Sample size planning for proportions based on Wilson score confidence intervals with precision and assurance

Estimating sample sizes for proportions and their differences are important tasks in medical studies. The existing methods were either based on hypothesis testing or the expected width of a confidence interval (CI), focusing on only one aspect of power or precision. In this article, we develop Wilson score CI-based approaches for such issues by incorporating a pre-specified probability of achieving the desired lower (or upper) limit of a CI, where such a probability represents assurance and the lower (or upper) limit reflects precision. To account for the asymmetry of the Wilson score CI, we construct the variance function based on the MOVER (method of variance estimate recovery) technique. Both simulations and real data analysis demonstrate that our methods achieve empirical assurance and coverage probabilities close to the pre-specified level and provide better sample size estimates than the Wald and exact methods.