Multivariate Stochastic Orders Induced by Case-Control Sampling

Ori Davidov () and Amir Herman ()
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Ori Davidov: University of Haifa
Amir Herman: University of Haifa

Methodology and Computing in Applied Probability, 2011, vol. 13, issue 1, 139-154

Abstract: Abstract 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.

Keywords: Dependence concepts; Monotonicity; Regression; Multivariate stochastic orders; Total positivity; 60E15; 62G99; 62H05 (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s11009-009-9136-4

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