Editorial Annals of Clinical Biochemistry 0(0) 1–3 ! The Author(s) 2020 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/0004563220961751 journals.sagepub.com/home/acb
Calcium – An adjustment too far or not far enough? Gary Weaving
This issue of the Annals sees the publication of two papers by Jassam et al.1,2 which, together with their two previously published papers,3,4 make a short series on the broad theme of calcium albumin adjustment equations. The authors examine a number of issues related to the performance and use of these equations. Their findings show that the analytical variation of both calcium and albumin methods is wider than is acceptable. They also show that it may not be possible to use a harmonized reference interval for either calcium or for albumin. The derivation of two separate adjustment equations is of particular interest. Jassam et al. show that an equation derived using data from hospitalized patients performs poorly when applied to individuals in the community as assessed by the percentage of patients classified as being hypo/hypercalcaemic. However, improvements are seen when an equation is derived using data from the population to which it is applied (i.e. derived from community data applied to the community). Before considering this further, it is worth briefly reexamining the work of Payne et al.5 He was one of a number of researchers working in the area of calcium adjustment equations, but it is his work, published in 1973, which has become the model for others to follow, to the extent that his approach is now often simply referred to as ‘the method of Payne’. In brief, Payne utilized data from hospitalized patients, removed data which he believed would unduly influence his analysis (e.g. data for patients with renal disease) and then performed a regression analysis of calcium on albumin. Making use of the slope and intercept from the
regression analysis, he then derived his adjustment formula which is frequently written: adjusted calcium ¼ total calcium ðslope albuminÞ þ ðmean calcium interceptÞ with the final adjustment equation being written as adjusted calcium ¼ total calcium slope ðalbumin albumin set pointÞ It is easy to show that the albumin set point is in fact equal to the mean albumin for the population, i.e. adjusted calcium ¼ total calcium slope ðalbumin population mean albuminÞ (Note: For both ordinary linear regression and for Deming regression the regression lines must pass through the point (mean x, mean y). Therefore: mean calcium ¼ slope mean albumin þ intercept and so: mean calcium – intercept ¼ slope mean albumin)
Brighton and Sussex University Hospitals NHS Trust, Brighton, UK Corresponding author: Gary Weaving, Brighton and Sussex University Hospitals NHS Trust, Eastern Road, Brighton BN2 5BE, UK. Email: [email protected]
2 Presented in this way, it is now easy to see the importance of the mean albumin of the population. If the albumin value used in the calcium adjustment equation is not the same as the mean albumin of the population to which it is applied, then the adjustment equation will not perform well. Some thought now needs to be given to the mean calcium. Briefly returning to Payne, his idea was to use routine patient data and avoid recruiting healthy individuals, the underlying philosophy being that if patients with known causes of disordered calcium metabolism are removed from the routine data then that data should reasonably represent a healthy population – at least as far as calcium metabolism is concerned. If that is the case, and if a sufficiently large amount of data is used, then the mean total calcium for the ‘cleaned’ data should be close to the mid-point of the calcium reference interval. So what if we find that the mean of the adjusted calcium does not align with the mid-point of the reference interval – is our adjustment equation wrong? No, the mean of the adjusted calcium is always the same as the mean of the total calcium if the procedure above is followed. If the mean calcium values are not close to the mid-point of the reference interval, then there are a number of possible explanations including: (i) the ‘cleaned’ data do not represent a healthy population (ii) there are insufficient data (i.e. the sample number is too small) (iii) there is a problem with the calcium assay – e.g. bias (iv) the reference interval being used is not appropriate It is possible to ‘force’ the adjustment equation such that the mean adjusted calcium is any value of ones choosing – simply replace the mean albumin in the adjustment equation with an arbitrary value that shifts all the results, and indeed, this is what Payne did. He forced his adjustment equation such that the mean adjusted calcium was the same as the mid-point of his reference interval – this fact is obscured by the way in which his equations are frequently reproduced in the literature. To truly reflect Payne’s procedure, the very first equation presented above should actually use the term ‘mid-point of reference interval’ and not ‘mean calcium’. There are some additional considerations in trying to make the data fit a reference interval. Following Payne’s procedure exactly (i.e. adjusting to the midpoint of the reference interval) shifts all results by a fixed amount – is this appropriate? One would assume probably not. If the fundamental issue is one of calibration, then there may be a proportional error,
