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Multivariate Stochastic Orders Induced by Case-Control Sampling

Author

Listed:
  • Ori Davidov

    (University of Haifa)

  • Amir Herman

    (University of Haifa)

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.

Suggested Citation

  • Ori Davidov & Amir Herman, 2011. "Multivariate Stochastic Orders Induced by Case-Control Sampling," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 139-154, March.
    • Handle: RePEc:spr:metcap:v:13:y:2011:i:1:d:10.1007_s11009-009-9136-4
    DOI: 10.1007/s11009-009-9136-4
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    References listed on IDEAS

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    1. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities II. Multivariate reverse rule distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 499-516, December.
    2. Colangelo, Antonio & Hu, Taizhong & Shaked, Moshe, 2008. "Conditional orderings and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 358-371, March.
    3. Moshe Shaked & J. George Shanthikumar, 1990. "Multivariate Stochastic Orderings and Positive Dependence in Reliability Theory," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 545-552, August.
    4. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 467-498, December.
    5. Hu, Taizhong & Khaledi, Baha-Eldin & Shaked, Moshe, 2003. "Multivariate hazard rate orders," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 173-189, January.
    6. Lucas, Larry A. & Wright, F. T., 1991. "Testing for and against a stochastic ordering between multivariate multinomial populations," Journal of Multivariate Analysis, Elsevier, vol. 38(2), pages 167-186, August.
    7. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2005. "Some notions of multivariate positive dependence," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 13-26, August.
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