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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. [ABSTRACT FROM PUBLISHER]

In multiple regression problems when covariates can be naturally grouped, it is important to carry out feature selection at the group and within-group individual variable levels simultaneously. The existing methods, including the lasso and group lasso, are designed for either variable selection or group selection, but not for both. We propose a group bridge approach that is capable of simultaneous selection at both the group and within-group individual variable levels. The proposed approach is a penalized regularization method that uses a specially designed group bridge penalty. It has the oracle group selection property, in that it can correctly select important groups with probability converging to one. In contrast, the group lasso and group least angle regression methods in general do not possess such an oracle property in group selection. Simulation studies indicate that the group bridge has superior performance in group and individual variable selection relative to several existing methods. [ABSTRACT FROM AUTHOR]