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Repeated Challenge Studies: A Comparison of Union-Intersection Testing with Linear Modeling

Published online by Cambridge University Press:  01 January 2025

Richard A. Levine  and
Pamela A. Ohman
Richard A. Levine*
Affiliation:
University of California, Davis
Pamela A. Ohman
Affiliation:
Cornell University
*
Requests for reprints should be sent to Richard A. Levine, Division of Statistics, University of California, Davis CA 95616.
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Abstract

Challenge studies are often implemented for assessing whether a subject is sensitive to a certain agent or allergen. In particular, researchers test groups of subjects to determine if there really exists a causal relationship between some agent of interest and a response. To answer such a question, we need to detect the presence of the phenomenon in just one individual. Typically, however, there are a large number of unknown risk factors associated with the response and a potentially small population prevalence. Hence, standard statistical techniques, by averaging the treatment effect across the group, may miss a significant response of a single individual and lead to inconclusive results. We develop an alternative approach based on union-intersection testing that will allow a practitioner to correctly examine observations on an individual apart from the other subjects and test the hypothesis of interest: Does the phenomenon exist in the population? More specifically, we show how this technique adjusts for the multiple number of tests encountered when analyzing data for each individual subject separately. Furthermore, we demonstrate power calculations for the determination of sample size prior to performing the study. The performance of the union-intersection approach in comparison to linear models and semiparametric techniques is considered through sample size calculations and simulations. The union-intersection testing methodology out performs the Kolmogorov tests. However, the nested linear model performs as well if not better than the union-intersection tests. To illustrate the ideas presented in the paper, we provide an application in which we analyze psychological data collected by way of a challenge study design.

Keywords

hypothesis testmultiple testspower analysispopulation prevalenceKolmogorov testsapplication
Type
Original Paper
Information
Psychometrika , Volume 62 , Issue 3 , September 1997 , pp. 435 - 455
Copyright
Copyright © 1997 The Psychometric Society

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Footnotes

1

Research supported by the Office of Naval Research Graduate Fellowship and NIH Training Grant No. ES07261

2

Research supported by NSF Training Grant No. DMS956682

We would like to thank Professor George Casella and Susan Alber for many helpful discussions and advice during the course of this research and for comments on drafts of this manuscript. We would also like to express gratitude to Lorna Bayer and Professor Barbara Strupp for providing the data on dopamine exposure in rats. Finally, we would like to thank three referees and the editor for very helpful and insightful remarks that lead to a much improved version of this paper.

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