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Biometrika 2001 88(4):949-960; doi:10.1093/biomet/88.4.949
© 2001 by Biometrika Trust
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Two-sample tests for growth curves under dependent right censoring

Yehuda Vardi1, Zhiliang Ying1 and Cun-Hui Zhang1

1 Department of Statistics, Hill Center, Busch Campus, Rutgers University, Piscataway, New Jersey 08854, U.S.Avardi{at}stat.rutgers.eduzying{at}stat.rutgers.educunhui{at}stat.rutgers.edu

In many tumour growth inhibition studies, tumour sizes are recorded over a period of time, forming a growth curve for each experimental animal.A frequently asked question in these studies is whether or not different treatment agents/inhibitors result in different growth rates. To compare tumour growth rates under two treatments, either the t-test or the Wilcoxon–Mann–Whitney test could be used under suitable assumptions, provided that a one-dimensional variable, such as the area under the curve, is used to summarise a growth curve. Such tests may not be valid in the presence of informative heterogeneous censoring, in that a subject's continued participation in the experiment may depend on the tumour size and/or the level of toxicity of the treatment given. We propose test statistics that naturally correct the bias caused by the censorship and retain high efficiency. They are easy to construct and are nonparametric in nature, making no assumption on the distributions of the growth curves. The method is illustrated with an example from a tumour growth inhibition study on mice. Simulation results are also reported showing that the method performs well with moderate sample sizes.

Key Words: Area under curve; Hoeffding decomposition; Informative censoring; Tumour growth inhibition; U-statistic; Wilcoxon–Mann–Whitney test

Received September 1999. Revised April 2001


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