Harmonising Reference Intervals for Three Calculated Parameters used in Clinical Chemistry

Abstract

For more than a decade there has been a global effort to harmonise all phases of the testing process, with particular emphasis on the most frequently utilised measurands. In addition, it is recognised that calculated parameters derived from these measurands should also be a target for harmonisation. Using data from the Aussie Normals study we report reference intervals for three calculated parameters: serum osmolality, serum anion gap and albumin-adjusted serum calcium. The Aussie Normals study was an a priori study that analysed samples from 1856 healthy volunteers. The nine analytes used for the calculations in this study were measured on Abbott Architect analysers. The data demonstrated normal (Gaussian) distributions for the albumin-adjusted serum calcium, the anion gap (using potassium in the calculation) and the calculated serum osmolality (using both the Bhagat et al. and Smithline and Gardner formulae). To assess the suitability of these reference intervals for use as harmonised reference intervals, we reviewed data from the Royal College of Pathologists of Australasia/Australasian Association of Clinical Biochemists (RCPA/AACB) bias survey. We conclude that the reference intervals for the calculated serum osmolality (using the Smithline and Gardner formulae) may be suitable for use as a common reference interval. Although a common reference interval for albumin-adjusted serum calcium may be possible, further investigations (including a greater range of albumin concentrations) are needed. This is due to the bias between the Bromocresol Green (BCG) and Bromocresol Purple (BCP) methods at lower serum albumin concentrations. Problems with the measurement of Total CO₂ in the bias survey meant that we could not use the data for assessing the suitability of a common reference interval for the anion gap. Further study is required.

Introduction

The reference interval (RI) is the most common support tool for the interpretation of clinical chemistry results.¹ Most commonly, it is used to distinguish between those who have a disease and those who do not. When used for this purpose, the preferred approach is to use the central 95% of a normally distributed healthy population.² The importance of the RI in decision making requires both a robust approach in its development and a periodic review of its applicability.³ The latter is particularly important if analytical methods change.⁴

Over the last 15 years there has been a concerted global effort to harmonise all phases of the testing process; the pre-analytical, analytical and post-analytical phases.⁵ This has included a move, where possible, to the use of common reference intervals for some analytes measured by all laboratories within a particular jurisdiction. Since the publication of common reference intervals by the Nordic Reference Interval Project (NORIP) in 2003, a number of jurisdictions have followed suit.⁶ This includes the Auckland Regional Quality Assurance Group (ARQAG) and the South Island Quality Assurance Group for Biochemistry (SIQAG) in New Zealand, UK Pathology Harmony in the United Kingdom, and the joint Australasian Association of Clinical Biochemists (AACB)/Royal College of Pathologists of Australasia (RCPA) harmonisation program in Australia.^7–9 The advantages of common reference intervals have been discussed elsewhere.¹⁰

The main focus has been on harmonisation of the most frequently measured analytes.^6,9 However, it is also recognised that the calculated parameters derived from these measurands are a post-analytic part of the total testing process. As such, they should also be a target for harmonisation.⁵ This includes the harmonisation of both the terminology and the formula used for the calculation which is discussed elsewhere in this edition of the Clinical Biochemist Reviews.

The aim of this study was to derive reference intervals directly, for three commonly used calculated parameters (calculated serum osmolality, serum anion gap and albumin-adjusted serum calcium) and to test the applicability of a common reference interval for each parameter. We used data from the Aussie Normal Study, a direct a priori study of over 1800 healthy individuals in the Canberra region.¹¹

Calculated Parameters

Calculated parameters are values obtained from a formula using one or more measured values and/or an empirical constant. They are mainly derived for three purposes:

• the estimation of an otherwise unmeasured parameter (e.g. calculated serum osmolality)

• to add further diagnostic value (e.g. the anion gap)

• to adjust a result to reflect actual clinical effect (e.g. albumin-adjusted calcium).

