Attribution of tumour lethality and estimation of the time to onset of occult tumours in the absence of cause-of-death information

A new statistical approach is developed for estimating the carcinogenic pot ential of drugs and other chemical substances used by humans. Improved stat istical methods are developed for rodent tumorigenicity assays that have in terval sacrifices but not cause-of-death data. For such experiments, this p aper proposes a nonparametric maximum likelihood estimation method for esti mating the distributions of the time to onset of and the time to death from the tumour. The log-likelihood function is optimized by using a constraine d direct search procedure. Using the maximum likelihood estimators, the num ber of fatal tumours in an experiment can be imputed. By applying the proce dure proposed to a real data set, the effect of calorie restriction is inve stigated. In this study, we found that calorie restriction delays the tumou r onset time significantly for pituitary tumours. The present method can re sult in substantial economic savings by relieving the need for a case-by-ca se assignment of the cause of death or context of observation by pathologis ts. The ultimate goal of the method proposed is to use the imputed number o f fatal tumours to modify Peto's International Agency for Research on Cance r test for application to tumorigenicity assays that lack cause-of-death da ta.