Albumin-corrected calcium and ionized calcium in stable haemodialysis patients

Catherine M. Clase1,, Geoffrey L. Norman2, Mary Louise Beecroft3 and David N. Churchill2,3

1 Division of Nephrology, Dalhousie University, Halifax, NS, 2 Department of Clinical Epidemiology and Biostatistics and 3 Division of Nephrology, McMaster University, Hamilton, ON, Canada



   Abstract
 Top
 Abstract
 Introduction
 Subjects and methods
 Results
 Discussion
 Conclusions
 References
 
Background. It is ionized calcium that is physiologically active and under homeostatic control; however, total calcium is more conveniently measured. Formulae for correction of calcium to account for albumin binding have not been validated in a dialysis setting.

Methods. We measured ionized calcium simultaneously with total calcium (t[Ca]), albumin, total protein and pH before dialysis in 50 stable outpatients and convalescent inpatients.

Results. Although 92% of patients were taking calcium supplements and 70% taking alphacalcidol, 11 patients (22%) had ionized hypocalcaemia. To facilitate comparison of calculated ionized calcium, measured total calcium (t[Ca]), and ‘corrected’ calcium (c[Ca]), with the criterion measure of ionized calcium, all measurements were converted to z scores, standardized on the normal range for each variable. Results are expressed as intraclass correlation coefficients (ICC: 0, all differences are due to error; 1, all differences are due to between patient variation).

Conclusions. None of the published formulae greatly improved the test characteristics beyond simply using the total calcium. A correction formula in widespread use (Payne), quoted in reference texts, agreed less well with ionized calcium than did the unadjusted measured calcium. Correction formulae should be abandoned in favour of the use of uncorrected calcium. In cases of doubt, ionized calcium should be directly measured.

Keywords: adjustment; albumin; calcium; correction; measurement; validation



   Introduction
 Top
 Abstract
 Introduction
 Subjects and methods
 Results
 Discussion
 Conclusions
 References
 
There are no data to support the use of mathematical corrections of serum calcium among patients with end-stage renal disease (ESRD). In unselected patients, a variety of formulae have been proposed to permit calculation of the ionized calcium or of the ‘corrected’ total calcium (i.e. an estimation of the expected total calcium were the serum albumin normal) from the total calcium and protein concentration. The methodologies used in the development of these formulae varied: few were derived from clinically relevant material and none were developed and validated in separate, independent data sets. The literature on correction of calcium is, therefore, deficient in evidence supporting the use of formulae for the correction of calcium in any population. A previous large, well-designed study comparing correction algorithms with measured ionized calcium in unselected patients found that none performed significantly better than measured total calcium [1].

Calcium in serum exists in three fractions: bound to plasma proteins (approximately 40%), chelated to serum anions (13%) and free ionized calcium (47%) [2,3]. It is this last fraction which has biological activity and is under homeostatic control. The equilibrium between the fractions is dependent on a number of variables, most importantly, the concentrations of serum proteins and the pH. While the measurement of total calcium, albumin and total protein is available in standard laboratories, measurement of ionized calcium remains more difficult and is generally performed only in reference laboratories. In addition, great care must be taken with the method of venepuncture and subsequent sample handling [4]. Patient posture and the use of a tourniquet, through changes in pH and total protein concentration, alter the concentration of ionized calcium. Samples should be drawn anaerobically (to minimize loss of carbon dioxide), transported on ice and processed within hours (to minimize lactate generation). Heparin contamination must be avoided as it interferes with the assay. These stringent conditions make accurate measurement of ionized calcium problematic in many settings.

Previous studies have used Pearson correlation coefficients as the metric of goodness of fit between measured and predicted values. Under this estimate, predictions which are systematically biased will correlate as highly as those which are not, provided the closeness of the data to a linear relationship is similar. For estimating clinical utility, a measure of agreement (an intraclass correlation coefficient) is more appropriate than a measure of correlation. Rather than being a measure of closeness of fit to an unspecified linear relationship, agreement describes how well the data correspond to the line of identity (i.e. the relationship y=x). We investigated the agreement between calculated ionized calcium, or ‘corrected’ total calcium, and ionized calcium drawn and analysed under carefully controlled conditions, in a population of stable haemodialysis patients, using the intraclass correlation coefficient as the measure of agreement between each formula and the criterion measure.



