# Guest Essay

## Interpretation of Differences in Serial Troponin Results

**Despite years of intensive use and the recent advent of “high sensitivity” assays, fundamental questions about cardiac Troponin methods remain. Is precision of 10% CV required at the ****upper 99th percentile value of the reference population***? *Are methods with CV > 20% unacceptable? Is a change of 20% in an individual significant? Callum G Fraser, the internationally respected expert on biological variation, provides a logical technique for the interpretation of serial test results.

## Interpretation of Differences in Serial Troponin Results

#### December 2010

#### Callum G Fraser PhD

Scottish Bowel Screening Centre Laboratory

Kings Cross Dundee DD3 8EA

Scotland

- Introduction
- Imprecision and interpretation of single troponin results
- Imprecision and interpretation of differences in troponin results
- Change
- Probability that a change has occurred
- Rise or fall
- Probability that a rise or a fall has occurred
- Differences in cTn in clinical practice
- cTnI
- cTnT
- A final plea
- References

### Introduction

Over recent years, many guidelines relevant to the investigation of individuals with acute chest pain and the interpretation of the results of serum cardiac troponin (cTn) assays have been published. These include the Universal Definition of Myocardial Infarction (MI) [1], the National Academy of Clinical Biochemistry (NACB) Laboratory Practice guidelines on the use of cardiac troponin and B-type natriuretic peptide or N-terminal proB-type natriuretic peptide for etiologies other than acute coronary syndromes (ACS) and heart failure [2], a joint European and American statement on imprecision of measurement of cTn [3], and, most recently, the detailed recommendations for the use of cTn measurement in acute cardiac care [4]. While these and the many other guidelines and recommendations in the literature on cTn differ to some extent, they seem generally in agreement that:

*the analytical quality specification for imprecision at the upper 99th percentile value of the reference population should be < 10% CV and assays with a CV > 20% should not be used because of the risk of misclassification, and**a 20% change in serial results from an individual is usually significant since the analytical imprecision [expressed as CV] for most assays is ca. 5–7%*.

These concepts appear to be supported by a very important recent paper, which states that use of the Universal Definition of MI, together with a >20% cTnI change, appears to improve the discrimination of acute from chronic causes of cTnI release, and allows a reliable identification of patients at risk [5].

However, there are other opinions. For example, Apple et al [6] stated that using >30% change in cTnI in addition to either the baseline or follow-up concentration improved both specificity and risk assessment in patients presenting with symptoms of acute coronary syndromes.

One of Dr Westgard’s many important achievements over the years is in encouraging objective thinking about the validity of guidelines, recommendations, and statements from expert groups, especially those from professional bodies [7]. I concur absolutely with the view that all of us in laboratory medicine should examine the truth of supposedly evidence-based publications. Here, the recommendations regarding interpretation of differences in troponin results will be examined. This is particularly timely since newer “high sensitivity” assays for both cTnI and cTnT have become available and more will undoubtedly follow. These assays allow quantitation of troponin concentrations in many apparently healthy individuals and the results of such studies will impact on the above guidelines.

### Imprecision and interpretation of single troponin results

The number reported by laboratories for use by health care professionals is not, of course, a single number but represents a dispersion of values.

From a purely analytical point of view, it is simple to calculate the dispersion of any single result due to imprecision. If the imprecision is CV_{A}, this dispersion is +/- Z * CV_{A}, where Z is the number of standard deviations appropriate for the chosen probability. Thus, since Z is 1.96 for 95% probability (P < 0.05) – which is often called significant, and 2.58 for 99% probability (P < 0.01) – which is often called highly significant, the dispersions of a result of, for example, 14 ng/mL can be calculated at different levels of imprecision.

For a cTnT concentration of 14.0 ng/L, if the assay was almost perfect and the CV_{A} was 1%, the 95% dispersion would be 13.9 – 14.1 ng/L.

As the assay gets more imprecise, the dispersion increases in a linear manner, so that, if

CV_{A} was 5%, the 95% dispersion would be 13.3 – 14.7 ng/L,

CV_{A} was 10%, the 95% dispersion would be 12.6 – 15.4 ng/L,

CV_{A} was 15%, the 95% dispersion would be 11.9 – 16.1 ng/L,

CV_{A} was 20%, the 95% dispersion would be 11.2 – 16.8 ng/L,

CV_{A} was 25%, the 95% dispersion would be 10.5 – 17.5 ng/L, and

CV_{A} was 30%, the 95% dispersion would be 9.8 – 18.2 ng/L.

