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November, 1992 Modelling Heterogeneity in Survival Analysis by the Compound Poisson Distribution
Odd O. Aalen
Ann. Appl. Probab. 2(4): 951-972 (November, 1992). DOI: 10.1214/aoap/1177005583


When making probabilistic models for survival times, one should consider the fact that individuals are heterogeneous. The observed changes in population intensities (or hazard rates) over time are a mixed result of two influences: on the one hand, the actual changes in the individual hazards, and, on the other hand, the selection due to high-risk individuals leaving the risk group early. I will consider the common multiplicative model for heterogeneity, but with the new feature that the random proportionality factor has a compound Poisson distribution. This distribution is studied in some detail. It is pointed out how its application to the survival situation extends a model of Hougaard, inheriting several nice properties. One important feature of the model is that it yields a subgroup of zero susceptibility, which "survives forever." This is a relevant model in medicine and demography. Two examples are given where the model is fitted to data concerning marriage rates and fertility.


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Odd O. Aalen. "Modelling Heterogeneity in Survival Analysis by the Compound Poisson Distribution." Ann. Appl. Probab. 2 (4) 951 - 972, November, 1992.


Published: November, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0762.62031
MathSciNet: MR1189425
Digital Object Identifier: 10.1214/aoap/1177005583

Primary: 60E05
Secondary: 62M05

Keywords: compound Poisson distribution , frailty , Heterogeneity , Survival analysis

Rights: Copyright © 1992 Institute of Mathematical Statistics


Vol.2 • No. 4 • November, 1992
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