American Journal of Epidemiology Vol. 108, No. 3: 214-222
Copyright © 1978 by The Johns Hopkins University School of Hygiene and Public Health
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ESTIMATING EXPOSURE-SPECIFIC DISEASE RATES FROM CASECONTROL STUDIES USING BAYES' THEOREM
1Division of Epidemiology, UCLA School of Public Health Los Angeles, CA 90024
2Department of Biostatistics, Harvard School of Public Health Boston, MA
1address for reprint requests.
The methods used for selecting subjects yield three types of case-control studies: 1) incident cases are compared to non-cases chosen to be representative of the exposure distribution among the person-years which produced the cases. In this type of study the exposure-odds ratio equals the incidence density ratio; 2) Incident cases are compared to residual non-cases at the end of the risk period (exposure-odds ratio = cumulative Incidence-odds ratio); 3) prevalent cases are compared to non-cases (exposure-odds ratio = prevalence-odds ratio). In study type 1 the equivalence of odds ratio to rate ratio requires no "rare disease assumption;" this permits estimation of exposure-specific illness rates when the overall rate Is known. In study types 2 and 3 the exposure-odds ratio equals the corresponding rate ratios only when exposure-specific rates are low. Nonetheless, exposure-specific rates can be calculated without making any rare disease assumption using Bayes' theorem and Information on the overall disease rate. A method for obtaining approximate confidence limits around the exposure-specific rates is presented.
biometry; epidemiologlc methods; retrospective studies; statistics
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