Can ionized calcium-estimating equations replace albumin-corrected calcium?—a narrative review

Introduction

Serum total calcium (T_Ca) is made up of three fractions of calcium ions in equilibrium with each other (1,2). The physiologically active fraction (~50%) consists of solvated calcium ions and is commonly referred to as the ionized calcium (I_Ca) fraction. Its concentration is regulated, with a typical reference range of 1.15–1.29 mmol/L, although its chemical activity is only about 30% of its concentration (3). The second fraction (~40%) is bound to protein, mainly albumin. Binding of calcium to albumin is reduced by hydrogen, magnesium, and chloride ions, but increased by free fatty acids (4-7). The remaining fraction (~10%) is complexed by small anions such as bicarbonate (the least calcium-avid but most abundant such anion), phosphate, lactate, and citrate (most avid but with a typical serum concentration of only 0.12 mmol/L) (1,8). I_Ca has been shown to be of prognostic value in critical care, COVID-19, and even the general population (9-11). Since direct I_Ca measurement is relatively costly and laborious, and has stringent sampling requirements, it is still not an entirely routine test, especially in developing countries (12-14). There is a need for an indirect method of screening for patients at risk of abnormal I_Ca based on routine data to serve as a guide for direct testing. This review compares the traditional albumin-corrected calcium method, which was derived without I_Ca testing, with newer regression models of measured I_Ca that utilize routine data in addition to T_Ca and albumin as independent variables, with a focus on models that have undergone successful external validation. We present the following article in accordance with the Narrative Review reporting checklist (available at https://jlpm.amegroups.com/article/view/10.21037/jlpm-22-16/rc).

Methods

We searched the PubMed and Google Scholar databases through February 14, 2022 using these terms: corrected calcium; adjusted calcium; calcium equation; ionized calcium; hypocalcemia; hypercalcemia. We selected articles published in English that either reported new models to estimate I_Ca status or tested the external validity of previously published models. We further examined the references of the resulting articles to identify additional relevant publications. Using these sources, we traced the history of (I) published albumin-corrected calcium models and of (II) models of pH-unadjusted I_Ca that rely solely on routine biochemical data (not, for example, on pH or lactate) as independent variables. We reviewed how well these two classes of models align with the underlying biochemistry of I_Ca, how well they performed on internal and external validation, and what the limitations to their clinical application are (Table 1).

Discussion

Corrected calcium

It is well-known that the concentrations of T_Ca and albumin co-vary (15). This trend has been quantified by the slope of the linear regression of T_Ca on albumin (T_Ca = slope × albumin + intercept) in a multitude of studies. Possibly the earliest example is the study by Gutman and Gutman in 1937, which found the relationship to be T_Ca (mmol/L) = 0.0207 × albumin (g/L) + 1.747 [T_Ca (mg/dL) = 0.83 × albumin (g/dL) + 7.0] in a mixed cohort including normal subjects, and patients with various disorders including nephrotic syndrome, cirrhosis, lymphogranuloma inguinale, and miscellaneous hyperproteinemic conditions (16). Ultimately, this linear relationship inspired a method to produce a value of T_Ca corrected for altered albumin concentrations (cT_Ca). Popularized in the 1970s, it uses the slope of the regression of T_Ca on albumin to “correct” measured T_Ca to the hypothetical value it would have if albumin concentration were at the population mean of healthy subjects (15). Using this method, cT_Ca is calculated as: measured T_Ca + slope × (reference albumin − current albumin). One might conceive of cT_Ca as the T_Ca value that would result if a hypoalbuminemic plasma sample were subjected to ultrafiltration, concentrating its albumin to the reference value while removing plasma water and its associated non-colloidal solutes (with an “opposite” maneuver for a hyperalbuminemic sample). Notwithstanding the equilibrium among the three calcium fractions, the cT_Ca method ascribes the change in T_Ca concentration entirely to the albumin-bound fraction, and explicitly assumes that the I_Ca concentration remains constant (2,16). The resultant cT_Ca value is then simply compared to the reference range of T_Ca. Many different estimates of the slope have been published (generally unaccompanied by a 95% CI), although a consensus value of 0.02 mmol/L calcium per g/L of albumin (0.8 mg/dL per g/dL) is most commonly used (15).