Annals of Clinical Biochemistry 0(0) a systematic bias or both. Shifting results by a fixed quantity may compensate for systematic bias, but it will not correct for proportional bias. If, after consideration, we deem that it is in fact acceptable to shift our results to ensure that our adjusted calcium equation aligns our results to our reference interval then, for consistency, should we not also be doing something about our total calcium results and indeed all our other routine assays? It may be pragmatic therefore to adjust to the midpoint of the reference interval but this is undesirable, as its requirement indicates that something is amiss. If we are following the guidelines of good statistical practice, then we should be closely inspecting our raw data before we attempt any form of mathematical manipulation. Among their work, Jassam et al. also confirm previous findings that serum albumin concentrations change with age.6 So this raises the question ‘if we need different equations for in-patients vs. community do we also need different equations for age, perhaps sex and maybe other sub-populations?’ and a more fundamental question ‘if, when deriving our equations, it is necessary to remove certain unrepresentative results from patients with, e.g. renal disease then, once derived, what justification is there for routinely applying that equation to patients with renal disease etc.?’ So far, we have not considered the effect of the slope in the equation, which is a measure of the binding of calcium to albumin. This is usually assumed to be constant, but as Jassam et al. discuss, this may not be true. The authors refer to works that suggest there might be considerable intraindividual variation of the binding affinity of albumin for calcium and also that calcium albumin binding may change with protein concentration. If the latter point is true, may we also see the need for different equations dependent on albumin concentration? If we do indeed need to derive a multitude of equations, then we will need to consider how we maintain governance of these – both keeping track of which equation has been applied to an individual patient under which circumstances and also perhaps regularly reviewing these equations with time to see if they require re-deriving. We also need to be mindful of the fact that there are many online resources available for calculating adjusted calcium – how can we ensure that our users are aware that these may not be appropriate for use if adjustments should be both population and method specific? Will the implementation of population-matched equations be helpful to users of the service? It is easy to imagine that for an individual patient, even if their total calcium and albumin remain the same, their adjusted calcium will be different as they move from
Weaving one setting to another – will this just cause confusion? It is also all too easy when presented with a calculated result given to two decimal places to forget that this is just an approximation which may not be applicable to the individual. Fundamentally, the users of our services, when presented with either a high or low total calcium, are interested in whether there is still an abnormality of calcium metabolism once the albumin concentration has been taken into account. Perhaps, although it would still be necessary to ensure that the underlying equations are fit for purpose, we should just report an appropriate comment, rather than a numeric result, for adjusted calcium? The topic of calcium adjustment equations arises periodically in the literature. Perhaps, the time has now come to finally address the various issues once and for all and to develop best practice guidelines. Pulling together all the various threads and also the issues highlighted by Jassam et al. I would suggest a. there needs to be a concerted effort to address the issues of method performance and standardization of both total calcium and albumin assays and their impact on reference intervals b. further work is required regarding the derivation of adjustment calculations including aspects such as identifying the populations for which we might need specific equations and how frequently these equations need to be re-derived or re-verified c. consideration needs to be given to how these equations are implemented to be of greatest benefit to our users and their patients d. thought should be given regarding how to best clinically audit the use of calcium adjustment equations to ensure that they are truly fit for purpose and serve our users well. There is much work that can be done here that requires neither specialist equipment nor techniques, and anyone with some data, enthusiasm and patience can very usefully contribute. Once we have finally addressed calcium adjustment equations, should we then turn our attention to other similar equations such as those used for magnesium albumin adjustments? Returning to Payne one last time, was it his intention to derive a formula for adjusted calcium that could
3 be applied universally and for all time? No, his primary focus was on investigating the difference between equations that adjusted to albumin as compared with those that adjusted to total protein. Regarding the adjustment equation he derived, in his words: ‘the adjustment cannot be applied to calcium values on patients with the nephrotic syndrome and hypoalbuminaemia’. . . ‘nor can it be applied to data from another laboratory if the accuracy and precision of calcium and albumin measurements, and therefore the normal ranges differ greatly from ours’. Payne said it all, we quote his method but not his guiding principles. Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding The author(s) received no financial support for the research, authorship, and/ or publication of this article.
