Multivariate Stochastic Orders Induced by Case-Control Sampling

Ori Davidov; Amir Herman

doi:10.1007/s11009-009-9136-4

Multivariate Stochastic Orders Induced by Case-Control Sampling

Ori Davidov, Amir Herman

Department of Statistics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	139-154
Number of pages	16
Journal	Methodology and Computing in Applied Probability
Volume	13
Issue number	1
DOIs	https://doi.org/10.1007/s11009-009-9136-4
State	Published - Mar 2011

Bibliographical note

Funding Information:
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.

Keywords

Dependence concepts
Monotonicity
Multivariate stochastic orders
Regression
Total positivity

ASJC Scopus subject areas

Statistics and Probability
General Mathematics

Access to Document

10.1007/s11009-009-9136-4

Cite this

@article{125186bbc6644ac8a8c5cfd9e2197398,

title = "Multivariate Stochastic Orders Induced by Case-Control Sampling",

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, Multivariate stochastic orders, Regression, Total positivity",

author = "Ori Davidov and Amir Herman",

note = "Funding Information: 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.",

year = "2011",

month = mar,

doi = "10.1007/s11009-009-9136-4",

language = "English",

volume = "13",

pages = "139--154",

journal = "Methodology and Computing in Applied Probability",

issn = "1387-5841",

publisher = "Springer",

number = "1",

}

TY - JOUR

T1 - Multivariate Stochastic Orders Induced by Case-Control Sampling

AU - Davidov, Ori

AU - Herman, Amir

N1 - Funding Information: 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.

PY - 2011/3

Y1 - 2011/3

N2 - 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.

AB - 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.

KW - Dependence concepts

KW - Monotonicity

KW - Multivariate stochastic orders

KW - Regression

KW - Total positivity

UR - http://www.scopus.com/inward/record.url?scp=78651444213&partnerID=8YFLogxK

U2 - 10.1007/s11009-009-9136-4

DO - 10.1007/s11009-009-9136-4

M3 - Article

AN - SCOPUS:78651444213

SN - 1387-5841

VL - 13

SP - 139

EP - 154

JO - Methodology and Computing in Applied Probability

JF - Methodology and Computing in Applied Probability

IS - 1

ER -

Multivariate Stochastic Orders Induced by Case-Control Sampling

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this