Additional crossovers in cluster randomised crossover trials do not always increase statistical power

When an exchangeable or block-exchangeable within-cluster correlation structure and a time-invariant effect of treatment are assumed, power calculations for CRXO designs are invariant to the specific ordering of treatment conditions. In particular, a CRXO design with additional crossovers does not lead to increased statistical power compared to a CRXO design with just one crossover for these within-cluster correlation structures. Further work is required to investigate the utility of multiple crossovers in situations where the treatment effect varies over time.