Precise confidence intervals of regression-based reference limits: Method comparisons and sample size requirements

Abstract

Covariate-dependent reference limits have been extensively applied in biology and medicine for determining the substantial magnitude and relative importance of quantitative measurements. Confidence interval and sample size procedures are available for studying regression-based reference limits. However, the existing popular methods employ different technical simplifications and are applicable only in certain limited situations. This paper describes exact confidence intervals of regression-based reference limits and compares the exact approach with the approximate methods under a wide range of model configurations. Using the ratio between the widths of confidence interval and reference interval as the relative precision index, optimal sample size procedures are presented for precise interval estimation under expected ratio and tolerance probability considerations. Simulation results show that the approximate interval methods using normal distribution have inaccurate confidence limits. The exact confidence intervals dominate the approximate procedures in one- and two-sided coverage performance. Unlike the current simplifications, the proposed sample size procedures integrate all key factors including covariate features in the optimization process and are suitable for various regression-based reference limit studies with potentially diverse configurations. The exact interval estimation has theoretical and practical advantages over the approximate methods. The corresponding sample size procedures and computing algorithms are also presented to facilitate the data analysis and research design of regression-based reference limits.