Calcium is a ubiquitous mineral that has a critical role across several physiological processes (1, 2). Intracellular calcium is involved in action potential regulation, cell signalling, glycogen metabolism, and hormone secretion (1, 2). Extracellular calcium plays a vital role in the coagulation cascade, maintenance of membrane integrity and muscle contraction (2, 3). Only 1% of total body calcium is present within body tissues or extracellular fluid, whereas the majority resides in bone with hydroxyapatite crystals acting as a calcium reservoir (3, 4).

Over a century ago, Rona and Takashi discovered that total serum calcium (TCa) separates into diffusible (~55%) and non-diffusible fractions (~45%) (5, 6), depending on pH and temperature (7). Of the non-diffusible calcium, ~81% is albumin-bound and ~19% is globulin-bound (7). The majority (~80%) of the diffusible calcium portion is free ionized calcium (Ca²⁺) (7) and the remainder (5-15%) is complexed with small anions such as bicarbonate, citrate and phosphate (8). McLean and Hastings provided evidence that Ca²⁺ was the biologically active component (9, 10), with its concentration predominantly dictated by parathyroid hormone (PTH) and vitamin D (11). Crucially, several studies have demonstrated that changes in Ca²⁺, rather than TCa, most strongly regulate PTH secretion (12–14). Thus, estimation of Ca²⁺ is paramount for correct interpretation of PTH levels when assessing patients with disorders of calcium homeostasis. This can be particularly important when patients have borderline calcium levels, whereby the interpretation of PTH levels can diverge between being an appropriate physiological response, to being inappropriate for that calcium status and thus consistent with parathyroid disorders.

However, measuring Ca²⁺ concentrations requires direct ion selective electrodes (ISE) that are not universally available in the biochemistry laboratory (15). TCa concentration can vary according to albumin concentration (16), however the ionized calcium fraction (Ca²⁺) remains unaltered (17). Consequently, calcium is usually adjusted for the level of albumin with the aim of deriving a closer representation of Ca²⁺. The first formula used to adjust TCa for albumin was described by Payne and colleagues in 1973 (18). Since then several formulae have been derived and compared to this formula (19–21), however whether the accuracy of some of these formulae is better than the unadjusted TCa has been questioned (21–26).

This study aims to assess whether routinely measured analytes and baseline factors can be used to better predict Ca²⁺ and assess how this compares with established formulae and unadjusted TCa. We audited samples analysed during routine clinical practice from patients who had contemporaneous measurement of both Ca²⁺ (using blood gas analyser ISEs) and TCa (using automated lab analyser) to evaluate the effect of parameters including gender, age, creatinine, total protein, albumin, globulin, phosphate, sodium, potassium, creatinine, hemoglobin, and hematocrit, that could affect prediction of Ca²⁺ from TCa. We also identified boundaries for these parameters beyond which the relationship between TCa and Ca²⁺ was lost e.g., extremes of albumin.

Thereafter, having evaluated the performance of existing formulae to reflect Ca²⁺ and having derived a novel formula to predict Ca²⁺, we then evaluated the performance of this formula (as well as other available established formulae for adjustment of TCa for albumin) to assess their ability to predict PTH in samples from a second cohort of patients with known vitamin D and PTH levels.

This work was conducted as part of a service evaluation of calcium estimation at Imperial College Healthcare NHS Trust (ICHT), reference number: ASM_044.

Baseline characteristics of both the first and second cohorts are summarized in Table 1 , including both the unrestricted datasets, as well as restricted datasets (i.e., only those with pH 7.35-7.45, creatinine <120 μmol/L, albumin >15 g/L, total protein >40 g/L and calcium 2.2-2.6 mmol/L).

Ca²⁺ is considered the gold standard representation of biological calcium activity. However, measurement of Ca²⁺ is not practical, as most commercial vendors do not currently offer Ca²⁺ assay on large-scale automated instruments (27). Furthermore, even if Ca²⁺ assays were available on automated assay lines, most of these involve uncapping the tubes after centrifuging, which risks changing the pH of the sample and thus the Ca²⁺ concentration (27). Direct measurement of Ca²⁺ in clinical practice is most frequently conducted using blood gas analyser ISEs, which are not usually available in the outpatient setting. However, Ca²⁺ is more closely related to PTH levels than TCa and thus, a reliable formula for the estimation of Ca^2+/adjustment of TCa from routinely measured biochemical parameters would aid in the interpretation of PTH levels. In particular, estimation of Ca²⁺ levels would be helpful in the interpretation of PTH in patients with borderline calcium results, whereby the classification of PTH can diverge between being an appropriate physiological response vs a pathological indicator of parathyroid disorders (28). In the present study, we found that the proportion of patients with borderline TCa levels (between 2.59-261 mmol/L) that would be classified as hypercalcemic varied hugely between 13.9 to 84.3% depending on the formula used for calcium adjustment, with a corresponding impact on the interpretation of PTH levels. This wide variation would therefore potentially result in different clinical management which may be ‘incorrect’ in some cases.