Ethical approval Not applicable.
Guarantor GW.
Contributorship Sole author.
ORCID iD Gary Weaving
https://orcid.org/0000-0002-1437-0163
References 1. Jassam N, Luvai A, Narayanan D, et al. Albumin and calcium reference interval using healthy individuals and a data-mining approach. Ann Clin Biochem. Epub ahead of print 27 July 2020. DOI: 10.1177/ 0004563220944204 2. Jassam N, Thomas A, Hayden K, et al. The impact of the analytical performance specifications of calcium and albumin on adjusted calcium. Ann Clin Biochem. Epub ahead of print 26 July 2020. DOI: 10.1177/ 0004563220944426 3. Jassam N, Narayanan D, Turnock D, et al. The effect of different analytical platforms and methods on the performance of population-specific adjusted calcium equation. Ann Clin Biochem 2020; 57: 300–311. 4. Jassam N, Hayden K, Dearman R, et al. Prospective study comparing the outcome of a population-specific adjusted calcium equation to ionized calcium. Ann Clin Biochem 2020; 57: 316–324. 5. Payne RB, Little AJ, Williams RB, et al. Interpretation of serum calcium in patients with abnormal serum proteins. Br Med J 1973; 4: 643. 6. Weaving G, Batstone G and Jones RG. Age and sex variation in serum albumin concentration: an observational study. Ann Clin Biochem 2016; 53: 106–111.
Calcium – An adjustment too far or not far enough? Gary Weaving
This issue of the Annals sees the publication of two papers by Jassam et al.1,2 which, together with their two previously published papers,3,4 make a short series on the broad theme of calcium albumin adjustment equations. The authors examine a number of issues related to the performance and use of these equations. Their findings show that the analytical variation of both calcium and albumin methods is wider than is acceptable. They also show that it may not be possible to use a harmonized reference interval for either calcium or for albumin. The derivation of two separate adjustment equations is of particular interest. Jassam et al. show that an equation derived using data from hospitalized patients performs poorly when applied to individuals in the community as assessed by the percentage of patients classified as being hypo/hypercalcaemic. However, improvements are seen when an equation is derived using data from the population to which it is applied (i.e. derived from community data applied to the community). Before considering this further, it is worth briefly reexamining the work of Payne et al.5 He was one of a number of researchers working in the area of calcium adjustment equations, but it is his work, published in 1973, which has become the model for others to follow, to the extent that his approach is now often simply referred to as ‘the method of Payne’. In brief, Payne utilized data from hospitalized patients, removed data which he believed would unduly influence his analysis (e.g. data for patients with renal disease) and then performed a regression analysis of calcium on albumin. Making use of the slope and intercept from the
regression analysis, he then derived his adjustment formula which is frequently written: adjusted calcium ¼ total calcium ðslope albuminÞ þ ðmean calcium interceptÞ with the final adjustment equation being written as adjusted calcium ¼ total calcium slope ðalbumin albumin set pointÞ It is easy to show that the albumin set point is in fact equal to the mean albumin for the population, i.e. adjusted calcium ¼ total calcium slope ðalbumin population mean albuminÞ (Note: For both ordinary linear regression and for Deming regression the regression lines must pass through the point (mean x, mean y). Therefore: mean calcium ¼ slope mean albumin þ intercept and so: mean calcium – intercept ¼ slope mean albumin)
Brighton and Sussex University Hospitals NHS Trust, Brighton, UK Corresponding author: Gary Weaving, Brighton and Sussex University Hospitals NHS Trust, Eastern Road, Brighton BN2 5BE, UK. Email: [email protected]