   Subjects and methods
 Top
 Abstract
 Introduction
 Subjects and methods
 Results
 Discussion
 Conclusions
 References
 
Patients
Consecutive haemodialysis patients who were either outpatients dialysing in a hospital setting, or stable haemodialysis inpatients undergoing rehabilitation were studied. Exclusion criteria were: inability to obtain a sample without the use of a tourniquet; dialysis through a heparinized catheter; inability to analyse the sample within 10 h of venepuncture; multiple myeloma; known monoclonal gammopathy; uncontrolled hyperthyroidism; malignancy; jaundice; haemolysis; and acute intercurrent illness. The time constraint on sample handling led to the selection of patients from the first haemodialysis shift of the day, one third of the total dialysis population.

Venepuncture and sample handling
Arterialized venous blood was collected from each patient's fistula or graft after the patients had been seated for 10 min. Patients were not asked to fast on the morning of the test. Where possible, no tourniquet was applied. If a tourniquet was required, it was released for 30 s before sampling, and a discard tube was drawn before the sample. Care was taken to avoid muscular contraction in the limb or the ingress of air into the tube at the end of sampling. Total calcium was collected in tubes heparinized with 14.3 U heparin/ml blood, and ionized calcium in heparin-free tubes. Samples for ionized calcium and pH determination were transported on ice to the laboratory. Serum was separated within 2 h and sent to the reference laboratory for analysis within 8 h.

Analytic methods
All subjects had total calcium, ionized calcium, albumin, total protein, pH, phosphate and parathyroid hormone (PTH) determinations. Total calcium, ionized calcium, albumin, total protein and pH were determined in duplicate on two samples of blood drawn 5 min apart. Albumin was assayed by an automated bromcresol green (BCG) method, total calcium by arsenazo III dye binding and ionized calcium by ion-selective electrode using the Ciba-Corning 634. No anticoagulant was used in the vacuum collection tubes. pH was measured by electrode, PTH by two-site immunoradiometric assay for the intact molecule.

Selection of formulae
Equations from the literature were selected for study if they included a correction for serum albumin and were derived from patient-related data. The formula of Marshall and Hodgkinson [5], and three empiric linear relationships originally described by Orrell [6], Berry et al. [7] and Payne et al. [8] met these criteria. The former is an expression of the equilibrium between the various variables that is consistent with the law of mass action, first applied to the problem of calcium and protein binding by McLean and Hastings [9]. In the work reported here, the mass action formula was applied in two ways: using constants calculated from the patient's measured pH, and using constants in which pH=7.4 was substituted for patient's pH.

Statistical analysis
A C++ program (Borland C++ 5.0 Inprise Corporation, Scotts Valley, CA, USA) was written to solve the cubic mass action equation numerically. Linear regression was performed using BMDP 2R, and analysis of variance components using BMDP 8V (both SPSS Inc., Chicago, IL, USA). In the analysis of variance, method was regarded as a fixed effect and patients and time as random effects. For those formulae yielding a calculated ionized calcium [5], direct comparison of one set of values with the other was possible. For formulae yielding ‘corrected’ total calcium, values were normalized by conversion to a z score based on the usual normal range in our laboratory (not a data-derived z score), as were the corresponding values for ionized calcium; the z scores were then compared. Z scores were calculated as follows: the upper and lower limits of the normal range were treated as 95% confidence intervals (i.e. mean±1.96 standard deviations) (SD) and used to calculate mean and SD. Each measured value was then converted to a z score using the formula zCa=(Cameasured-mean)/SD. Transformation to a z score based on the normal range effectively changes each value to a measure of how extreme that measured value is, compared with the normal range. It therefore permits the direct comparison of measurements that have different normal ranges: in this case, the comparison of ionized (normal range 1.18–1.32 mmol/l in our laboratory, derived from literature values) with total calcium (normal ranges 2.20–2.58 mmol/l in our laboratory, derived from sampling of normal individuals). The intraclass correlation coefficient (ICC) describes the ratio of variance due to patient differences (signal) to total variance (signal+noise): it takes a value from 0 to 1, where 0 indicates complete unreliability (all measured differences are due to noise) and 1 perfect agreement (all measured differences are due to true differences between patients).



