Determining reference ranges and sample sizes in parallel-group studies

Background and objectives: Reference ranges are widely used to locate the major range of the target probability distribution. When future measurements fall outside the reference range, they are classified as atypical and require further investigation. The fundamental principles and statistical properties of reference ranges are closely related to those of tolerance interval procedures. Existing investigations of reference ranges and tolerance intervals mainly devoted to the primitive cases of one- and paired-sample designs. Although reference ranges hold considerable promise for parallel group designs, the corresponding methodological and computational issues for determining reference limits and sample sizes have not been adequately addressed. Methods: This paper describes a complete collection of one- and two-sided reference ranges for assessing measurement differences in parallel-group studies that assume variance homogeneity. Results: The problem of sample size determination for precise reference ranges is also examined under the expected half-width and assurance probability considerations. Unlike the current methods, the suggested sample size criteria explicitly accommodate desired interval width in precise interval estimation. Conclusions: Theoretical examinations and empirical assessments are presented to validate the usefulness of the proposed reference range and sample size procedures. To enhance the usages of the recommended techniques in practical applications, computer programs are developed for efficient calculation and exact analysis. A real data example regarding tablet absorption rate and extent is presented to illustrate the suggested assessments between two drug formulations.