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June, 1989 On Permutation Tests for Hidden Biases in Observational Studies: An Application of Holley's Inequality to the Savage Lattice
Paul R. Rosenbaum
Ann. Statist. 17(2): 643-653 (June, 1989). DOI: 10.1214/aos/1176347131

Abstract

Randomized experiments and observational studies both attempt to estimate the effects produced by a treatment, but in observational studies, subjects are not randomly assigned to treatment or control. A theory of observational studies would closely resemble the theory for randomized experiments in all but one critical respect: In observational studies, the distribution of treatment assignments is not known. The problems that are special to observational studies revolve around our uncertainty about how treatments were assigned. In this connection, tools are needed for describing distributions of treatment assignments that do not assign equal probabilities to all assignments. Two such tools are a lattice of treatment assignments first studied by Savage and an inequality due to Holley for probability distributions on a lattice. Using these tools, it is shown that certain permutation tests are unbiased as tests of the null hypothesis that the distribution of treatment assignments resembles a randomization distribution against the alternative hypothesis that subjects with higher responses are more likely to receive the treatment. In particular, these tests are unbiased against alternatives formulated in terms of a model previously used in connection with sensitivity analyses.

Citation

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Paul R. Rosenbaum. "On Permutation Tests for Hidden Biases in Observational Studies: An Application of Holley's Inequality to the Savage Lattice." Ann. Statist. 17 (2) 643 - 653, June, 1989. https://doi.org/10.1214/aos/1176347131

Information

Published: June, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0684.62038
MathSciNet: MR994256
Digital Object Identifier: 10.1214/aos/1176347131

Subjects:
Primary: 62G10
Secondary: 06D99 , 60C05

Keywords: decreasing in transposition , decreasing reflection function , Holley's inequality , lattice theory , Mantel-Haenszel test , McNemar-Cox test , observational studies , Permutation test , rank sum test , signed rank test , unbiased test

Rights: Copyright © 1989 Institute of Mathematical Statistics

Vol.17 • No. 2 • June, 1989
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