The properties of the non-parametric maximum likelihood estimator (NPMLE) of the cumulative distribution function (cdf) of the survival times of a population have been studied for a long time under the standard right censorship (RC) model, which assumes independent censoring. The independent assumption is sometimes not justified in applications. In this project a new RC model that allows dependent censoring is introduced. The new model is more realistic in many applications including the analysis of survival times of cancer patients in a follow-up study that the investigator and his collaborators are engaged in. Under the new model, the PI plans to establish the asymptotic properties of the NPMLE of the survival function on the real line. New models that allow the dependent censoring for doubly censored data and other types of interval-censored data will also be investigated.
Right censored and doubly-censored data occur frequently in industrial experiments and medical research. The new models proposed by the investigator are motivated by the needs in the cancer research in which the investigator is analyzing certain breast cancer data provided by the Memorial Sloan-Kettering Cancer Center. The results from this project will be useful in the analysis of the data from clinical trials and engineering reliability studies. The theoretical results will contritute to the advancement of the statistical theory of survival analysis.