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The simplest form of retrospective study allows the reconstruction of the dependence between a binary outcome, Y, representing the contrast between cases and controls, and one or more explanatory variables. A different objective for such situations is considered, in which there are distinct explanatory variables, say (W,X) determining Y. Reconstruction of the originating distribution of (W,X) from the case-control data is considered for both continuous and binary variables. Emphasis is on the linear regression coefficient of W on X. That coefficient, but not the relevant intercept, shows considerable stability, as shown by theory and simulations. An approximation to the value of the coefficient not conditioning on Y is given.1

Original publication




Journal article


Econometrics and Statistics

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