Comparison of alternative approaches for difference, noninferiority, and equivalence testing of normal percentiles

Background: Percentiles are widely used in scientific research for determining the comparative magnitude and reference limit of quantitative measurements. The investigations for point and interval estimation of normal percentiles are well documented in the literature. However, the corresponding statistical tests of hypothesis have received relatively little attention. Methods: To facilitate data analysis and design planning of percentile study, this paper aims to present hypothesis testing procedures and associated power functions for assessing the difference, noninferiority, and equivalence of normal percentiles. Results: Numerical illustrations about drug dissolution are provided to demonstrate the usefulness of the suggested exact approaches and the deficiency of approximate methods. Conclusions: The exact approaches are superior to the approximate methods on the basis of control of Type I errors. Computer algorithms are constructed to implement the recommended test procedures and sample size calculations for percentile analysis.