Basic methods to compute the required sample size are well understood and supported by widely available software. However, the sophistication of the sample size methods commonly used has not kept pace with the complexity of the experimental designs most often employed in practice. In this paper, we compile available methods for sample size calculations for continuous and binary outcomes with and without covariates, for both clustered and non-clustered RCTs. Formulae for panel data and for unbalanced designs (where there are different numbers of treatment and control observations) are also provided. The paper includes three extensions: (1) methods to optimize the sample when costs constraints are binding; (2) simulation methods to compute the power of a complex design; and (3) methods to consider in the sample size calculation adjustments for multiple testing. The paper is provided together with spreadsheets and STATA code to implement the methods discussed.
Power analysis Sample size calculations Randomised Control Trials Cluster Randomised Control Trial Covariates Cost Minimisation Multiple outcomes Simulation