Two-sample tests for growth curves under dependent right censoring

In many tumour growth inhibition studies, tumour sizes are recorded over a period of time, forming a growth curve for each experimental animal. A freq uently asked question in these studies is whether or not different treatmen t agents/inhibitors result in different growth rates. To compare tumour gro wth rates under two treatments, either the t-test or the Wilcoxon-Mann-Whit ney test could be used under suitable assumptions, provided that a one-dime nsional 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 he terogeneous censoring, in that a subject's continued participation in the e xperiment may depend on the tumour size and/or the level of toxicity of the treatment given. We propose test statistics that naturally correct the bia s caused by the censorship and retain high efficiency. They are easy to con struct and are nonparametric in nature, making no assumption on the distrib utions of the growth curves. The method is illustrated with an example from a tumour growth inhibition study on mice. Simulation results are also repo rted showing that the method performs well with moderate sample sizes.