Annals of Statistics

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

Robert Bartoszynski, Barry W. Brown, Charles M. McBride, and James R. Thompson

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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.

Article information

Source
Ann. Statist., Volume 9, Number 5 (1981), 1050-1060.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345584

Digital Object Identifier
doi:10.1214/aos/1176345584

Mathematical Reviews number (MathSciNet)
MR628760

Zentralblatt MATH identifier
0475.62084

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62P10: Applications to biology and medical sciences 65K05: Mathematical programming methods [See also 90Cxx]

Keywords
Metastatic process melanoma hazard function maximum penalized likelihood estimation proportional hazards model

Citation

Bartoszynski, Robert; Brown, Barry W.; McBride, Charles M.; Thompson, James R. Some Nonparametric Techniques for Estimating the Intensity Function of a Cancer Related Nonstationary Poisson Process. Ann. Statist. 9 (1981), no. 5, 1050--1060. doi:10.1214/aos/1176345584. https://projecteuclid.org/euclid.aos/1176345584


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