Precision-Based Sample Size Determination: Implications for Decision-Making

Power-based sample size calculation is the standard approach in confirmatory clinical trials, where adequate statistical power is essential for study success. In other decision-making contexts, however, a precision-based approach to sample size determination is sometimes adopted. One such area is consumer studies that evaluate consumers' ability to appropriately select nonprescription medications. Compared with power-based designs, precision-based approaches typically require fewer study participants and can therefore reduce study costs. However, the extent of loss in statistical power has not been well quantified. In this paper, we evaluate the statistical power of precision-based sample size determination and illustrate its practical implementation. Our analysis demonstrates that when the target precision is set to the difference between the expected proportion and the null threshold, the resulting design achieves only approximately 50% power. This underpowering is further exacerbated when normal approximation is used for sample size determination, commonly practiced for convenience, but exact methods are used for analysis. For studies that plan to use a precision-based approach to support hypothesis testing in decision-making contexts, it is important to be aware of the potential underpower issue in this approach.