Comparison of 7 methods for sample size determination based on confidence interval estimation for a single proportion

Abstract

To compare different methods for calculating sample size based on confidence interval estimation for a single proportion with different event incidences and precisions. We compared 7 methods, namely Wald, AgrestiCoull add z2, Agresti-Coull add 4, Wilson Score, Clopper-Pearson, Mid-p, and Jefferys, for confidence interval estimation for a single proportion. The sample size was calculated using the search method with different parameter settings (proportion of specified events and half width of the confidence interval [ω=0.05, 0.1]). With Monte Carlo simulation, the estimated sample size was used to simulate and compare the width of the confidence interval, the coverage of the confidence interval and the ratio of the noncoverage probability. For a high accuracy requirement (ω =0.05), the Mid-p method and Clopper Pearson method performed better when the incidence of events was low (P < 0.15). In other settings, the performance of the 7 methods did not differ significantly except for a poor symmetry of the Wald method. In the setting of ω=0.1 with a very low p (0.01-0.05), failure of iteration occurred with nearly all the methods except for the Clopper-Pearson method. Different sample size determination methods based on confidence interval estimation should be selected for single proportions with different parameter settings.