Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-13T04:13:20.206Z Has data issue: false hasContentIssue false
  • English
  • Français

Representation of disease etiologies by certain stochastic models

Published online by Cambridge University Press:  14 July 2016

Leo Katz
Leo Katz*
Affiliation:
Michigan State University, East Lansing
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers the appropriateness of certain stochastic models for the representation of disease etiologies. Models for disease as the result of multiple events, and as the endpoint of a network of events, are discussed.

Keywords

STOCHASTIC MODELDISEASE ETIOLOGYASSOCIATION AND CAUSATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 4 , December 1977 , pp. 663 - 674
Copyright
Copyright © Applied Probability Trust 1977 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Professor Katz was working on it just before his untimely death in Haifa on 6 May 1976, and it is being published with only minor editorial changes. An obituary appears on pages 890–896.

Research supported by NSF Grant MPS75–08044.

References

References

Chung, K.-L. (1941) On the probability of the occurrence of at least m events among n arbitrary events. Ann. Math. Statist. 12, 328–338.Google Scholar
Chung, K.-L. (1942) On mutually favorable events. Ann. Math. Statist. 13, 338–349.Google Scholar
Chung, K.-L. (1943) Generalization of Poincaré's formula in the theory of probability. Ann. Math. Statist. 14, 63–65.Google Scholar
Chung, K.-L. and Hsu, L. C. (1945) A combinatorial formula and its application to the theory of probability of arbitrary events. Ann. Math. Statist. 16, 91–95.Google Scholar
Erdös, P. and Renyi, A. (1960) On the evolution of random graphs. Magyar Tud. Akad. Mat. Kutato Intéz. Közl. 5, 17–61.Google Scholar
Fisher, R. A. (1958) Cigarettes, cancer, and statistics. Centennial Review 2, 151–166.Google Scholar
Fréchet, M. (1940), (1943) Les probabilités associées à un système d'événements compatibles et dépendants. Actualités Sci. Indust. 859, 942.Google Scholar
Good, I. J. (1961), (1962) A causal calculus (I), (II). Brit. J. Philos. Sci. 11, 305–318 and 12, 43–51.Google Scholar
Jordan, K. (1927) A valószinüsegszámitás alapfogalmai. (Les fondements du calcul des probabilités.) Mathematikai es Physikai Lapok. 34, 109–136.Google Scholar
Malinvaud, E. (1966) Pour une axiomatique de la causalité. In Model Building in the Human Sciences, Wold, H. O. A. (Scientific Organizer), Entretiens de Monaco: Union Européenne d'Editions, 297–302.Google Scholar
Neyman, J. (1950) First Course in Probability and Statistics. Holt, New York. (pp. 69–95).Google Scholar
Poincaré, H. (1896) Calcul des Probabilités. Gauthier-Villars, Paris.Google Scholar
Suppes, P. (1970) A Probabilistic Theory of Causality. Acta. Philosophica Fennica, Fasc. XXIV.Google Scholar
Takács, L. (1967) On the method of inclusion and exclusion. J. Amer. Statist. Soc. 62, 102–113.Google Scholar
Tautu, P. (1975) Some examples of probability models in cancer epidemiology. Bull. Internat. Statist. Inst. 46(2), 144–158 and 164–171.Google Scholar
Arley, N. and Iversen, S. (1952) On the mechanism of experimental carcinogenesis. III. Further development of the hit theory of carcinogenesis. Acta Pathol. Microbiol. Scand. 30, 21–53.Google Scholar
Armitage, P. and Doll, R. (1954) The age distribution of cancer and a multi-stage theory of carcinogenesis. Brit. J. Cancer 8, 1–12.Google Scholar
Armitage, P. and Doll, R. (1961) Stochastic models for carcinogenesis. Proc. 4th Berkeley Symp. Math. Statist. Prob. 4, 19–38.Google Scholar
Burch, P. R. J. (1975) The Biology of Cancer; A New Approach. Medical and Technical Publishing Co., Lancaster.Google Scholar
Burch, P. R. J., Jackson, E. and Rowell, N. R. (1972) Growth, disease and ageing: a unified approach. Z. Alternforschung 26, 1–28.Google Scholar
Iversen, S. and Arley, N. (1950) On the mechanism of experimental carcinogenesis. Acta Pathol. Microbiol. Scand. 27, 773–803.Google Scholar
Kendall, D. G. (1960) Birth-and-death processes, and the theory of carcinogenesis. Biometrika 47, 13–21.Google Scholar
Neyman, J. (1958) A stochastic model of carcinogenesis. Mimeographed lectures, U.S. National Institutes of Health, 12 and 26 November 1958.Google Scholar
Neyman, J. and Scott, E. L. (1967) Statistical aspects of the problem of carcinogenesis. Proc. 5th Berkeley Symp. Math. Statist. Prob 4, 745–776.Google Scholar