Optimizing the use of simulation methods in multilevel sample size calculations

Simulation-based methods are an alternative approach to sample size calculations, particularly for complex multilevel models where analytical calculations may be less straightforward. A criticism of simulation-based approaches is that they are computationally intensive, so in this paper we contrast different approaches of using the information within each simulation and sharing information across scenarios. We describe the “standard error” method (using the known effect estimate and simulations to estimate the standard error for a scenario) and show that it requires far fewer simulations than other methods. We also show that transforming power calculations onto different scales results in linear relationships with a particular family of functions of the sample size to be optimized, resulting in an easy route to sharing information across scenarios.