Testing for the presence of cured patients: a simulation study

An important but difficult problem in clinical trials is to determine the p resence of cured patients when long-term survivors are observed. The likeli hood ratio test has been studied for this purpose in the gamma mixture mode l. However, its asymptotic null distribution is not readily available due t o a violation of boundary conditions in the standard asymptotic theory. In this paper, a simulation study is employed to examine a proposed asymptotic null distribution of the likelihood ratio test. We find that the distribut ion can also be used to approximate the asymptotic null distribution of the likelihood ratio test in the Weibull and log-normal mixture models when th e censoring rate is not too light. However, the simulation study also shows that null distribution of the likelihood ratio test deviates significantly from the suggested distribution under moderate sample sizes when the censo ring rate is small or the hazard rate is large. Consequently caution is nee ded in this case to determine the presence of cured patients. Finally, the results are used to confirm the presence of cured patients in a leukaemia s tudy. Copyright (C) 2001 John Wiley & Sons, Ltd.