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American Journal of Epidemiology Vol. 122, No. 1: 149-162
Copyright © 1985 by The Johns Hopkins University School of Hygiene and Public Health

research-article

GENERAL RELATIVE RISK FUNCTIONS FOR CASE-CONTROL STUDIES

N. E. BRESLOW1 and B. E. STORER2

1Department of Biostatistics, SC-32, University of Washington Seattle, WA 98195
2Fred Hutchinson Cancer Research Center 1124 Columbia Street, Seattle, WA 98104

Reprint requests to Dr. N. E. Breslow

While multiplicative (log-linear and logistic) models have a firmly established place in epidemiologic methodology, additive and other more general model structures are needed also. The authors propose a parametric family of relative risk functions ranging from subadditive to supramultiplicative that is generated by varying the exponent in a power transform for the log relative risk. The choice of model is facilitated by graphic analysis of goodness-of-fit statistics computed for various values of the exponent. Intermediate quantities available as byproducts of the fit are useful for checking the influence of particular observations on the estimated regression coefficients. Three examples illustrate the applications of these methods to random, stratified, and matched samples of cases and controls. Computer software is available for each of these situations. Even though different relative risk models may have markedly different implications for the multifactorial nature of the disease process, it may be difficult to distinguish between them unless the data are quite extensive.

biometry; epidemiologic methods; retrospective studies


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