A Quantile-Quantile Toolbox for Reference Intervals

Abstract

Background: Parametric statistical methods are generally better than nonparametric, but require that data follow a known, usually normal, distribution. One important application is finding reference limits and detection limits. Parametric analyses yield better estimates and measures of their uncertainty than nonparametric approaches, which rely solely on a few extreme values. Some reference data follow normal distributions; some can be transformed to normal; some are normal or transformable to normal apart from a few extreme values; and detection and quantitation limits can lead to data censoring.

Methods: A quantile-quantile (QQ) toolbox provides powerful general methodology for all these settings.

Results: QQ methodology leads to a family of simple methods for finding optimal power transformations, testing for normality before and after transformation, estimating reference limits, and constructing confidence intervals.

Conclusions: These parametric methods have a particular appeal to clinical laboratorians because, while statistically rigorous, they do not require specialized software or statistical expertise, but can be implemented even in spreadsheets. We conclude with an exploration of reference values for amyloid beta proteins associated with Alzheimer disease.