One statement [2] documents that *“the policy of precluding the use of assays that do not achieve a level of 10% imprecision at the 99th percentile value does not have a sound rationale.”* In addition, the authors concur with many guideline statements that, if CV_{A} > 20%, because there are no available data regarding what effect this assay imprecision would have on clinical accuracy, the use of such an assay should be discouraged.

However, the data above do provide a sound rationale for the concept that the better the assay (the lower the imprecision), the lower will be the dispersion of a single test result and likely the more accurate will be the classification, irrespective of how the result is interpreted.

### Imprecision and interpretation of differences in troponin results

Serial testing using cTn is of vital important in a variety of clinical situations which are well described in guidelines [1.4]. It must be recognized that, when two samples are analysed and the difference (sometimes referred to as the delta-value) is considered, then the analytical imprecision will increase, not twice, but by (CV_{A}^{2} + CV_{A}^{2})^{½} since CV must be added as variances (CV squared), which equals 2^{½} * CV_{A}. Thus, to state that an analytically significant difference has occurred, this must be greater than Z * 2^{½} * CV_{A}.

### Change

Semantics are important here. The word **change **is often used. Change implies a difference that can be a rise **or** a fall. This is termed bi-directional and the two-tailed Z-score must be used. Z-scores (equivalent to the number of standard deviates) can be found in statistical tables and, for 95% probability Z is 1.96, and for 99% probability Z is 2.58.

The NACB guidelines [2] state *“a recommended cutoff cTn value of > 20% in the 6–9 h after presentation represents a significant (3 SD) change in cTn on the basis of a 5% – 7% analytical CV typical for most assays in the concentration range indicating AMI.”* In fact, the quoted factor of 3 actually represents the Z-score of 3/2^{½} = 2.12, which is 96.9% probability, a little more than “significant”.

The Study Group on Biomarkers in Cardiology [4] state that,* “statistically, if the follow-up sample is outside the mean +3 standard deviation (SD) range of the baseline sample, the difference is significant,”* using the factor of 3 again. However, more correctly, they state:* “the formula for the calculation of a significant difference is + 1.96 × 2 ^{½} × SD = 2.77 × SD, assuming that the variability is similar for both values being measured.”* Of course, CV

_{A}can be substituted for SD, again assuming the CV is similar across the first and second result (in practice an average can be taken if SD or CV differ at the two results).

Using this formula, it is easy to calculate, at 95% probability, how analytical imprecision affects what is required for a significant change in two cTn results. If:

CV_{A} was 5%, a change of 13.9% would be required for significance,

CV_{A} was 10%, a change of 27.7% would be required for significance,

CV_{A} was 15%, a change of 41.6% would be required for significance,

CV_{A} was 20%, a change of 55.4% would be required for significance,

CV_{A} was 25%, a change of 69.2% would be required for significance, and

CV_{A} was 30%, a change of 83.1% would be required for significance.

These data again provide a sound rationale for the concept that the better the assay (the lower the imprecision), the smaller will be the change required for significance in serial results from an individual.

If it is indeed clinically appropriate that a change in results of 20% is required at 95% probability, then the analytical imprecision has to be lower than 20/2.77, that is, 7.2%. Thus, the two main recommendations in many guidelines and studies are intrinsically contradictory. If the first criterion for an assay, that is, imprecision <10%, is just met, then the second, that a change of 20% is significant, cannot hold.

### Probability that change has occurred

The above formula can be simply rearranged to make Z the unknown as: Z = change/ (2^{½} * CV_{A}^{2}). Thus, the probability that any change is significant can easily be calculated. For example, if a change of 20% had occurred in serial results from an individual, the probability of significance would depend on the analytical imprecision. If:

CV_{A} was 5%, a change of 20% would have a 99.5% probability,

CV_{A} was 10%, a change of 20% would have a 84.2% probability,

CV_{A} was 15%, a change of 20% would have a 64.8% probability,

CV_{A} was 20%, a change of 20% would have a 52.2% probability,

CV_{A} was 25%, a change of 20% would have a 42.7% probability, and

CV_{A} was 30%, a change of 20% would have a 36.2% probability.