The terminology for calculating the concentration of osmotically active substances in serum is often confusing and inconsistent in the medical sciences literature. When the serum concentration of osmotically active substances is measured with an osmometer it is correctly described as serum osmolality and the unit used is mOsm/kg. When it is calculated from individual serum measurands with units of mmol/L, it is serum osmolarity. However, for practical use, equations have been developed empirically using regression analysis of measured serum osmolality against various serum measurands and so the resulting calculation can be described as calculated serum osmolality with the units mOsm/kg. The Standardisation of Pathology Units and Terminology (PUTS) project of the RCPA, recommends the term calculated serum osmolality with mOsm/kg as the unit used.¹²

Whatever formula is used for calculating serum osmolality the result is essentially an estimate (or approximation) of the otherwise measured serum osmolality. The difference between measured serum osmolality and calculated serum osmolality has been described by Smithline and Gardner as the “osmolal gap”.¹³

The osmolal gap is an important indicator of potentially unmeasured osmotically active constituents. It can provide an important clue as to the presence of toxins such as ethanol, methanol and ethyleneglycol,¹⁴ and a useful indicator of dehydration in elderly patients.¹⁵ There are many variations of the formula used for calculating serum osmolality, with one review discussing the merits of 36 different formulae.¹⁶ Of these 36, we use two of the more common formulae to derive reference intervals: the Bhagat formula,¹⁷ and the Smithline and Gardner formula (also known as the “simple” formula).¹³

The serum anion gap is an estimate of unmeasured anions and is a parameter used in the assessment of the acid-base status. It can also indicate erroneous results or the presence of abnormal amounts of some forms of immunoglobulin if the anion gap should be negative.¹⁸ There are two variations of formula used for calculating the anion gap, [Na⁺ + K⁺ − (Cl⁻ + HCO3⁻)] or [Na⁺ − (Cl⁻ + HCO3⁻)], with fairly even usage of either. In both of these equations, the term bicarbonate (HCO₃⁻) is used although most commercial methods measure total CO₂ and the two terms are used interchangeably. In this study we derived reference intervals for both formulae.

Albumin-adjusted serum calcium is considered to be a better indicator of serum calcium in those patients who are hypoand hyper-albuminaemic.¹⁹ Whilst there are some variations of the albumin-adjusted serum calcium formula, we looked at the one most commonly used in Australia; that is, [total serum calcium − 0.02(40 − albumin)].²⁰

With all of these calculation formulae, it is also important to recognise that uncertainty in measurement of the constituent measurands will contribute to the uncertainty in the output from the formula. This is because the uncertainty in measurement for a calculation is a function of the combined uncertainties of each of the input measurands.^21,22 In particular, for the calculation of osmolality and the anion gap (both of which may use up to five different parameters) the uncertainty of measurement of the calculation may be of considerable significance. For parameters that have a small absolute value, such as the anion gap and the osmol gap, the uncertainty may be greater than the absolute value.

Reference Intervals

Historically, there has been a less robust approach to the production of reference intervals for calculated parameters than the reference intervals of their measured counterparts. For calculated osmolality, the reference interval is usually derived by transference of the reference interval of the measured osmolality.²³ This assumes a good comparison between the measured and calculated parameters which in turn will depend on the chosen formula. The same applies to the albumin-adjusted serum calcium where the measured total serum calcium RI is commonly used.

For the anion gap, reference intervals might simply be based on a traditional clinically determined set of values with little supporting evidence and with little regard for differences or changes in measuring systems.²⁴

There are a number of benefits from directly obtaining a reference interval for a calculated analyte using rigorous methodology. First, it ensures the reference interval is appropriate for the designated measuring system; second, it may provide further verification of the formula used; and thirdly, if a sufficiently large reference population is used, it mitigates the variability associated with the uncertainty in measurement (although it must be remembered individual patient results will still be subject to such uncertainty).²⁵

Methods

Data from the Aussie Normals Study were used to obtain reference intervals for the anion gap, albumin-adjusted serum calcium and calculated serum osmolality. A detailed description of the Aussie Normals Study has been published previously.¹¹ Briefly, healthy volunteers were screened with detailed clinical and medication histories collected. Measurements were performed using proprietary reagents on the Abbott Architect c8000 and c16000 analysers (Abbott Diagnostics, Sydney, Australia). Table 1 summarises the details of the methods used.

Table 1.

Summary of the methodologies used for the measurement of component analytes

Analyte	Kit Supplier	Methodology
Sodium	ABBOTT	Crown Ether Indirect ISE
Potassium	ABBOTT	Valinomycin Indirect ISE
Chloride	ABBOTT	AgCl Indirect ISE
CO2	ABBOTT	Phosphoenol Pyruvate Carboxylase
Glucose	ABBOTT	Hexokinase
Calcium	ABBOTT	Arsenazo III dye
Albumin	ABBOTT	Bromocresol Green dye
Urea	ABBOTT	Urease

The measurement of the total CO₂ was performed prior to a restandardisation of the assay by Abbott Diagnostics in 2013. Measurements after this time were approximately 1 mmol/L lower with the resultant anion gap calculation 1 mmol greater (Abbott Product Information September 2013: Passing and Bablok y = 1.03x + 0.5, r² = 0.9994).

