On testing tumor onset times

Abstract

In a typical assay toxicologists study a substance with respect to its cancerogenicity by comparing a control group of rats with a treatment group. One is interested in the distribution of the unobservable onset time T of a certain type of tumor. When a rat dies at a time point C , say, one knows apart from C only whether T ⩽ C or T > C holds true. Data of this kind are called interval censored . In the present paper by means of local asymptotic normality (LAN) combined with counting process theory asymptotically optimal nonparametric tests (in a specific sense) are derived for comparing the distributions of the tumor onset time of the control and of the treatment group. The resulting tests are under the null hypothesis of equal distributions of the onset times in both samples asymptotically distribution free even if the distributions of the times to death C are different in both samples.