Using a mixed effects model to estimate geographic variation in cancer rates

Biometrics
G A PennelloM H Gail

Abstract

Commonly used methods for depicting geographic variation in cancer rates are based on rankings. They identify where the rates are high and low but do not indicate the magnitude of the rates nor their variability. Yet such measures of variability may be useful in suggesting which types of cancer warrant further analytic studies of localized risk factors. We consider a mixed effects model in which the logarithm of the mean Poisson rate is additive in fixed stratum effects (e.g., age effects) and in logarithms of random relative risk effects associated with geographic areas. These random effects are assumed to follow a gamma distribution with unit mean and variance 1/alpha, similar to Clayton and Kaldor (1987, Biometrics 43, 671-681). We present maximum likelihood and method-of-moments estimates with standard errors for inference on alpha -1/2, the relative risk standard deviation (RRSD). The moment estimates rely on only the first two moments of the Poisson and gamma distributions but have larger standard errors than the maximum likelihood estimates. We compare these estimates with other measures of variability. Several examples suggest that the RRSD estimates have advantages compared to other measures of variability.

References

Oct 1, 1992·Current Opinion in Oncology·R J Biggar, C S Rabkin
May 15, 1991·Journal of the National Cancer Institute·M H GailS Broder
Feb 15, 1995·American Journal of Epidemiology·M Martuzzi, M Hills
Jan 1, 1996·Cancer Causes & Control : CCC·J D Potter
Oct 5, 1996·BMJ : British Medical Journal·S F OlsenP Elliott

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Citations

Aug 30, 2001·Evolution; International Journal of Organic Evolution·L W SimmonsJ T Rotenberry
Oct 21, 2006·Journal of the American Academy of Dermatology·Hugh M Gloster, Kenneth Neal
Jun 6, 2002·Cadernos de saúde pública·Guilherme L Werneck, James H Maguire

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