A really useful tool, in my view, would be a calculator in which one entered the change that had occurred in percentage terms, than entered the CV_{A} and the calculator would find Z and then go to embedded statistical tables and report the probability of significance. The tool could be available also in reporting units such as ng/L so that the absolute change could be entered, then the analytical imprecision as SD, and again the probability of significance reported; an example would be that the change was 3.1 ng/L and the SD was 1.2 ng/L, Z would be 1.83 and the probability that the found change was significant would be reported as 93.1%.

### Rise or fall

As stated above, semantics are extremely important when considering interpretation of serial results. The words rise and fall are often used. For example, the Study Group on Biomarkers in Cardiology [4] state that, *“with the increasing sensitivities of cTn assays, it has become important to differentiate acute from chronic myocardial damage by evaluating the rise and fall of cTn concentration in serially drawn blood samples.”* When such terms are used, they are uni-directional and one-tailed Z-scores must be used. One-tailed Z-scores can be found in statistical tables and, for 95% probability Z is 1.65, and for 99% probability Z is 2.33.

As above, the formula for the calculation of a significant rise or a fall is Z * 2^{½} * CV_{A} = 2.33 * CV_{A}. Using this formula, it is easy to calculate, at 95% probability, how analytical imprecision affects what is required for a significant rise or fall in two cTn results. If:

CV_{A} was 5%, a rise or fall of 11.7% would be required for significance,

CV_{A} was 10%, a rise or fall of 23.3% would be required for significance,

CV_{A} was 15%, a rise or fall of 35.0% would be required for significance,

CV_{A} was 20%, a rise or fall of 46.6% would be required for significance,

CV_{A} was 25%, a rise or fall of 58.3% would be required for significance, and

CV_{A} was 30%, a rise or fall of 69.9% would be required for significance.

Note again that these data again provide a sound rationale for the concept that the better the assay (the lower the imprecision), the smaller will be the rise or fall required for significance in serial results from an individual.

If it is indeed clinically required that a rise or a fall in results of 20% is required, then the analytical imprecision has to be lower than 20/2.33 = 8.6%.

### Probability that a rise or a fall has occurred

As above, the above formula can be simply rearranged to make Z the unknown as:

Z = change/ (2^{½} * CV_{A}). Thus, the probability that any rise or fall is significant can easily be calculated, For example, if a rise or fall of 20% had occurred in serial results from an individual, the probability of significance would depend on the analytical imprecision. If:

CV_{A} was 5%, a rise or fall of 20% would have a 99.9% probability,

CV_{A} was 10%, a rise or fall of 20% would have a 92.2% probability,

CV_{A} was 15%, a rise or fall of 20% would have a 76.1% probability,

CV_{A} was 25%, a rise or fall of 20% would have a 70.9% probability, and

CV_{A} was 30%, a rise or fall of 20% would have a 68.1% probability.

At every imprecision, the probability of a rise or a fall for a certain difference is always higher than that for change, since uni-directional Z-scores are smaller than bi-directional Z-scores. If the calculator suggested above were to be created, then options for both uni-direction and bi-directional differences might be of interest. However, in the real world, most clinical decision-making seems concerned with assessment of whether the cTn has risen or fallen and not whether it has changed and thus use of uni-directional Z-scores would be the choice. Following the example above, if cTn rose by 3.1 ng/L and the SD was 1.2 ng/L, Z would be 1.83 (as above) but the probability of significance would be 96.6%.

### Differences in cTn in clinical practice

The imprecision of cTn assays has been the subject of many publications and most guidelines on the use of cTn and the interpretation of cTn results do have some discussion on this performance characteristic.

However, differences in serial results of cTn assays in an individual do not occur simply to imprecision (random analytical variation). Differences occur due to pre-analytical, analytical, and intrinsic within-subject biological variation [8]. Pre-analytical sources of variation are inherent in preparation of the patient for sampling and in sample collection, transport, storage and handling prior to analysis. These sources of variation should be minimized by good training of phlebotomists and laboratory staff, creation of Standard Operating Procedures, and then ensuring that all adhere to these. In consequence, pre-analytical sources of variation can be considered negligible.

