Cross–Over Design

  • Helge Toutenburg
  • Shalabh
Part of the Springer Texts in Statistics book series (STS)


Clinical trials form an important part of the examination of new drugs or medical treatments. The drugs are usually assessed by comparing their effects on human subjects. From an ethical point of view, the risks which patients might be exposed to must be reduced to a minimum and also the number of individuals should be as small as statistically required. Cross{ over trials follow the latter, treating each patient successively with two or more treatments. For that purpose, the individuals are divided into randomized groups in which the treatments are given in certain orders. In a 2 × 2 design, each subject receives two treatments, conventionally labeled as A and B. Half of the subjects receive A first and then cross over to B while the remaining subjects receive B first and then cross over to A. Between two treatments a suitable period of time is chosen, where no treatment is applied. This washout period is used to avoid the persistence of a treatment applied in one period to a subsequent period of treatment.

The aim of cross{over designs is to estimate most of the main effects using within–subject differences (or contrasts). Since it is often the case that there is considerably more variation between subjects than within subjects, this strategy leads to more powerful tests than simply comparing two independent groups using between–subject information. As each subject acts as his own control, between–subject variation is eliminated as a source of error.


Null Hypothesis Contingency Table Classical Approach Unbiased Estimator Total Response 
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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Institut für StatistikLudwig-Maximilians-UniversitätMünchenGermany
  2. 2.Department of Mathematics & StatisticsIndian Institute of TechnologyKanpurIndia

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