Robust assessment of two-treatment higher-order cross-over designs against missing values

In scientific experiments where human behaviour or animal response is intrinsically involved, such as clinical trials, there is a strong possibility of recording missing values. Missing data in a clinical trial has the potential to impact severely on study quality and precision of estimates. In studies which use a cross-over design, even a small number of missing values can lead to the eventual design being disconnected. In this case, some or all of the treatment contrasts under test cannot be estimated and the experiment is compromised since little can be achieved from it. Experiments comparing two treatments that use a cross-over design with more than two experimental periods are considered. Methods to limit the impact of missing data on study results are explored. It is shown that the breakdown number and, if it exists, perpetual connectivity of the planned design are useful robustness properties which guard against the possibility of a disconnected eventual design. A procedure is proposed which assesses planned designs for robustness against missing values and the method is illustrated by assessing several designs that have been previously considered on cross-over studies.