Information on analytical imprecision, CV_{A}, and within-subject biological variation, CV_{I}, must be taken into account for a variety of clinical purposes [9] including noting that the true dispersion of any single result is +/- Z * (CV_{A}^{2} + CV_{I}^{2})^{½}, larger than that due to analytical imprecision alone. CV_{A} should, as above, be kept low so as to make the dispersion low and improve clinical classification against either reference limits or fixed decision limits.

One of the most important uses of data on analytical and biological variation is the assessment of the significance of differences in serial results from an individual. In order to decide whether a patient is deteriorating or improving the Critical Difference, or better termed, the Reference Change Value (RCV) that is due to the inherent sources of error must be exceeded.

This can be calculated as: RCV = Z * 2^{½} * (CV_{A}^{2} + CV_{I}^{2})^{½}.

Fortunately, newer high sensitivity (lower analytical detection limit) assays for cTn are now beginning to become available that allow measurement in at least some healthy individuals. Thus, at last, we can measure the components of biological variation for cTn: this is a necessary prerequisite to the correct introduction and subsequent use of any new laboratory investigation [10].

### cTnI

Wu et al [11] have studied the short- (within-day) and long-term (between-day) biological variation in cTnI. Their excellent report documented that the within-day CV_{A}, CV_{I}, and between-subject biological variation (CV_{G}) were 8.3%, 9.7%, and 57%, respectively; the corresponding between-day values were 15%, 14%, and 63%. One of the striking findings is that the individuality of cTnI is very marked, the Indices of Individuality being 0.21 and 0.39 respectively, these being calculated with the correct formula, II = (CV_{A}^{2} + CV_{I}^{2})^{½}/CV_{G}. cTnI has very low within-subject biological variation and large between-subject biological variation. In consequence, the span of cTnI found in any healthy individual occupies only a small part of the dispersion of the conventional population-based reference interval. As a result, individuals can have values that are highly unusual for them but these values will still lie well within the population-based reference interval (or below a population-based clinical decision-making point). Such values will not be flagged by laboratories nor considered worthy of note by clinicians or other health care workers. This is one reason that RCV are so much better for detecting differences in serial results from an individual. This concept is nicely elaborated in a recent Editorial on the utility of monitoring changes in cTn [12].

Traditional RCV can be calculated from these data. The RCV for change in the short-term at 95% probability is: RCV = Z * 2^{½} * (CV_{A}^{2} + CV_{I}^{2})^{½} = 1.96 * 2^{½} * (8.32 + 9.72)^{½} = 35.4%, and for the long-term, 56.9%. Note that, when within-subject biological variation is included, what is required for a significant change is much higher than the 20% documented in guidelines, which is of course based on considerations of analytical imprecision alone.

The RCV depend on analytical imprecision. Analogously to above, it is simple to calculate the effect of CV_{A} on RCV. If:

CV_{A} was 5%, the 95% RCV for change would be 30.3%,

CV_{A} was 10%, the 95% RCV for change would be 38.7%,

CV_{A} was 15%, the 95% RCV for change would be 49.5%, and

CV_{A} was 20%, the 95% RCV for change would be 61.6%.

As previously, low imprecision would seem to have considerable advantages in monitoring individuals using cTn assays. Indeed, it is widely accepted that the desirable imprecision, so that analytical “noise” does not add significantly (any more than 10%) to biological and clinical “signal”, is CV_{A} < 1/2CV_{I} [13]. Thus, analytical imprecision for cTn should be ca 5% (not 10% as in many guidelines) to achieve this goal.

This RCV calculation is concerned with change in serial results. As outlined earlier, in clinical practice, the concern is much more directed to whether a rise or a fall has occurred, in which case uni-directional one-tailed Z-scores must be used. If this is done, then, if:

CV_{A} was 5%, the 95% RCV for rise or fall would be 25.5%,

CV_{A} was 10%, the 95% RCV for rise or fall would be 32.5%,

CV_{A} was 15%, the 95% RCV for rise or fall would be 41.7%, and

CV_{A} was 20%, the 95% RCV for rise or fall would be 51.9%.

