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The probability of disease development in a defined time period is described by a logistic regression model. A model for the regression variable, given disease status, is induced and is applied to case-control data. It is shown that the odds ratio estimators and their asymptotic variance matrices may be obtained by applying the original logistic regression model to the case-control study as if the data had been obtained in a prospective study. This result gives a flexible and convenient method of analysis for a range of case-control studies in which stratum sizes are reasonably large. The work extends Anderson's (1972) results on logistic discrimination and generalizes the findings of Breslow & Powers (1978) on the equivalence of odds ratio estimators when both prospective and retrospective logistic models are applied to case-control data.
Biometrika © 1979 Biometrika Trust