Department of Medicine, University of Calgary, Calgary, Alberta, Canada

Department of Community Health Sciences, University of Calgary, Calgary, Alberta, Canada

Calgary Laboratory Services, Calgary, Alberta, Canada

Abstract

Background

Previously published equations to adjust calcium for albumin concentration may vary depending on factors such as the type of reagents used. Albumin-adjusted calcium equations derived from laboratories using the bromocresol purple (BCP) albumin binding reagent have not been described.

Methods

The linear regression equation for the binding of calcium and BCP-albumin was derived in a cohort of 4613 outpatients, and the albumin-adjusted calcium equation was internally validated in a separate cohort of 1538 subjects. The performance of this equation was compared with a previously published equation (

Results

The local adjustment equation was expressed by the relationship; ^{2 }= -0.0059). Classification of calcium status differed between the two equations in 47 of 343 subjects with low serum albumin (weighted κ = 0.46; moderate agreement).

Conclusion

A locally derived and internally validated albumin-adjusted calcium equation differed from previously published equations and resulted in important differences in classification of calcium status in hypoalbuminemia patients. Individual laboratories should determine their own linear regression equation for calcium on albumin rather than relying on published formulas.

Background

Measurement of serum total calcium is commonly used to assess calcium status. At physiological pH albumin binds approximately 45% of serum total calcium. Variation in serum albumin concentration therefore alters the concentration of serum total calcium, while the concentration of physiologically important ionized calcium remains constant

The purpose of this study was to derive and internally validate an albumin-adjusted calcium equation by applying linear regression to our own laboratory data for individual patient total calcium and serum albumin measurements. We hypothesized that 1) a locally derived equation would differ from the previously published equations, and 2) that there would be differences in the classification of calcium status between equations when applied to patients with hypoalbuminemia.

Methods

Consecutive outpatients with simultaneous serum total calcium and albumin measurements determined by Calgary Laboratory Services (CLS) over a 2 month time period were included. CLS provides laboratory testing for the Calgary Health Region (population 1.1 million) using instruments and reagents from a single vendor (Roche Diagnostics Ltd, Laval, PQ, Canada). Tests were conducted using the Arsenazo III dye binding method for calcium and the BCP reagent for albumin. Quality was satisfactory during the study period and assured by use of multi-rule quality control procedures at three levels

The study cohort was divided randomly into a 75% derivation sample and a 25% validation sample. A simple (ordinary least squares) linear regression equation for the association between total calcium and albumin was determined from the derivation sample ^{2 }for the validation sample was subtracted from that of the derivation sample to arrive at an estimate of the amount of shrinkage, an indication of how much the predictive ability decreases when the equation is applied to other samples. If the shrinkage is small the regression is considered internally valid

To compare discrepancies in the classification of calcium status with a published equation

Results

The cohort consisted of 6151 subjects, with 60% females, and a mean age of 55 years. The mean (SD) calcium and albumin concentrations were 2.35 (0.12) mmol/L and 39.9 (4.3) g/L respectively. The relationship between serum total calcium and albumin obtained from the derivation subset (n = 4613) is shown in Figure ^{2 }shrinkage value of -0.0059 when the equation was applied to the validation subset (n = 1538). Similar results were obtained from the bootstrapping procedure, confirming the validity of the derived equation.

Linear regression relationship of serum total calcium on albumin derived from a cohort of 4613 patients with simultaneous total calcium and BCP-albumin measurements

**Linear regression relationship of serum total calcium on albumin derived from a cohort of 4613 patients with simultaneous total calcium and BCP-albumin measurements.**

To assess agreement between the derived equation and the previously published equation

**Bland-Altman plot including 95% limits of agreement between adjusted calcium by the previously published equation and adjusted calcium by the locally derived equation (Note: mean difference = 0.09, 95% limits of agreement: 0.043 to 0.136, units = mmol/L).** Abbreviations: Adj. = Adjusted.

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Classification of 343 patients with hypoalbuminemia (albumin < 33 g/L) as hypo-, normo, or hyper-calcemic using local and previously published albumin-adjusted calcium equations.

**Local Equation***
^{
1
}

**Published Equation***
^{
2
}

**Hypocalcemia**

(Ca < 2.10 mmol/L)

**Normocalcemia**

(Ca 2.10 – 2.55 mmol/L)

**Hypercalcemia**

(Ca > 2.55 mmol/L)

**Hypocalcemia**

(Ca < 2.10 mmol/L)

2

0

0

**Normocalcemia**

(Ca 2.10 – 2.55 mmol/L)

**5**

272

0

**Hypercalcemia**

(Ca > 2.55 mmol/L)

0

**42**

22

*^{1 }adjusted [Ca](mmol/L) = total [Ca](mmol/L) + 0.012 (39.9 - [albumin](g/L))

*^{2 }adjusted [Ca](mmol/L) = total [Ca](mmol/L) + 0.02 (40 - [albumin](g/L))

Discussion

We derived an albumin-adjusted calcium equation using local laboratory data that differs from those previously published. Its application in patients with abnormal low albumin concentration illustrates clinically important differences in the classification of calcium status compared with the most commonly used published adjustment equation. Our findings suggest that the use of a local equation for albumin adjusted-calcium in hypoalbuminemic patients would result in a small increase in the number of patients characterized as hypocalcemic and significantly fewer patients being characterized as hypercalcemic.

Measurement of total calcium concentration remains a common initial test in the assessment of calcium status. While accurate measurement of ionized calcium would be ideal, its strict sampling handling requirements make it more prone to measurement error and impractical to use as a screening test

While we did not seek to determine the reasons for the difference between our equation and other published versions, a likely explanation may be differences in analytical techniques employed. Ashby et al. noted a change in the regression coefficient for binding of calcium on albumin within a single laboratory following a change of analytical methodology

There are limitations to our study. First, we did not measure ionized calcium concentrations to determine the accuracy of the hypercalcemic, normocalcemic, and hypocalcemic classifications using different equations. Comparison against such a gold standard would be needed to confirm the greater validity of the locally derived equation. Second, the equation we report is applicable only over the albumin range studied (20–50 g/L), although this would include the majority of the population with low serum albumin levels to which this equation would be applied. Third, generalization of our equation beyond our health region may be limited given the interlaboratory variation previously described. Furthermore, generalization to inpatient settings may also be inappropriate since our equation was derived in an outpatient setting and previous literature has demonstrated poor reliability of this approach in the critically ill

Conclusion

In conclusion, a locally derived and internally validated albumin-adjusted calcium equation differed from previously published equations and resulted in important differences in classification of calcium status compared to results from a previously published equation. Our results illustrate that clinicians should be cautious applying a previously published albumin-adjusted calcium equation in modern settings with different analytical techniques. Using the methods described in this report institutions can derive their own equations rather than relying upon existing published formulas.

Abbreviations

Ca: Calcium; BCP: Bromocresol purple; BCG: Bromocresol green; CLS: Calgary Laboratory Services.

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

MJ, AL, and BH contributed to study conception and design, acquisition and interpretation of data, and were involved in drafting the manuscript and revising it critically for important intellectual content. JZ contributed to analysis and interpretation of data. All authors gave final approval of the version to be published.

Appendix: Derivation of working form of albumin-adjusted calcium equation

Acknowledgements

Mathew James is supported by fellowship awards from the Kidney Research Scientist Core Education Training Program and the Alberta Heritage Foundation for Medical Research. Brenda Hemmelgarn is supported by a New Investigator Award from the Canadian Institutes of Health Research and a Population Health Investigator Award from the Alberta Heritage Foundation for Medical Research.

Pre-publication history

The pre-publication history for this paper can be accessed here: