Nonparametric Prevalence and Mortality Estimators for Animal Experiments With Incomplete Cause-of-Death Data

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Abstract
Age-specific prevalence and mortality estimators are important descriptors of disease development and the subsequent effects of a disease on longevity. Nonparametric maximum likelihood estimators for the prevalence and mortality functions are available for the case in which incidental and fatal occurrences of a disease can always be distinguished. This article generalizes these methods to allow the role of a disease in causing death to be uncertain for a subset of the animals dying with the disease. The proposed analysis makes no assumptions about the degree of disease lethality. Data from sacrificed animals can be incorporated easily, although sacrifices are not necessary if a certain representativeness assumption holds. No restrictions are imposed on the distribution of survival times, but the prevalence function is held constant over time intervals for stabilization purposes. Variances are estimated by inverting the observed information matrix. An EM algorithm simplifies the analysis when the prevalence function is constrained to be monotone or when cause of death is classified into ordered categories, according to how likely it was that the disease was responsible for death. The proposed methods are illustrated with some data on nonrenal vascular disease in female RFM mice.

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