The appropriateness of Bland-Altman’s approximate confidence intervals for limits of agreement

BACKGROUND: Percentiles are widely used as reference limits for determining the relative magnitude and substantial importance of quantitative measurements. An important application is the advocated Bland-Altman limits of agreement. METHODS: To contribute to the data analysis and design planning of reference limit or percentile research, the purpose of this paper is twofold. The first is to clarify the statistical features of interval estimation procedures for normal percentiles. The second goal is to provide sample size procedures for precise interval estimation of normal percentiles. RESULTS: The delineation demonstrates the theoretical connections between different pivotal quantities for obtaining exact confidence intervals. Moreover, the seemingly accurate approximate methods with equidistant from the principal estimators are shown to have undesirable confidence limits. It is found that the optimal sample size has a minimum for median or mean, and increases as the percentile approaches the extremes. CONCLUSIONS: The exact interval procedure should be used in preference to the approximate methods. Computer algorithms are presented to implement the suggested interval precision and sample size calculations for planning percentile research. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (10.1186/s12874-018-0505-y) contains supplementary material, which is available to authorized users.