Ordinal Data: Crossover Design Analysis

Authored by: Kung-Jong Lui

Encyclopedia of Biopharmaceutical Statistics

Print publication date:  August  2018
Online publication date:  August  2018

Print ISBN: 9781498733953
eBook ISBN: 9781351110273
Adobe ISBN:


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We may commonly encounter, in a crossover trial, the underlying patient response of interest on an ordinal scale—worse, same, slightly improved, and better. Since these ordinal responses are not continuous or interval data, the ordinal responses are generally not appropriate for arithmetic operation. We discuss the approaches to analyze ordinal data under a crossover design. These include the normal random effects proportional odds model, the simple change score method, and the conditional approach with using the generalized odds ratio to measure the relative treatment effects. We focus our discussion on the most frequently used AB/BA (or simple crossover) design. We present both asymptotic and exact test procedures, as well as asymptotic and exact interval estimators. We further extend the discussion to a three-treatment three-period crossover trial. We note that one can easily apply the ideas presented here to derive the corresponding test procedures and estimators when using a Latin squares to reduce the large number of groups for comparing four or more treatments in a crossover trial with a complete set of treatment-receipt sequences, or when employing an incomplete block crossover design to decrease the risk of being lost to follow-up in a crossover trial with long duration.

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