Testing for the presence of cured patients: a simulation study

Authors

  • Yingwei Peng,

    Corresponding author
    1. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland A1C 5S7, Canada
    • Department of Mathematics and Statistics, Memorial University of Newfoundland, St John's, Newfoundland A1C 5S7, Canada
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  • Keith B. G. Dear,

    1. National Centre for Epidemiology and Population Health, and Centre for Mental Health Research, The Australian National University, Canberra, ACT 0200, Australia
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  • K. C. Carriere

    1. Department of Mathematical Sciences, University of Alberta, Alberta T6G 2G1, Canada
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Abstract

An important but difficult problem in clinical trials is to determine the presence of cured patients when long-term survivors are observed. The likelihood ratio test has been studied for this purpose in the gamma mixture model. However, its asymptotic null distribution is not readily available due to 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 distribution can also be used to approximate the asymptotic null distribution of the likelihood ratio test in the Weibull and log-normal mixture models when the 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 censoring rate is small or the hazard rate is large. Consequently caution is needed 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 study. Copyright © 2001 John Wiley & Sons, Ltd.

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