2 Presented in this way, it is now easy to see the importance of the mean albumin of the population. If the albumin value used in the calcium adjustment equation is not the same as the mean albumin of the population to which it is applied, then the adjustment equation will not perform well. Some thought now needs to be given to the mean calcium. Briefly returning to Payne, his idea was to use routine patient data and avoid recruiting healthy individuals, the underlying philosophy being that if patients with known causes of disordered calcium metabolism are removed from the routine data then that data should reasonably represent a healthy population – at least as far as calcium metabolism is concerned. If that is the case, and if a sufficiently large amount of data is used, then the mean total calcium for the ‘cleaned’ data should be close to the mid-point of the calcium reference interval. So what if we find that the mean of the adjusted calcium does not align with the mid-point of the reference interval – is our adjustment equation wrong? No, the mean of the adjusted calcium is always the same as the mean of the total calcium if the procedure above is followed. If the mean calcium values are not close to the mid-point of the reference interval, then there are a number of possible explanations including: (i) the ‘cleaned’ data do not represent a healthy population (ii) there are insufficient data (i.e. the sample number is too small) (iii) there is a problem with the calcium assay – e.g. bias (iv) the reference interval being used is not appropriate It is possible to ‘force’ the adjustment equation such that the mean adjusted calcium is any value of ones choosing – simply replace the mean albumin in the adjustment equation with an arbitrary value that shifts all the results, and indeed, this is what Payne did. He forced his adjustment equation such that the mean adjusted calcium was the same as the mid-point of his reference interval – this fact is obscured by the way in which his equations are frequently reproduced in the literature. To truly reflect Payne’s procedure, the very first equation presented above should actually use the term ‘mid-point of reference interval’ and not ‘mean calcium’. There are some additional considerations in trying to make the data fit a reference interval. Following Payne’s procedure exactly (i.e. adjusting to the midpoint of the reference interval) shifts all results by a fixed amount – is this appropriate? One would assume probably not. If the fundamental issue is one of calibration, then there may be a proportional error,
Annals of Clinical Biochemistry 0(0) a systematic bias or both. Shifting results by a fixed quantity may compensate for systematic bias, but it will not correct for proportional bias. If, after consideration, we deem that it is in fact acceptable to shift our results to ensure that our adjusted calcium equation aligns our results to our reference interval then, for consistency, should we not also be doing something about our total calcium results and indeed all our other routine assays? It may be pragmatic therefore to adjust to the midpoint of the reference interval but this is undesirable, as its requirement indicates that something is amiss. If we are following the guidelines of good statistical practice, then we should be closely inspecting our raw data before we attempt any form of mathematical manipulation. Among their work, Jassam et al. also confirm previous findings that serum albumin concentrations change with age.6 So this raises the question ‘if we need different equations for in-patients vs. community do we also need different equations for age, perhaps sex and maybe other sub-populations?’ and a more fundamental question ‘if, when deriving our equations, it is necessary to remove certain unrepresentative results from patients with, e.g. renal disease then, once derived, what justification is there for routinely applying that equation to patients with renal disease etc.?’ So far, we have not considered the effect of the slope in the equation, which is a measure of the binding of calcium to albumin. This is usually assumed to be constant, but as Jassam et al. discuss, this may not be true. The authors refer to works that suggest there might be considerable intraindividual variation of the binding affinity of albumin for calcium and also that calcium albumin binding may change with protein concentration. If the latter point is true, may we also see the need for different equations dependent on albumin concentration? If we do indeed need to derive a multitude of equations, then we will need to consider how we maintain governance of these – both keeping track of which equation has been applied to an individual patient under which circumstances and also perhaps regularly reviewing these equations with time to see if they require re-deriving. We also need to be mindful of the fact that there are many online resources available for calculating adjusted calcium – how can we ensure that our users are aware that these may not be appropriate for use if adjustments should be both population and method specific? Will the implementation of population-matched equations be helpful to users of the service? It is easy to imagine that for an individual patient, even if their total calcium and albumin remain the same, their adjusted calcium will be different as they move from
