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

Abstract

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 F ₂ 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 F ₁ of the time of onset of the disease. After a brief review of some past works on the estimation of F ₁ and F ₂, we demonstrate the strong uniform consistency of the NPMPLE of F ₁.

Keywords:

• non-parametric estimation
• pseudo-likelihood
• disease onset distribution
• consistency

Acknowledgements

The author is grateful to two anonymous referees for their constructive comments which have contributed to the substantial improvement of the paper.

Additional information

Notes on contributors

A.E. Gomes

Email: [email protected]