Limitations of corrected calcium

The cT_Ca method was developed in the era before measurements of I_Ca were readily available, and remains popular in spite of its poor diagnostic performance, often no better than that of T_Ca, in later external validation studies performed after the I_Ca electrode became more clinically available (14,17-21). The various factors that contribute to the method’s poor performance can be classified as follows.

Biochemical

The cT_Ca equation doesn’t account for variation in I_Ca resulting from variation in pH, magnesium, free fatty acids, and complexing small anions. The method also assumes that I_Ca remains constant when albumin varies, when, in fact, I_Ca and albumin have been found to co-vary (22). That direct correlation might be partly causal, resulting from the Donnan effect, and partly due to confounding by disease-severity, which might progressively but independently decrease both albumin and I_Ca, the latter, perhaps, by disrupting the physiologic regulation of I_Ca or by increasing the anion-complexed fraction as small anions such as lactate and phosphate accumulate.

Statistical

Even if a regression model included all known explanatory variables and accurately estimated group means, its application to individual subjects can be limited by substantial imprecision, often quantified as a 95% prediction interval (PI) (23). A minimal estimate of the cT_Ca equation’s imprecision might be obtained by cumulating the random analytic error of its two inputs. To illustrate this, consider a patient having a T_Ca measurement of 2.45 mmol/L (9.8 mg/dL) with a coefficient of variation (CV) of 1.3% and reference interval of 2.10–2.54 mmol/L (8.4–10.2 mg/dL), and a concomitant albumin measurement of 34 g/L with a CV of 1.8% [CV values taken from a recent study by the authors (24)]. Calculating cT_Ca, with a slope 0.02 and a population mean albumin of 40 g/L, yields a point prediction of 2.57 mmol/L (10.3 mg/dL), suggesting borderline hypercalcemia. However, the combined, weighted standard deviation of the cT_Ca prediction is 0.034 mmol/L {i.e., the square root of [(0.013×2.45)²+0.02²×(0.018×34)²]} with a resultant 95% imprecision range of ±0.067 mmol/L (±0.27 mg/dL). Imprecision of this size is large enough to lead to a significant rate of misclassification of patients having cT_Ca values near the boundaries of the reference range. Moreover, this doesn’t include the other sources of imprecision, such as uncertainty of the estimate of the slope, and biological variation. Bias can be an important limitation for cT_Ca too. It typically stems from the temporal and geographic differences in calcium and albumin assays, and even the use of entirely different assays for albumin (bromocresol purple yields lower albumin values than does bromocresol green) (25-27). Bias is often correctible by local model recalibration (27).

Epidemiologic

Another likely source of the poor generalizability of cT_Ca equations to seriously ill patients is that such patients were underrepresented in the cohorts used to derive the equations (27,28).

Estimating I_Ca: anions get a vote

Could a linear model of I_Ca based solely on T_Ca and albumin perform better than cT_Ca? To examine this question, we took an unpublished model derived during our recent study of I_Ca in critical care (24) [I_Ca = 0.353 × T_Ca − 0.0045 × albumin + 0.568 (in conventional units: I_Ca = 0.088 × T_Ca − 0.045 × albumin + 0.568)] and tested its discrimination for ionized hypocalcemia in the same study’s validation cohort. The model’s ROC curve area (AUC) was 0.82, similar to what we had found for cT_Ca (0.81) (24). Thus, I_Ca models based on linear combinations of albumin and T_Ca alone are unlikely to significantly outperform cT_Ca, suggesting the need for either additional explanatory variables or non-linear terms. A great many equations that estimate I_Ca from non-linear combinations of T_Ca and albumin (or total protein) were published since 1935, when the pioneering model of McLean and Hastings appeared (2). Unfortunately, as was the case for cT_Ca, their poor diagnostic performance was disclosed in later validation studies (17,18,29).

