Nonparametric joint estimators for disease resistance and survival functions in survival/sacrifice experiments

The nonparametric estimators proposed in this paper simultaneously estimate the disease resistance function, S(t), for the distribution of time to occurrence of disease, and the survival function, P(t), for the distribution of time to death caused by the disease. The estimators are applicable to animal survival data when the disease of interest is irreversible and the cause of death of each animal can be determined. Diseases need not be classified as universally lethal or universally nonlethal, and time to occurrence of the disease of interest need not be observable directly. It is shown that the proposed estimators are maximum likelihood estimators under the condition that S(t)/P(t) is monotonically decreasing. Application of the derived estimators is illustrated with experimental survival/sacrifice data, and results of a simulation study of the estimators' performance are reported.