  Crossover designs are an extremely useful tool to investigators, whilst group
sequential methods have proven highly proficient at improving the efficiency of
parallel group trials. Yet, group sequential methods and crossover designs have
rarely been paired together. One possible explanation for this could be the
absence of a formal proof of how to strongly control the familywise error rate
in the case when multiple comparisons will be made. Here, we provide this
proof, valid for any number of initial experimental treatments and any number
of stages, when results are analysed using a linear mixed model. We then
establish formulae for the expected sample size and expected number of
observations of such a trial, given any choice of stopping boundaries. Finally,
utilising the four-treatment, four-period TOMADO trial as an example, we
demonstrate group sequential methods in this setting could have reduced the
trials expected number of observations under the global null hypothesis by over
33%.