The inclusion of certain anions in I_Ca-estimating models as predictors—specifically phosphate (30,31) or chloride (17,32,33)—to account for small anion complexation appears to be a promising strategy, especially in the renal and inpatient settings (Table 2 and Table S1). Adjusted for T_Ca and albumin, an increase in phosphate, a calcium-chelator (36,37), decreases the estimate of I_Ca (30,31) while an increase in chloride increases estimated I_Ca (32,33). The basis for the latter association might be confounding, with higher chloride simply acting as a marker of the lack of complexing anions and/or the presence of hyperchloremic acidosis, or it might even be causal, reflecting the direct interaction of chloride with albumin (6).

Three of these newer anion-based models underwent validation. The inpatient canine I_Ca model of Danner et al. was validated both internally, in a large cohort (32), and externally, in a small, retrospective cohort drawn from three centers using multiple different chemistry analyzers (38). A similar inpatient feline model was derived and internally and externally validated by Hodgson et al. (33). Each model includes ten predictors treated as splines, with the three most important predictors being T_Ca, chloride and albumin. With slight exception, the discrimination of these models for ionized hypocalcemia and hypercalcemia tended to match or exceed those of T_Ca and cT_Ca. Since these models are complex, the authors made a web-based calculator available for user-support (39). It provides both the point prediction of I_Ca and the 95% PI (canine model: ±0.14 mmol/L; feline model: ±0.11 mmol/L), which together define a range that permits the user to intuitively assess the probability of abnormal I_Ca (23). The model of Obi et al. (30), derived in dialysis patients, was validated for the diagnosis of ionized hypercalcemia in a contemporary but geographically distant dialysis cohort, albeit using the exact same laboratory, while its discrimination for hypocalcemia was not assessed.

In 1989, Nordin et al. reported a simple and practical way to account for anion complexation. They deduced that the fraction of calcium complexed by small anions should vary directly with the anion gap, a previously overlooked relationship, and derived a non-linear model that estimated I_Ca from T_Ca, albumin, total protein, and the anion gap in a large outpatient cohort of post-menopausal women (40). They also confirmed model’s calibration in a group of inpatients (40), but its diagnostic performance for hypocalcemia and hypercalcemia was poor in a later external validation study (18). There was an apparent lull in the use of this approach until approximately three decades later when Sakaguchi et al. and our group each described new models that adjusted T_Ca for the anion gap (34) or its components (24). The models by Sakaguchi et al., which estimate I_Ca in non-dialysis renal patients and dialysis patients, respectively, have not been validated (Table 2) (34). In a large critical care cohort, our group derived a pair of linear models of I_Ca and a pair of logistic models of hypocalcemia (I_Ca <1.10 mmol/L), with one member of each pair using the anion gap as a predictor and the other using the anion gap’s ionic components as three independent predictors (“ion models”) (24). Each of the four equations was much better than cT_Ca or T_Ca for detecting hypocalcemia on ROC analysis in the study’s internal validation cohort (AUC values: 0.89 for each anion gap-based model; 0.92 for each ion model; 0.81 for cT_Ca; 0.78 for T_Ca). Moreover, the ion models (Table 2) were significantly better than the anion gap models (0.92 vs. 0.89, P<0.01). The point predictions of the linear ion model were associated with a mean 95% PI of ±0.115 mmol/L. We recently externally validated our linear ion model for detecting hypocalcemia in a small cohort of inpatients with COVID-19 and renal failure at a different center using a different chemistry analyzer (35). The model had good discrimination and calibration. The performance of our equations for hypercalcemia has not been formally tested.