The Aussie Normals Study recruited 1877 subjects from three separate recruitment programs. Not all analytes were measured on all subjects. A cohort of 480 persons with a total CO₂ (bicarbonate) measurement was used for the calculation of the anion gap. For the calculated serum osmolality a cohort of 793 subjects was used. As albumin and calcium were measured on all participants, the full cohort of 1877 subjects was used for the calculation of albumin-adjusted serum calcium.

Distributions were assessed for normality using the Shapiro-Wilk test (p>0.05).²⁶ For the serum anion gap and the calculated serum osmolality, exclusion of outliers was made using the method of Tukey. Tukey defines an outlier as a result that is further from the first or third quartile by more than 1.5 times the difference between the first and third quartiles.^27,28 For the albumin-adjusted serum calcium results greater than three standard deviations (SD) were excluded (the method of Tukey failed to demonstrate a Gaussian distribution). After the establishment of a Gaussian distribution the reference interval was based on biological variation taking the central 95% in accordance with IFCC recommendations.²⁹ Analysis was undertaken using the statistical software Analyse-It³⁰ with Microsoft Excel.

Results

A summary of the key results is shown in Table 2.

Table 2.

Summary of data

Parameter	Units	Number of samples	p value	Central 95%	Median
Calculated Osmolality (Bhagat et al.)	mOsm/Kg	782	0.831	280 – 297	289
Calculated Osmolality (Simple)	mOsm/Kg	781	0.312	282 – 299	290
Anion Gap (with K+)	mmol/L	480	0.227	10.0–18.0 (11.0–19.0*)	14.0 (15.0*)
Anion Gap (without K+)	mmol/L	480	<0.001	6 – 14	10.0
Albumin-adjusted calcium	mmol/L	1866	0.074	2.14 – 2.67	2.40

^*Corrected for the Restandardisation of the Abbott Architect Total CO2 assay

Anion Gap

There were 480 people included in the calculation of the reference interval for the anion gap. As shown in Figure 1, for the calculation using potassium [(Na⁺ + K⁺) − (HCO₃⁻ + Cl⁻)], the distribution was Gaussian (p=0.227) with a central 95% falling between 10 mmol/L and 18 mmol/L (median; 14 mmol/L). When an adjustment was made to correct for the restandardisation of the Abbott total CO2 (bicarbonate) assay (see methods section for an explanation) the central 95% became 11 mmol/L to 19 mmol/L (median; 15 mmol/L).

Figure 1.

Distribution and Reference Interval for Anion Gap (with potassium)

For the calculation without the inclusion of potassium [Na⁺ − (HCO₃⁻ + Cl⁻)], the distribution was not normal (p<0.001) although it appeared to approximate a Gaussian distribution. The central 95% obtained was 6 mmol/L to 14 mol/L with a median of 10 mmol/L.

Albumin-adjusted Serum Calcium

Using the formula [total calcium − 0.02(40 −albumin)], 11 subjects (from a total of 1877) were excluded if outside three standard deviations from the mean (leaving 1866 subjects). The distribution was Gaussian (p=0.074) after log transformation as shown in Figure 2. The central 95% ranged from 2.14 mmol/L to 2.67 mmol/L, with a median of 2.40 mmol/L.

Figure 2.

Distribution and Reference Interval for Albumin-adjusted Calcium

Calculated Serum Osmolality

To obtain the reference interval for calculated serum osmolality with the simple (or Smithline and Gardner) calculation twelve subjects (leaving a total of 781) were excluded using the method of Tukey. With these 787 samples, the distribution was Gaussian (p=0.312) with the central 95% falling between 282 mOsm/kg and 299 mOsm/kg having a median of 290 mOsm/kg as shown in Figure 3. A Gaussian distribution was also found using the Bhagat et al. formula (p=0.831) after the exclusion of eleven subjects using the method of Tukey (leaving a total of 782). The central 95% fell between 280 to 297 mOsm/kg (median of 289 mOsm/kg).

Figure 3.

