Regression Reconstruction from a Retrospective Sample

Christiana Kartsonaki; D R Cox

doi:10.1016/j.ecosta.2020.10.003

Regression Reconstruction from a Retrospective Sample

Econom Stat. 2023 Jan:25:87-92. doi: 10.1016/j.ecosta.2020.10.003.

Authors

Christiana Kartsonaki¹, D R Cox²

Affiliations

¹ MRC Population Health Research Unit, Nuffield Department of Population Health, University of Oxford, Oxford OX3 7LF, UK.
² Nuffield College, Oxford OX1 1NF, UK.

Abstract

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.

Keywords: Bias removal; Case-control study; Indirect sampling.