   Results
 Top
 Abstract
 Introduction
 Subjects and methods
 Results
 Discussion
 Conclusions
 References
 
Data distribution
Fifty-four consecutive patients met eligibility criteria and samples were obtained from 50 of these (93%). Patient characteristics are shown in Table 1Go. Distributions of the variables are summarized in Table 2Go. Stepwise linear regression was performed to determine whether any of the variables (i.e. time on dialysis, calcium dose, use of calcium carbonate versus calcium acetate, alphacalcidol dose, use of pulsed versus daily alphacalcidol, or serum PTH) was predictive of ionized calcium, but none of these variables proved statistically significant at the 0.05 level.


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Table 1. Patient demographics

 

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Table 2. Laboratory values

 

Agreement
The intraclass correlation coefficients for unadjusted measured total calcium and the five formulae (the results of each compared with measured ionized calcium) are shown in Table 3Go. Reasonable agreement with ionized calcium is observed for total measured calcium, without any adjustment (ICC=0.78). Slightly better agreement was observed for the linear correction of Orrell, [cCa]=[tCa]-0.176([Alb]-34) (ICC=0.84). Figure 1Go shows the contribution of both random error (scatter) and systematic bias (tendency to overestimate at low serum calcium and underestimate at high calcium) to inaccuracy.


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Table 3. Intraclass correlation coefficients

 


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Fig. 1. Agreement between ionized calcium and total calcium, and between ionized calcium and corrected calcium by Orrell's formula. Results been have normalized to the laboratory normal range for ionized calcium and total calcium, respectively, and are expressed as z scores.

 
The other linear approximations tested [7,8], which are numerically similar to formulae quoted in reference texts [10,11], resulted in lower levels of agreement at 0.45 and 0.68, respectively. It is apparent from Figure 2Go that systematic bias is prominent, with consistent overestimation of ionized calcium by both formulae. Both versions of the Marshall and Hodgkinson formula performed well (Fig. 3Go and Table 3Go). The substitution of pH=7.4 into the equations, rather than the use of true measured pH, had only a minor effect on agreement (ICC decreased from 0.83 to 0.79). Very little of the observed variation was due to laboratory variation. Agreement between the two samples drawn 5 min apart was excellent with ICC >0.95 for each method.



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Fig. 2. Agreement between measured ionized calcium and that predicted by the formulae of Berry and Payne. Results have been normalized to the laboratory normal range for ionized calcium and total calcium, respectively, and are expressed as z scores.

 


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Fig. 3. Agreement between measured ionized calcium and ionized calcium predicted by mass action formulae of Marshall and Hodgkinson.

 
A scatter plot of the difference between ionized and total calcium (both expressed as z scores) against serum albumin (Fig. 4Go) demonstrates that some of the variance in the parameter is explained by albumin (r2=0.19). The univariate regression line for these data is:



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Fig. 4. Scatter plot of differences between ionized and measured calcium against serum albumin.

 
In usual units (non-normalized), this may be rearranged:

which is remarkably similar to that of Orrell [6] (Table 3Go).

Multivariate analysis of the relationship between ionized calcium (dependent) and total calcium, albumin, phosphorus, pH, phosphate binders, use of alphacalcidol, and serum PTH (independent) revealed highly statistically significant (P<0.01) relationships for calcium, albumin, phosphorus and pH; the other variables were not significant at a conventional level (P=0.05). Total r2 for the final model was 0.79. The results are summarized in Table 4Go. Forcing PTH into the model did not change the significance level or the beta coefficient for any variable (data not shown).