Distribution and Reference Interval for Calculated Osmolality (simple formula)

Discussion

In this study we have determined reference intervals for the three calculated parameters: calculated serum osmolality, anion gap and albumin-adjusted serum calcium.

Anion Gap Reference Interval

The distribution of the anion gap with potassium was normally distributed whereas the calculation without potassium was not. The reason for this is not known but it is possible this may be an artefact of the significant figures used. The calculation without potassium uses whole numbers with a very small absolute range of values (from 3 to 18 mmol/L). The calculation with potassium uses one significant figure and a slightly higher absolute range of values (from 7.4 to 21.9 mmol/L).

The RCPA Manual states the reference interval for the anion gap to be 4 to 13 mmol/L without potassium and 8 to 16 mmol/L with potassium.³¹ Both of these are a little lower than those that were found in this study (6 to 14 mmol/L and 11 to 19 mmol/L respectively).

Albumin-adjusted Serum Calcium Reference Interval

The reference interval for the albumin-adjusted serum calcium was slightly higher than the agreed reference interval from the RCPA/AACB harmonisation project (2.10 to 2.60) and was slightly wider than that suggested in the UK Pathology Harmony project (2.2 to 2.6 mmol/L).³²

Calculated Serum Osmolality Reference Interval

A recent publication has indicated the suitability of the Smithline and Gardner (sometimes referred to as “the simple”) formula for the estimation of serum osmolality.³³ We have also found that by using this formula, the reference interval was comparable to those observed from reference interval studies of measured serum osmolality using freezing point depression, (280 to 298 mOsm/kg).³⁴

Common Reference Intervals

The underlying basis for the use of common reference intervals is that the bias between methods is of an acceptable level.³⁵ As part of the joint AACB/RCPA harmonisation program a bias survey was undertaken.³⁶ This covered 27 common measurands using eight different analysers with the participation of 27 laboratories. Of these 27 measurands, 19 were found to have no impediment to harmonisation because of bias.

From this survey we see that for the purpose of the calculation of serum osmolality (using either the simple or Bhagat et al. formulae), the component measurands (sodium, potassium, glucose and urea) were suitable for harmonisation across most methods with the notable exception of the Beckman-Coulter DxC (where bias was demonstrated with sodium). Figure 4 is a difference plot of the calculated serum osmolality (simple formula) using the data from the bias survey. No significant bias was observed with seven of the eight methods. As expected, given the bias seen with sodium, bias was demonstrated with the Beckman-Coulter DxC.When the Bhagat et al. formula was used a similar pattern was observed. This suggests that a common reference interval could be used with either formula for the seven suitable methods. Further studies using data mining for post hoc analysis and flagging rates would also be useful.

Figure 4.

% Difference Plot for Calculated Serum Osmolality (Simple Equation) across eight Platforms (44 samples). Broken lines indicate the RCPA Allowable limits of error.

Of the measurands used for the calculation of the serum anion gap, sodium, chloride and potassium were suitable for harmonisation of their respective reference intervals. Total CO₂ (bicarbonate) was more problematic in the bias survey, with variability that was probably related to methodologies, matrix issues and stability. For this reason we could not perform further analysis of the bias survey data for calculated serum anion gap. A more robust bias study, focused on total CO₂ with careful consideration of stability and matrix may be required to confirm the suitability of common reference intervals for both CO₂ and the anion gap.

When considering the albumin-adjusted serum calcium calculation, albumin was also a problematic assay due largely to the use of both the bromocresol green and bromocresol purple methods by laboratories. Analysis of the bias survey data demonstrated a bias between the two albumin methods (5% to10% as serum albumin concentration decreased).³⁶ In the context of the albumin-adjusted serum calcium calculation, this has been discussed previously with the suggestion of a different calculation applicable for the different methods.^37,38 However, for the albumin-adjusted serum calcium calculation, the bias survey data difference plot showed reasonable agreement between methods with the possible exception of the Siemens Dimension RxL. This suggests that a common reference interval might be suitable for use with this calcium correction. Importantly, it is notable that most of the samples used in the bias survey had albumin concentrations greater than 35 g/L where there is the least bias demonstrated between the two methods. Further studies are needed using a greater range of albumin concentrations to demonstrate the general suitability of a common reference interval for albumin-adjusted serum calcium.

Figure 5.

% Difference Plot for Albumin-adjusted Calcium across eight Platforms (44 samples). Broken lines indicate the RCPA Allowable limits of error.