Robustness of crossover trials against subject drop-out - Examples of perpetually connected designs

When performing a repeated measures experiment, such as a clinical trial, there is a risk of subject drop-out during the experiment. If one or more subjects leave the study prematurely, a situation could arise where the eventual design is disconnected, implying that very few treatment contrasts for both direct effects and carryover effects are estimable. This paper aims to identify experimental conditions where this problem with the eventual design can be avoided. It is shown that in the class of uniformly balanced repeated measurement designs consisting of two or more Latin squares, there are planned designs with the following useful property. Provided that all subjects have completed the first two periods of study, such a design will not be replaced by a disconnected eventual design due to drop-out, irrespective of the type of drop-out behaviour that may occur. Designs with this property are referred to as perpetually connected. These experimental conditions are identified and examined in the paper and an example of at least one perpetually connected uniformly balanced repeated measurement design is given in each case. The results improve upon previous contributions in the literature that have been confined largely to cases in which drop-out occurs only in the final periods of study.