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Table 4. Multivariate regression

 



   Discussion
 Top
 Abstract
 Introduction
 Subjects and methods
 Results
 Discussion
 Conclusions
 References
 
Accurate assessment of serum calcium in patients with chronic renal failure (CRF) and ESRD is important for a number of reasons. First, both hypercalcaemia [12] and hypocalcaemia [12,13] have been identified as predictors of mortality. Secondly, vitamin D metabolites offer therapeutic options in the normalization of serum calcium and the prevention and treatment of hyperparathyroidism in patients with CRF [14] and ESRD [15], and improvements in bone histology with treatment have been observed [16]. However, with the use of vitamin D metabolites, increases in serum calcium are common [15], and serial monitoring is necessary to permit detection of the increase and dose adjustment.

Appropriately-measured ionized calcium is the gold standard against which other measures of serum calcium should be judged. With consistent and careful sample handling ionized calcium values that are close to physiological can be obtained, but time constraints both at the bedside and for subsequent sample disposition, the extra demands on those who perform venepuncture, and the inability to distinguish an improperly-collected specimen based on the results, limit the practicality and usefulness of this test. Total calcium, therefore, remains the most commonly used test in clinical practice. Moreover, only total calcium, albumin and protein values are available in the large databases used for prognostic cohort studies. Both clinical practice and outcomes research would benefit from a validated surrogate measure for ionized calcium.

We determined the usefulness of a number of surrogate measures. The most widely quoted formula [8] resulted in agreement with the criterion measure that was substantially less than that of unadjusted total calcium; i.e., it resulted in an increase in error. Agreement with ionized calcium was greatest for the raw total calcium, the formula of Orrell [6], and the Marshall and Hodgkinson formulae [6] (0.78–0.84). The differences in agreement between these methods are unlikely to be clinically significant: the small gain in agreement is associated with an increase in complexity. Previous work on the validity of correction of calcium in nonuraemic patients compared measured and predicted ionized calcium for 13 published formulae [1] in 2454 samples obtained from 61 normal controls and 1494 patients. Although Pearson correlation coefficients between calculated and measured free calcium were high (r=0.76–0.87), only one formula (which incorporated measured pH), performed as well or better than measured total calcium (r=0.870 and 0.868, respectively). A new algorithm derived from, and tested against this same database improved r to only 0.889. Similarly, Morton and Hercz compared unadjusted total calcium and calcium adjusted according to a number of formulae with ionized calcium in a dialysis population and found that total calcium (r=0.86) performed better than any of the correction formulae (next best r=0.82) [17]. Ring and coworkers also found that a correction formula performed badly in this population, though they did not report their results in detail [18]. The correlation between ionized and total calcium in this work was similar to results discussed above at 0.88: typically 57–77% of the variance in ionized calcium is explained by total calcium. Our work combines a criterion measure drawn under carefully-controlled conditions with the use of an appropriate metric (i.e., the intraclass correlation rather than Pearson's product-moment correlation) to compare the results of the different correction approaches, and confirms that no correction results in clinically meaningful overall enhancement of ionized calcium prediction, beyond that provided by unadjusted total calcium. Because a strong linear relationship exists between variables, correlation coefficients artificially overestimate the degree of correspondence between the two (they estimate the goodness of fit to the best line or regression line through the data). Agreement methodology analyses the closeness of the data to the line of identity, and penalises systematic bias appropriately. It is the appropriate methodology when one is concerned with the absolute value of a measurement (with respect to a normal range or a therapeutic target), rather than comparisons between patients or occasions. Formulae for the correction of calcium were largely derived through correlation or regression methodology. Despite this theoretical problem, the lack of supportive independent validating data, and the emerging evidence of poor performance against a criterion measure [17,18] these formulae continue to be used in practice and quoted in textbooks [10,11].

