Calculating power by bootstrap, with an application to   cluster-randomized trials
  Background   A key requirement for a useful power calculation is that the calculation mimic the data analysis that will be performed on the actual data, once it is observed. Close approximations may be difficult to achieve using analytic solutions, however, and thus Monte Carlo approaches, including both simulation and bootstrap resampling, are often attractive. One setting in which this is particularly true is cluster-randomized trial designs. However, Monte Carlo approaches are useful in many additional settings as well. Calculating power for cluster-randomized trials using analytic or simulation-based methods is frequently unsatisfactory due to the complexity of the data analysis methods to be employed and to the sparseness of data to inform the choice of important parameters in these methods.   Methods   We propose that among Monte Carlo methods, bootstrap approaches are most likely to generate data similar to the observed data. Means of implementation are described.   Results   We demonstrate bootstrap power calculation for a cluster-randomized trial with a survival outcome and a baseline observation period.   Conclusions   Bootstrap power calculation, a natural application of resampling methods, provides a relatively simple solution to power calculation that is likely to be the most accurate option. It has several important strengths. Notably, it is simple to achieve fidelity to the proposed data analysis method and there is no requirement for estimates from outside settings. We are not aware of bootstrap power calculation being previously proposed or explored for cluster-randomized trials. We demonstrate power calculations for a time-to-event outcome in a cluster randomized trial setting, for which we are unaware of an analytic alternative. 
Ken Kleinman, Susan S. Huang
stat.AP