A myriad of methods: Calculated sample size for two proportions was dependent on the choice of sample size formula and software

Objectives Several methods exist to calculate sample size for the difference of proportions (risk difference). Researchers are often unaware that there are different formulae, different underlying assumptions, and what the impact of choice of formula is on the calculated sample size. The aim of this study was to discuss and compare different sample size formulae for the risk difference. Study Design and Setting Four sample size formulae were used to calculate sample size for nine scenarios. Software documentation for SAS, Stata, G*Power, PASS, StatXact, and several R libraries were searched for default assumptions. Each package was used to calculate sample size for two scenarios. Results We demonstrate that for a set of parameters, sample size can vary as much as 60% depending on the formula used. Varying software and assumptions yielded discrepancies of 78% and 7% between the smallest and largest calculated sizes, respectively. Discrepancies were most pronounced when powering for large risk differences. The default assumptions varied considerably between software packages, and defaults were not clearly documented. Conclusion Researchers should be aware of the assumptions in power calculations made by different statistical software packages. Assumptions should be explicitly stated in grant proposals and manuscripts and should match proposed analyses.