Analysis of Patient Results Distributions To Reevaluate A Reference Range Change For Calcium After A Change in Assay Reagents on the Roche Cobas c500 Analyzer

Abstract

A change in reagents for calcium (Ca) on the Roche Cobas c500 analyzer occurred in 2013. The previous reference range (8.5-10.5 mg/dL) was replaced with that from the manufacturer's study (8.6-10.0 mg/dL), based on correlation of results between the new and old assays. Given the historically large fraction (25%) of abnormal Ca results in our patient data, small changes in the reference range can greatly affect numbers of patient results flagged as abnormal. As a matter of quality assurance, therefore, we undertook a reevaluation of the reference range change, using a method based on that of Bhattacharya (1967). In short, this method relies on the assumption that the reference range is a normal distribution, and enables this distribution to be isolated mathematically from within patient distribution data that are not normally distributed. Primary data were all patient Ca results retrieved for a 1-month interval (January, 2014; n = 11,684). Isolation of the data subset compatible with a normal distribution was a two-stage process. First, the point of maximum slope of the cumulative patient results distribution was determined to define the mean/median of the embedded normal distribution (9.4 mg/dL). Second, for varying widths of intervals of results having symmetry around this midpoint, an iterative search was made to determine the central fraction of a normal distribution encompassed by each interval, as evidenced by the linearity of a normality plot when the correct fraction was specified. Results of these procedures converged on a reference range for Ca of 8.6-10.2 mg/dL, essentially identical (±0.1 mg/dL) to numerous “textbook” reference ranges. The results were used to update our Ca reference range. Normal distribution analysis of patient data subsets by this method can be a powerful tool to evaluate reference ranges simply because it can include an otherwise-impractical large number of patients.