Derivation and comparison of formulae for the adjustment of total calcium

Background: Free ionized calcium (Ca²⁺) is the biologically active component of total calcium (TCa) and hence responsible for its biological action. TCa is routinely adjusted for albumin using several formulae (e.g. James, Orell, Payne and Berry) to more closely reflect Ca²⁺. Here, we derive a novel formula to estimate Ca²⁺ and compare its performance to established formulae.

Methods: Cohort for prediction of Ca²⁺: 2806 serum samples (TCa) taken contemporaneously with blood gas samples (Ca²⁺) at Imperial College Healthcare NHS Trust were used to derive formulae to estimate Ca²⁺ using multivariable linear regression. Cohort for prediction of PTH: Performance of novel and existing formulae to predict PTH in 5510 patients was determined by Spearman correlation.

Results: Ca²⁺ prediction Cohort: Adjusted calcium (r² = 0.269) was less strongly associated with Ca²⁺, than TCa (r² = 0.314). Prediction of Ca²⁺ from a newly derived formula incorporating TCa, potassium, albumin, and hematocrit had an improved r² of 0.327, whereas inclusion of all available parameters increased the r² further to 0.364. Of the established formulae, James performed best in predicting Ca²⁺ (r² = 0.27). PTH prediction cohort: Berry resulted in higher whereas Orell in lower adjusted calcium levels. Prediction of PTH was strongest in the setting of hypercalcemia, with James having the highest Spearman correlation coefficient (+0.496) similar to including all parameters (+0.499).

Conclusion: Adjustment of calcium for albumin using established formulae does not always outperform unadjusted TCa in the reflection of Ca²⁺. Further prospective studies are needed to optimise adjustment of TCa and to establish bounds for validity.