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

Cluster randomised crossover designs (CRXOs) are a powerful type of longitudinal cluster randomised trial in which all participating clusters switch between two treatment conditions. "Multiple-period" CRXOs divide the trial duration into a number of periods of equal length and can allow for multiple crossovers between treatment conditions. It can be assumed that increasing the number of crossovers leads to an increase in statistical power. We investigate whether this is true for standard correlation structures, comparing CRXO designs with equal numbers of clusters, participants, and periods but differing in the number of crossovers, considering continuous outcomes.

We consider the formula for the variance of the treatment effect estimator for multiple-period CRXOs under exchangeable and block-exchangeable within-cluster correlation structures, assuming equal cluster-period sizes and different patterns of treatment conditions in the treatment sequences varying in the number of crossovers. We also conduct a simulation study to compare the statistical power between multiple-period CRXO designs with different numbers of crossovers that share the same number and duration of periods and the same number of participants in each cluster period.

Under exchangeable and block-exchangeable correlation structures and equal cluster-period sizes, the number of crossovers in the treatment sequences does not impact study power, provided the design is balanced in terms of the number of periods and clusters implementing each condition.

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.