement with predictions required that essentially all potential failures had been observed. The comparative properties of the parametric tests depended on whether the population survival functions crossed, with the power of the Wald test as good as or better than the others in the common situation when the survival functions do not cross. However, its size was sometimes less than nominal. The score test was often not defined and is therefore of limited value. The product-limit test often performed as well as the parametric tests, and despite being biased in some circumstances, may be a useful alternative to these, especially in small samples when some potential failures have not been observed.