Some Nonparametric Techniques for Estimating the Intensity Function of a Cancer Related Nonstationary Poisson Process

Abstract

An attempt is made to model the appearance times of metastases as a nonstationary Poisson process. Three algorithms are developed for this task. The first follows the kernel approach used in probability density estimation by Parzen and Rosenblatt; the second extends the work of Grenander on mortality measurements to a more general censoring scheme appropriate for the present application; the third employs a discrete maximum penalized likelihood approach. We obtain estimates using both stratification and the proportional hazards model. Contrary to customary belief, it seems that the intensity functions associated with the tumor systems under investigation are nonincreasing.