Sample size and power calculations for medical studies by simulation when closed form expressions are not available

This paper shows how Monte Carlo simulation can be used for sample size, power or precision calculations when planning medical research studies. Standard study designs can lead to the use of analysis methods for which power formulae do not exist. This may be because complex modelling techniques with optimal statistical properties are used but power formulae have not yet been derived or because analysis models are employed that divert from the population model due to lack of availability of more appropriate analysis tools. Our presentation concentrates on the conceptual steps involved in carrying out power or precision calculations by simulation. We demonstrate these steps in three examples concerned with (i) drop out in longitudinal studies, (ii) measurement error in observational studies and (iii) causal effect estimation in randomised controlled trials with non-compliance. We conclude that the Monte Carlo simulation approach is an important general tool in the methodological arsenal for assessing power and precision.