Introduction: 
A change in reagents for calcium (Ca) on the Roche Cobas c500 used in our laboratory analyzer took place in 2013. The previous reference range (8.5-10.5 mg/dL) was replaced with that from the manufacturer\u27s study (8.6-10.0 mg/dL), based on correlation of results between the new and old assays. As a matter of quality assurance, we undertook a post-assay-change reevaluation of the reference range change, using a method based on that of Bhattacharya [1]. In short, the method relies on the assumption that the reference range is a normal distribution, which assumption enables this distribution to be isolated mathematically from within all-comers patient distribution data that are not normally distributed

Joneja, MD, Upasana

McCloskey, MD, Laura J.

Stickle, MD, Douglas F.

Jefferson Digital Commons

Thomas Jefferson UniversityJefferson Digital CommonsPathology, Anatomy and Cell Biology Resident'sPostersDepartment of Pathology, Anatomy and CellBiology2015Analysis of patient results distributions to reevaluatea reference range change for calcium, after a changein assay reagents on the Roche Cobas c500analyzerUpasana Joneja, MDThomas Jefferson University Hospital, Philadelphia, PA, upasana.joneja@jefferson.eduLaura J. McCloskey, MDThomas Jefferson University Hospitals, Philadelphia, PA, Laura.McCloskey@jefferson.eduDouglas F. Stickle, MDThomas Jefferson University Hospitals, Philadelphia, PA, Douglas.Stickle@jefferson.eduLet us know how access to this document benefits youFollow this and additional works at: http://jdc.jefferson.edu/pacbresidentpostersPart of the Medical Anatomy Commons, Medical Cell Biology Commons, and the MedicalPathology CommonsThis Article is brought to you for free and open access by the Jefferson Digital Commons. The Jefferson Digital Commons is a service of ThomasJefferson University's Center for Teaching and Learning (CTL). The Commons is a showcase for Jefferson books and journals, peer-reviewed scholarlypublications, unique historical collections from the University archives, and teaching tools. The Jefferson Digital Commons allows researchers andinterested readers anywhere in the world to learn about and keep up to date with Jefferson scholarship. This article has been accepted for inclusion inPathology, Anatomy and Cell Biology Resident's Posters by an authorized administrator of the Jefferson Digital Commons. For more information,please contact: JeffersonDigitalCommons@jefferson.edu.Recommended CitationJoneja, MD, Upasana; McCloskey, MD, Laura J.; and Stickle, MD, Douglas F., "Analysis of patientresults distributions to reevaluate a reference range change for calcium, after a change in assayreagents on the Roche Cobas c500 analyzer" (2015). Pathology, Anatomy and Cell Biology Resident'sPosters. Paper 17.http://jdc.jefferson.edu/pacbresidentposters/17Results of these procedures converged on a reference range for Ca of 8.6-10.2 mg/dL  (Figure 5)..                             Figure 5. Results of best-fit normality plots as a function of assumed interval widths. A. Upper limit (UL) and lower limit (LL) of reference ranges. B. Linear correlation coefficient (r2) of best-fit. C. Percent inclusion of normal distribution within interval for best-fit. Vertical dashed lines: boundaries of region of converging analyses (based on r2).  Horizontal dashed lines (A): average UL and LL based on converging analyses. Varying widths of intervals of results having symmetry around this midpoint (a necessary condition for a normal distribution) were assigned for analysis (Figure 3).          Figure 3. Examples of intervals of results having symmetric percentages of results on either side of the defined midpoint. 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 Upasana Joneja, Laura J. McCloskey, Douglas F. Stickle  Jefferson University Hospitals, Philadelphia, PA  Isolation of the data subset compatible with a normal distribution was a two-stage process: 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; Figure 2).        Figure 2. Slope of the continuous cumulative patient results distribution vs. Ca. Maximum slope was centered at Ca = 9.4 mg/dL, which was then defined as the normal distribution midpoint/median.              For each of these intervals, 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 (Figure 4).         Figure 4. Example of normality plot. For interval = 30% of results centered on the midpoint (i.e., midpoint ± 15% of results), the maximum linearity of the normality plot (r2 >0.999) occurred when assuming that this interval was inclusive of 51% of a normal distribution. Correspondingly, the associated reference range was 8.65-10.14 mg/dL. Normality plot: x-axis = Ca result (mg/dL); y-axis: z value (-∞ to +∞) based on assumed percentile of results within the normal distribution.   