Weaving one setting to another – will this just cause confusion? It is also all too easy when presented with a calculated result given to two decimal places to forget that this is just an approximation which may not be applicable to the individual. Fundamentally, the users of our services, when presented with either a high or low total calcium, are interested in whether there is still an abnormality of calcium metabolism once the albumin concentration has been taken into account. Perhaps, although it would still be necessary to ensure that the underlying equations are fit for purpose, we should just report an appropriate comment, rather than a numeric result, for adjusted calcium? The topic of calcium adjustment equations arises periodically in the literature. Perhaps, the time has now come to finally address the various issues once and for all and to develop best practice guidelines. Pulling together all the various threads and also the issues highlighted by Jassam et al. I would suggest a. there needs to be a concerted effort to address the issues of method performance and standardization of both total calcium and albumin assays and their impact on reference intervals b. further work is required regarding the derivation of adjustment calculations including aspects such as identifying the populations for which we might need specific equations and how frequently these equations need to be re-derived or re-verified c. consideration needs to be given to how these equations are implemented to be of greatest benefit to our users and their patients d. thought should be given regarding how to best clinically audit the use of calcium adjustment equations to ensure that they are truly fit for purpose and serve our users well. There is much work that can be done here that requires neither specialist equipment nor techniques, and anyone with some data, enthusiasm and patience can very usefully contribute. Once we have finally addressed calcium adjustment equations, should we then turn our attention to other similar equations such as those used for magnesium albumin adjustments? Returning to Payne one last time, was it his intention to derive a formula for adjusted calcium that could
3 be applied universally and for all time? No, his primary focus was on investigating the difference between equations that adjusted to albumin as compared with those that adjusted to total protein. Regarding the adjustment equation he derived, in his words: ‘the adjustment cannot be applied to calcium values on patients with the nephrotic syndrome and hypoalbuminaemia’. . . ‘nor can it be applied to data from another laboratory if the accuracy and precision of calcium and albumin measurements, and therefore the normal ranges differ greatly from ours’. Payne said it all, we quote his method but not his guiding principles. Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding The author(s) received no financial support for the research, authorship, and/ or publication of this article.
Ethical approval Not applicable.
Guarantor GW.
Contributorship Sole author.
ORCID iD Gary Weaving
https://orcid.org/0000-0002-1437-0163
References 1. Jassam N, Luvai A, Narayanan D, et al. Albumin and calcium reference interval using healthy individuals and a data-mining approach. Ann Clin Biochem. Epub ahead of print 27 July 2020. DOI: 10.1177/ 0004563220944204 2. Jassam N, Thomas A, Hayden K, et al. The impact of the analytical performance specifications of calcium and albumin on adjusted calcium. Ann Clin Biochem. Epub ahead of print 26 July 2020. DOI: 10.1177/ 0004563220944426 3. Jassam N, Narayanan D, Turnock D, et al. The effect of different analytical platforms and methods on the performance of population-specific adjusted calcium equation. Ann Clin Biochem 2020; 57: 300–311. 4. Jassam N, Hayden K, Dearman R, et al. Prospective study comparing the outcome of a population-specific adjusted calcium equation to ionized calcium. Ann Clin Biochem 2020; 57: 316–324. 5. Payne RB, Little AJ, Williams RB, et al. Interpretation of serum calcium in patients with abnormal serum proteins. Br Med J 1973; 4: 643. 6. Weaving G, Batstone G and Jones RG. Age and sex variation in serum albumin concentration: an observational study. Ann Clin Biochem 2016; 53: 106–111.
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