Regression Reconstruction from a Retrospective Sample.

The simplest form of retrospective study allows the reconstruction of the dependence between a binary outcome, 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 determining . Reconstruction of the originating distribution of from the case-control data is considered for both continuous and binary variables. Emphasis is on the linear regression coefficient of on . 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 is given.