Group Sequential Crossover Trial Designs with Strong Control of the Familywise Error Rate M. J. Grayling $^{1}$, J. M. S. Wason$^{1,2}$, A. P. Mander1 1. Hub for Trials Methodology Research, MRC Biostatistics Unit, Cambridge, UK, 2. Institute of Health and Society, Newcastle University, Newcastle, UK. Running Head: Group Sequential Crossover Trials. Abstract: 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%. Keywords: Clinical trial; Crossover; Familywise error rate; Group sequential; Linear mixed model. Address correspondence to M. J. Grayling, MRC Biostatistics Unit, Forvie Site, Robinson Way, Cam- bridge CB2 0SR, UK; Fax: +44-(0)1223-330365; E-mail: mjg211@cam.ac.uk. 1 arXiv:1710.03492v1 [stat.ME] 10 Oct 2017