CONCLUSIONS REFERENCES [1] Bhattacharya CG. A simple method of resolution of a distribution into gaussian components. Biometrics. 1967 Mar;23(1):115-35.   [2] Burtis CA, Ashwood ER, Bruns DE (eds). Tietz Textbook of Clinical Chemistry and Molecular Diagnostics: 5th Edition. Elsevier Saunders, 2012, St. Louis.   [3] Hoffmann RG. Statistics in the practice of medicine. JAMA 1963;185:864-873.   [4] Horowitz GL. Estimating Reference Intervals. Am J Clin Pathol 2010 133:175-177. [5] Katayev A, Balciza C, Seccombe DW. Establishing Reference Intervals for Clinical Laboratory Test Results: Is There a Better Way? Am J Clin Pathol 2010;133:180-186.   [6] Erdogan E, Nelson GJ, Rockwood AL, Frank EL. Evaluation of reference intervals for methylmalonic acid in plasma/serum and urine. Clin Chim Acta 2010 Nov 11;411(21-22):1827-9.   [7] Shaw JL, Cohen A, Konforte D, Binesh-Marvasti T, Colantonio DA, Adeli K. Validity of establishing pediatric reference intervals based on hospital patient data: a comparison of the modified Hoffmann approach to CALIPER reference intervals obtained in healthy children. Clin Biochem. 2014 Feb;47(3):166-72.  A change in reagents for calcium (Ca) on the Roche Cobas c500 used in our laboratory analyzer took place 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. As a matter of quality assurance, we undertook a post-assay-change reevaluation of the reference range change, using a method based on that of Bhattacharya [1]. In short, the method relies on the assumption that the reference range is a normal distribution, which assumption enables this distribution to be isolated mathematically from within all-comers patient distribution data that are not normally distributed.  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 a large number of patients using retrospective data. In comparison, identification and testing of "normal" patients in similar numbers would be difficult or impractical. In particular, clinical verification of a normal population for Ca would be expensive for any large number of patients, involving combined evaluation of Ca, renal function, vitamin D status, and PTH. These results demonstrate that one can have reasonable confidence in an esoteric method for extraction of a reference range from an all-comers patient results distribution. The related method of Hoffman [3] is more well-known but less stringent, being applied with varying degrees of success in recent literature [4-7]. 6 7 8 9 10 11 120.00.10.20.30.40.50.60.7Slope (df/d[Ca])[Ca] (mg/dL)# of points 20 100 6009.1 9.2 9.3 9.4 9.5 9.6 9.7-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.0 30% interval data best-fit linez value[Ca] (mg/dL)0.1 0.2 0.3 0.4 0.5 0.68.59.09.510.010.5Reference range boundariesInterval width Lower limit (LL) Upper Limit (UL)0.1 0.2 0.3 0.4 0.5 0.60.99940.99950.99960.99970.99980.99991.0000Best-fit r2Interval width0.1 0.2 0.3 0.4 0.5 0.60.30.40.50.60.70.8Distribution inclusion fractionInterval width6 7 8 9 10 11 120.00.20.40.60.81.0Cumulative fraction[Ca] (mg/dL) A. Patient dist. B. Reference range dist.AB6 7 8 9 10 11 120100200300400500600700800COUNT[Ca] (mg/dL)A. Total distributionn = 11684B.Normal distributionn = 7542B (64.5%)A6 7 8 9 10 11 12050100150200250300350COUNT[Ca] (mg/dL)Residual = Total - Normal30.4%6.2%METHODS AND RESULTS INTRODUCTION A. B. C. B. C. Primary data were all patient Ca results retrieved for a one-month interval (Figure 1).         Figure 1. Primary data: cumulative results distribution for all patient Ca results retrieved for a one-month interval (January, 2014; n = 11,684). Solid line: distribution according to 0.1 mg/dL increments of reporting. Dashed line: continuous data distribution interpolated from original data. Vertical dashed lines: boundaries of reference range (8.5-10.0 mg/dL). For this distribution, low Ca = 24.9%, high Ca = 9.2%. 6 7 8 9 10 11 120.00.20.40.60.81.0 Primary data Interpolated dataCumulative fraction[Ca] (mg/dL)6 7 8 9 10 11 120.00.20.40.60.81.0c bCumulative fraction[Ca] (mg/dL)aInterval spansa: 20%b: 40%c: 60% centerA. The reference range from Figure 5 data was essentially identical (±0.1 mg/dL) to "textbook" reference ranges (e.g., [2]).  A comparison of the patient results distribution to the reference range distribution is shown in Figure 6.             Figure 6. A. Comparison of patient results cumulative distribution to reference range cumulative distribution. B. Comparison of patient results distribution to reference range distribution. C. Residuals between patient results distribution and normal patient distribution (residual = patient distribution - reference range distribution). 

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

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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

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