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A Stochastic Model of Carcinogenesis and Tumor Size at Detection

Part of: Distribution theory - Probability Applications

Published online by Cambridge University Press:  01 July 2016

L. G. Hanin ,
S. T. Rachev ,
A. D. Tsodikov  and
A. Yu. Yakovlev
L. G. Hanin*
Affiliation:
Wayne State University
S. T. Rachev*
Affiliation:
University of California at Santa Barbara
A. D. Tsodikov*
Affiliation:
Universität Leipzig
A. Yu. Yakovlev*
Affiliation:
University of Utah
*
∗ Postal address: Department of Mathematics, Wayne State University, Detroit, Ml 48202, USA.
∗∗ Postal address: Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106, USA.
∗∗∗ Postal address: IMISE, Universität Leipzig, Liebigstr. 27, 04103 Leipzig, Germany.
∗∗∗∗ Postal address: Huntsman Cancer Institute, Division of Public Health Science, University of Utah, 546 Chipeta Way, Suite 1100, Salt Lake City, Utah 84108, USA.
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Abstract

This paper discusses the distribution of tumor size at detection derived within the framework of a new stochastic model of carcinogenesis. This distribution assumes a simple limiting form, with age at detection tending to infinity which is found to be a generalization of the distribution that arises in the length-biased sampling. Two versions of the model are considered with reference to spontaneous and induced carcinogenesis; both of them show similar asymptotic behavior. When the limiting distribution is applied to real data analysis its adequacy can be tested through testing the conditional independence of the size, V, and the age, A, at detection given A > t*, where the value of t* is to be estimated from the given sample. This is illustrated with an application to data on premenopausal breast cancer. The proposed distribution offers the prospect of the estimation of some biologically meaningful parameters descriptive of the temporal organization of tumor latency. An estimate of the model stability to the prior distribution of tumor size and some other stability results for the Bayes formula are given.

Keywords

STOCHASTIC MODELASYMPTOTIC PROPERTIESCARCINOGENESISCONDITIONAL DISTRIBUTIONTUMOR SIZESTABILITY TO PRIORSBAYES THEOREMPROBABILITY METRICS

MSC classification

Primary: 60E05: Distributions
Secondary: 62P10: Applications to biology and medical sciences
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 29 , Issue 3 , September 1997 , pp. 607 - 628
Copyright
Copyright © Applied Probability Trust 1997 

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