Likelihood ratio test for the presence of cured individuals : a simulation study

Abstract

Likelihood ratio test plays an important role in testing for the presence of cured individuals in clinical studies. The asymptotic null distribution of the test in three commonly used mixture models is a 50-50 mixture distribution of a chi-squared distribution and the probability mass at zero under some mild conditions. In this practicum, we first study the power of the likelihood ratio test under those models via a simulation study. We find that the test is powerful for moderate large sample size. For small sample size, the result varies case by case, and the censoring distribution affects the power substantially. The Extended Generalized Gamma (EGG) mixture model is also considered, for it is more flexible than the three models mentioned above. It may be used when the data in study cannot be fit by those models. The bootstrap approach is then introduced to investigate the null distribution of the likelihood ratio test. Finally, we employ the bootstrap approach to determine the presence of cured individuals in two sets of real-life data.