Testing incidence of occult tumors by attributing tumor lethality in the absence of cause-of-death informatio

A new statistical estimation and testing approach is developed for rodent tumorigenicity assays that have a single terminal sacrifice or occasionally interval sacrifices but not cause-of-death data. For such experiments, we propose a nonparametric maximum likelihood estimation method for estimating the distributions of time-to-onset-of and the time-to-death-from the tumor of interest. The log-likelihood function is maximized using a constrained direct search procedure. Using the maximum likelihood estimators, the numbers of fatal tumors in an experiment can be imputed. The proposed estimation method can be applied to data with a single terminal sacrifice as well as data with interval sacrifices without implementing further assumptions.;The EM algorithm is also implemented to compare the time-to-onset-of and the time-to-death-from the tumor of interest with ones from the proposed NPMLE method. The proposed NPMLE method is found to be more efficient than the EM algorithm approach for the problem of constrained nonparametric maximum likelihood estimation in carcinogenicity studies.;For experiments that lack cause-of-death data, the proposed methods use statistically estimated numbers of fatal tumors to modify Peto's IARC (International Agency for Research on Cancer) test which is usually implemented using pathologist-assigned cause-of-death information. Because a statistically estimated cause of death is used to modify Peto's IARC test, the new testing approach is more valid than Peto's test using pathologist-assigned cause-of-death information in terms of controlling the probability of a Type I error by achieving its asymptotic normal distribution under the null hypothesis.;The proposed testing procedure is robust in various situations of both multiple-sacrifice and single-sacrifice animal experiments. In addition, the present method can result in substantial economic savings by relieving the need for case-by-case assignment of cause of death or context of observation by pathologists.;A Monte Carlo simulation study for the proposed methods are conducted to assess size and power of the test as well as the accuracy of cause of death attributed by the proposed estimation method. The proposed methods are illustrated using real experimental data sets.