It is shown that retrospective sampling induces stochastic order relations in case-control studies. More specifically if the regression function is increasing and the covariates are positively dependent, then the covariates for cases are larger, with respect to some multivariate stochastic order, than the covariates of the controls. Strong dependence concepts yield strong multivariate stochastic orders. Conversely, different multivariate stochastic orders imply different monotonicity properties on the regression function. The results carry over to marginal models, transformed models and to problems involving confounders. The results set forth a new theoretical foundation for the analysis of case-control studies.
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Acknowledgements We would like to thank the AE and an anonymous referee for their insightful comments. This research was supported by the Israel Science Foundation, grant 1049/06.
- Dependence concepts
- Multivariate stochastic orders
- Total positivity
ASJC Scopus subject areas
- Statistics and Probability
- Mathematics (all)