Establishing reference interval bounds for censored and contaminated data

Niels Henrik Bruun, Nanna Maria Uldall Torp and Stine Linding Andersen
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Nanna Maria Uldall Torp: Aalborg University Hospital
Stine Linding Andersen: Aalborg University Hospital

Stata Journal, 2025, vol. 25, issue 1, 151-168

Abstract: Reference intervals are essential across the medical and environmental fields. A reference interval (for example, the 95% central prediction interval) de- fines the normal range of measurements for a specific physiological parameter in healthy individuals. Inappropriate reference interval bounds may occur because of censored measurements (due to instrument limitations) or contaminated data (by accidentally sampling nonhealthy individuals). To address this, we propose using the regression-on-order-statistics (ROS) method combined with an optimal Box–Cox transformation. The ROS method involves regressing Gaussian scores based on ranks from ordered noncensored Box–Cox transformed measurements. To find the optimal Box–Cox transformation, we maximize the adjusted R2 when estimating the mean and standard deviation through regression of empirical Gaus- sian quantiles on measurements. We demonstrate how to identify contamination and introduce a new command, ros. Real-life data illustrate the effectiveness of the ROS method.

Keywords: ros; reference interval bounds; censored data; regression-of-order-statistics method; Box–Cox transformation (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1177/1536867X251322968

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