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Regression Reconstruction from a Retrospective Sample

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  • Kartsonaki, Christiana
  • Cox, D. R.

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.11Supplementary appendix with simulation code and results.

Suggested Citation

  • Kartsonaki, Christiana & Cox, D. R., 2023. "Regression Reconstruction from a Retrospective Sample," Econometrics and Statistics, Elsevier, vol. 25(C), pages 87-92.
    • Handle: RePEc:eee:ecosta:v:25:y:2023:i:c:p:87-92
    DOI: 10.1016/j.ecosta.2020.10.003
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    References listed on IDEAS

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    1. Jiawei Wei & Raymond J. Carroll & Ursula U. Müller & Ingrid Van Keilegom & Nilanjan Chatterjee, 2013. "Robust estimation for homoscedastic regression in the secondary analysis of case–control data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(1), pages 185-206, January.
    2. Wei, Jiawei & Carroll, Raymond & Muller, Ursula & Van Keilegom, Ingrid & Chatterjee, Nilanjan, 2013. "Robust estimation for homoscedastic regression in the secondary analysis of case–control data," LIDAM Reprints ISBA 2013007, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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