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Biometrika 1984 71(1):75-83; doi:10.1093/biomet/71.1.75
© 1984 by Biometrika Trust
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Life table methods for heterogeneous populations: Distributions describing the heterogeneity

PHILIP HOUGAARD

Institute of Mathematical Statistics, University of Copenhagen Copenhagen, Denmark

Taking account of heterogeneity between the individuals in population based mortality studies is important. A systematic way of describing heterogeneity is by an unobserved quantity called frailty, entering the hazard multiplicatively. Until now most studies have used a gamma distributed frailty, which is mathematically convenient; for example, the distribution among survivors is also gamma. This paper shows that several other distributions have equally simple properties, the main example being the inverse Gaussian distribution. Consequences of the different distributions are examined; the inverse Gaussian makes the population homogeneous with time, whereas for the gamma the relative heterogeneity is constant.

Key Words: Exponential family • Frailty • Heterogeneity • Inverse Gaussian distribution • Life table


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