Applications and limitations of new I_Ca-estimating equations

Most of the limitations cited above in regard to the cT_Ca equations apply to I_Ca models too. As is true of all models, the agreement between predictions of an I_Ca model and observed values needs to be examined in each new laboratory environment and, if bias is detected, minor local model recalibration may be needed (27). The I_Ca models’ reliance on additional analytes (Na, Cl, tCO₂, phosphate) compared to cT_Ca makes them more susceptible to test artifacts, and may reduce their ability to be requested retroactively [e.g., when the measurement of tCO₂ is requested to be added on to a serum sample that has been exposed to air for more than an hour, the resultant value tends to be spuriously low (41)]. Similarly, by their use of extra analytes, they cumulate more analytic and biologic imprecision. Consequently, even if a linear model’s point prediction of I_Ca is accurate on average, it needs to be used together with its 95% PI when applied to an individual subject. Given this uncertainty, the main application of the models will be to more efficiently identify patients for direct I_Ca measurement. However, we can foresee circumstances in which the output of an I_Ca model might be used to directly inform treatment decisions in those medical domains where decisions that affect I_Ca are often made without recourse to direct I_Ca testing. Consider, for example, a hypothetical hemodialysis outpatient with a high-normal I_Ca point prediction of 1.28 mmol/L with a 95% PI of 1.16–1.40 mmol/L for whom parathormone-lowering therapy is being entertained for severe secondary hyperparathyroidism. Despite the uncertainty about the actual I_Ca value, the data favor the prescription of a calcimimetic drug, which tends to lower I_Ca, over active vitamin D therapy, which does the opposite.

Based on their level of validation, the canine model of Danner et al. (32) and the feline model of Hodgson et al. (33) appear to be useful tools for screening for ionized hypocalcemia and hypercalcemia. In human medicine, the models of Yap et al. for critical care patients (24) and the model of Obi et al. for hemodialysis patients (30) appear to be the most promising, having undergone successful but limited validation for ionized hypocalcemia (24,35) and hypercalcemia (30) respectively, but their discrimination needs to be tested for both hypocalcemia and hypercalcemia and their calibration confirmed on a broader range of analytic platforms. Moreover, further validation is necessary before they can be generalized to other patient groups, such as less seriously ill patients in whom more frequent appraisal of I_Ca would be desirable (14) but in whom variation in small anion-complexation may be of lesser importance compared with the models’ respective derivation cohorts (27,28). Examples of such groups include patients with primary parathyroid disorders, cancer, myeloma, and the full spectrum of renal disease (chronic kidney disease, transplant, end-stage on peritoneal or hemodialysis) (14), and even perhaps the general population (11). The performance of I_Ca models also requires specific confirmation in critically ill patients receiving anticoagulation with citrate, an especially avid calcium-chelating anion. Since these newer models can be challenging to memorize, model predictions could be reported in routine metabolic panels, similar to the way the anion gap, estimated glomerular filtration rate, and other forms of laboratory-based decision support are provided. Alternatively, in accord with recommended guidelines for predictive models (42), web-based calculators or smartphone apps could be provided, as a number of the studies cited above have done (Table 2) (24,31-33).

Conclusions

In domains in which small anion complexation is important (critical care, inpatients, renal failure), models of I_Ca have been derived based on the further adjustment of T_Ca for phosphate or the components of the anion gap. Unlike cT_Ca, they have undergone successful validation and can be used as clinical tools to identify patients for I_Ca testing.

Acknowledgments

Funding: None.

Footnote

Provenance and Peer Review: This article was commissioned by the Guest Editor (Nuthar Jassam) for the series “Calcium Adjustment in Laboratory Medicine” published in Journal of Laboratory and Precision Medicine. The article has undergone external peer review.

Reporting Checklist: The authors have completed the Narrative Review reporting checklist (available at https://jlpm.amegroups.com/article/view/10.21037/jlpm-22-16/rc).

Peer Review File: Available at https://jlpm.amegroups.com/article/view/10.21037/jlpm-22-16/prf

Conflicts of Interest: Both authors have completed the ICMJE uniform disclosure form (available at https://jlpm.amegroups.com/article/view/10.21037/jlpm-22-16/coif). The series “Calcium Adjustment in Laboratory Medicine” was commissioned by the editorial office without any funding or sponsorship. The authors have no other conflicts of interest to declare.

Ethical Statement:The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

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