Sample size calculations for randomised trials including both independent and paired data

Randomised trials including a mixture of independent and paired data arise in many areas of health research, yet methods for determining the sample size for such trials are lacking. We derive design effects algebraically assuming clustering because of paired data will be taken into account in the analysis using generalised estimating equations with either an independence or exchangeable working correlation structure. Continuous and binary outcomes are considered, along with three different methods of randomisation: cluster randomisation, individual randomisation and randomisation to opposite treatment groups. The design effect is shown to depend on the intracluster correlation coefficient, proportion of observations belonging to a pair, working correlation structure, type of outcome and method of randomisation. The derived design effects are validated through simulation and example calculations are presented to illustrate their use in sample size planning. These design effects will enable appropriate sample size calculations to be performed for future randomised trials including both independent and paired data.