Interpretation of PTH levels is further challenged by the increasing recognition of normocalcemic hyperparathyroidism, whereby persistently raised PTH, which is unexplained by other abnormalities e.g. vitamin D < 50 nmol/L, could indicate parathyroid disease even without serum calcium levels becoming raised (28). In our data, PTH levels had a nadir at TCa levels between 2.4-2.49 mmol/L, although more typically endocrinologists use the upper limit of the reference range for TCa (~ 2.6 nmol/L) to interpret the appropriateness of that PTH level, which could have included patients with subclinical hyperparathyroidism in its derivation. Identifying the normal relationship between PTH and calcium is further complicated by the fact that patients have an individual set-point for calcium around which PTH secretion is altered (29), which is set at different levels on an individual basis within the reference range. Indeed, the relationship between calcium and PTH was strongest in the setting of hypercalcemia, with greater PTH levels begin associated with a greater degree of perturbation in calcium. Generally, PTH levels are used to distinguish hypercalcemia due to malignancy (physiologically suppressed) from that due to primary hyperparathyroidism (pathologically raised) (30). The lower limit of the reference range for PTH is typically used by most endocrinologists to distinguish these two conditions, however the rise in PTH levels in primary hyperparathyroidism especially in patients with higher calcium levels suggests that a higher threshold for PTH could be used to discriminate these two conditions, as otherwise a PTH level very close to the assay detection limit would be used. Furthermore, it is necessary to exclude renal calcium loss as an additional drive of increased PTH secretion (as a form of secondary hyperparathyroidism). Indeed, those labelled as being normocalcemic using TCa can in some instances have abnormal calcium when Ca²⁺ is assessed. Consistent with this, Koumakis et. al., found that only 16 of 39 patients with normocalcemic (by TCa) hyperparathyroidism had both normal TCa and Ca²⁺ levels, further demonstrating the benefits of Ca²⁺ assessment to clarify diagnosis (31).

Notably, in the present study, we found that TCa outperformed adjusted calcium in the prediction of Ca²⁺ when including all the patients (unrestricted cohort) similar to previous studies (25, 32). We also describe parameters around which the relationship between TCa and Ca²⁺ was altered e.g. extremes of albumin level. It is possible that the relationship between TCa and Ca²⁺ is altered in patients who are acutely unwell, with both low and high Ca²⁺ being associated with increased mortality (33, 34) and Ca²⁺ also being proposed as an indicator of severity of COVID-19 (35). However, adjusted calcium formulae outperformed TCa in the restricted cohort, whereby extreme values for albumin, creatinine etc were excluded, perhaps reflecting that many of these formulae have been derived in healthy individuals.

Of the existing formulae tested, the James formula appeared to perform best in both the prediction of Ca²⁺ in the first cohort (r² 0.271), and in the prediction of PTH in the second cohort in both hypocalcemic (r -0.11) and hypercalcemic patients (r +0.496), with similar performance to the newly derived formula (F1) incorporating all available biochemical parameters (F1) (r +0.499). Additionally, our study highlights that it may be necessary to derive bespoke reference ranges and formulae to adjust calcium in local centres to account for variations in assays used and population demographics, as well as to update these from time-to-time to take account of changes in performance of the assays (36, 37).

Strengths of the study include that this was a biochemistry laboratory centred audit enabling extraction of a large number of biochemical values analysed using the same analysers, however conversely a limitation is that granular clinical data on individual patient diagnoses/medications were not available. It is important to note that albumin measurements can differ depending on the assay used. For example, Roche BCP yields lower albumin readings than Abbott and differs from BCG and immunoturbidimetric methods. Consequently, it is important to note that older formulas such as Payne from 1973 (16) used a BCG method for albumin measurement. Additionally, due to Ca²⁺ being predominantly assessed in an acute setting, and PTH and vitamin D in the non-acute outpatient setting, it was not possible to directly assess both Ca²⁺ and PTH in the same cohort. Thus, we used the first cohort to derive a formula to estimate Ca²⁺, and then used a second cohort to correlate the estimated Ca²⁺ against PTH and vitamin D. Future prospective studies with concomitant measurement of Ca²⁺ and all other potentially relevant parameters e.g. FGF23 and patient histories in a controlled setting could enable more definitive exposition of the relationships between TCa and Ca²⁺ to enable more precise formulae to be derived. Additionally, urine calcium measures were not routinely available, to enable the exclusion of hypercalciuria as a cause of unexplained hyperparathyroidism.

We find that adjustment of TCa for albumin does not outperform unadjusted values in the prediction of Ca²⁺ in an unrestricted dataset and that the relationship between PTH and calcium is strongest in the setting of hypercalcaemia. Of the existing formulae, the James formula performed best at predicting PTH levels in the setting of both high and low calcium levels.

The original contributions presented in the study are included in the article/ Supplementary Material . Further inquiries can be directed to the corresponding author.

MP wrote the original draft. MP and AC contributed equally as first authors to this manuscript. AS, ML, PE, SC, PM analysed the data. TT, JC, WD, AA edit, review and finalise the manuscript. All authors contributed to the article and approved the submitted version.