Consistency of the non-parametric maximum pseudo-likelihood estimator of the disease onset distribution function for a survival–sacrifice model

Suppose that in a carcinogenicity experiment with animals where the tumour is not palpable, we observe only the time of death of the animal, the cause of death (the tumour or another independent cause, as sacrifice) and whether the tumour was present at the time of death. These last two indicator variables are evaluated after an autopsy. We can estimate the cumulative distribution function F2 of the time of death from the disease using the Kaplan–Meier estimator and then calculate the non-parametric maximum pseudo-likelihood estimator (NPMPLE) of the cumulative distribution function F1 of the time of onset of the disease. After a brief review of some past works on the estimation of F1 and F2, we demonstrate the strong uniform consistency of the NPMPLE of F1.