In haemodialysis patients, therefore, the unadjusted total calcium should be the preferred surrogate measurement for ionized calcium. Orrell's correction may result in a slight improvement in accuracy for those centres measuring albumin by BCG, though it is doubtful whether the slight increase in agreement is clinically important. In cases where a difference would lead to an important change in diagnosis or management, ionized calcium should be measured under the conditions described above. The interoccasion reliability of ionized calcium, under carefully controlled conditions, was very high. Our present study does not permit an estimate of the reliability of a casually-drawn ionized calcium, compared with the gold standard.

Errors associated with the measurement of the other variables contribute to the difficulty in producing a useful correction formula. We measured albumin by BCG: in non uraemic patients, an alternative dye-binding assay, using bromcresol purple (BCP), agrees more closely with the criterion measures of immunonephelometry [19] and electroimmunoassay [20]. However, uraemic serum appears to contain a ligand that competitively inhibits the binding of BCP, but not that of BCG [21], resulting in (falsely) lower results for BCP in this population [22]. In dialysis patients, therefore, systematic differences between BCG and BCP values of 5 g/l [19] and 16 g/l [20] have been observed, with BCG systematically over- and BCP systematically under-estimating albumin as measured by a criterion measure. The albumin determinations in the original work from which the formulae were derived were by BCG [68]. This, and the problems associated with BCP in uraemia, make it unlikely that significant improvement would result from application of these formulae to data in which albumin is measured by BCP.

We considered the gold standard to be the actual measured ionized calcium at measured pH. Disturbances of acid–base haemostasis are to be expected in haemodialysis patients (even in our stable patients, values between 7.33 and 7.51 were observed), and we feel that the in vivo physiologically-active ion is probably best represented by the in vitro measurement at actual pH. This approach depends upon proper specimen handling and the avoidance of development of in vitro acidosis in transport. For these specimens, we were confident that this was the case.

Although the relatively small size of the data set is a limitation of this work, the care with which the specimens were drawn and processed, and the use of duplicate values to enable separation of variance due to random error from that due to method, are its strengths. Pre-specified inclusion and exclusion criteria delineated a population in whom factors known greatly to perturb the relationships or assays in question were absent, in order to maximize the potential to demonstrate the utility of the correction formulae. Failure to do so under these circumstances casts doubts on the utility of a correction approach in less selected patients. Few patients in the study had extremely low albumin (only one patient with albumin below 30 g/l): this was likely because of the exclusion of acutely-ill patients. It is not possible to generalize this work to more extremely abnormal albumin values, but since correction formulae do not produce substantially improved agreement within the range studied, it is most unlikely that they would perform better at more extreme values.



   Conclusions
 Top
 Abstract
 Introduction
 Subjects and methods
 Results
 Discussion
 Conclusions
 References
 
We have identified no data to support the use of algorithms to enhance the prediction of ionized calcium by total calcium. In our own data among haemodialysis patients, the use of uncorrected total calcium, a formula based on the law of mass action, and the use of the formula of Orrell produced similar degrees of agreement with the gold standard. We recommend that total calcium be used in the day-to-day management of dialysis patients and that ionized calcium should be assayed when a more exact value in required. A correction formula in common use [8] resulted in lower levels of agreement with ionized calcium than unadjusted total calcium, and should be abandoned.



   Acknowledgments
 
The authors would like to thank Dr Michael Clase for the programming involved in solving the cubic equation, Michael St Pierre for laboratory support, and Paul Stratford and Professor David Streiner for their helpful comments on the statistical aspects of this work.



   Notes
 
Correspondence and offprint requests to: Dr Catherine M. Clase, Division of Nephrology, Room 5088 Dickson Building, 5820 University Avenue, Halifax, Nova Scotia B3H 1V8, Canada. Back



   References
 Top
 Abstract
 Introduction
 Subjects and methods
 Results
 Discussion
 Conclusions
 References
 

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Received for publication: 8.11.99
Revision received 13. 6.00.