Repeated challenge studies: A comparison of union-intersection testing with linear modeling

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.