If the CV_{A} and CV_{I} are known, then it is easy to calculate the probability that any change in results has occurred using the rearranged equation Z = change/[ 2^{½} * (CV_{A}^{2} + CV_{I}^{2})^{½}], so that, if, for example, a change of 20% had occurred, then the probability that this was significant with the CV_{A} and CV_{I} found by Wu et al [11] would be calculated from Z = 20/[2^{½} * (8.32 + 9.72)^{½}] = 1.11 which equates to a low probability of 73.9%. Less good analytical imprecision will lower this probability of significance. In contrast, if CV_{A} was the desirable 5%, then Z would be 1.30 and the probability would be higher at 80.7 %.

Again, such calculations are probably much more appropriately done using uni-directional Z-scores and, if CV_{A} was 8.3%, the probability of rise or of fall would be 86.6%. If CV_{A} was the desirable 5%, then the probability would be higher at 90.3 %. Any calculator created to look at the probability that a difference in cTn results had occurred should, of course, take estimates of within-subject biological variation into account.

Wu et al [11] found that the distributions of cTnI had a little “right-skewness” and calculated RCV with a log-normal approach using the formulae described by Fokkema et al [14]. Log-normal short-term RCV were 46% for a rise in results and -32% for a fall in results, respectively: the corresponding long-term RCV were 81% and -45%.This is an interesting approach, but has drawbacks in that the total CV of non–log-transformed data, which includes both analytical and within-subject biological variation components, is used evaluate the variance of the lognormal distribution. This makes it difficult to model the effect of analytical imprecision on RCV.

### cTnT

As for cTnI, there is as yet one study in the literature on components of analytical and biological variation using a high sensitivity assay. This work assessed short- and long-term variation of cTnT in healthy subjects. The study found that CV_{A}, CV_{I} and CV_{G} were 53.5%, 48.2% and 85.9%, respectively, for short-term studies, and 98%, 94% and 94% for long-term studies. RCV were calculated using a log-normal approach, owing to the skewed results, and were 58% and -57.5% for short-term rise and fall, and 103.4% and -87% for long-term rise and fall. The Indices of Individuality were 0.84 and 1.4, respectively. Personally, I have concerns with the data handling in this study and think that further work is required on the variation over time in cTnT. However, I do agree with the authors that their work for the cTnT assay, along with prior data for cTnI [11], does begin to develop the conceptual constructs necessary to use a changing pattern of results with cTn assays.

### A final plea

The availability of other, and in the future even more improved, high sensitivity cTn assays will undoubtedly stimulate further work on the analytical and biological variation of cTn. These data should influence clinical decision-making and may lead to new more evidence-based and consistent guidelines being developed and promulgated in the future. Further work on the significance of differences in serial cTn results from an individual and on the effect of analytical imprecision is required and this work needs to be translated into everyday practice Indeed, this is recognized in the (very well worth reading) work of the Study Group on Biomarkers in Cardiology who stated the following: *“This area is evolving rapidly so when additional biological, analytical, and clinical data are available, more robust recommendations may appear.”*

As I wrote in a Guest Editorial [9] some time ago, and discussed with respect to B-type natriuretic peptide assays [16], it is simple to calculate the number of samples needed to obtain an estimate of an individual's homeostatic setting point within a stated closeness at a predetermined probability. It is easy to calculate the dispersion of a single test result. The effects of analyzing a sample more than once and/or taking more than one sample can also be calculated. Here I have shown that, in addition, it is simple to create the Reference Change Value for either change or a rise or a fall and it is not difficult to calculate the probability that any change, rise or fall is significant. The effects of analytical imprecision on dispersions, RCV and the probability that a change or rise or fall has occurred are also simple to model and show why analytical quality specifications based on biological variation are indeed the best. All of these calculations require numerical knowledge of both analytical imprecision and biological variation.

Finally, again I would urge those that are involved in the generation of allegedly evidence-based guidelines, recommendations, and scientific statements to do all of these calculations before disseminating their work, ensure that their numerical statements do use correct semantics and terminology and are not inherently contradictory, and carefully consider the ramifications on clinical utility.

### References

- Thygesen K, Alpert JS, White HD, et al. Universal definition of myocardial infarction. Circulation 2007;116:2634–53
- National Academy of Clinical Biochemistry Laboratory Medicine Practice Guidelines: Use of cardiac troponin and B-type natriuretic peptide or n-terminal proB-type natriuretic peptide for etiologies other than acute coronary syndromes and heart failure. Clin Chem 2007;53:2086 - 96
- Jaffe AS, Apple FS, Morrow DA, Lindahl B, Katus HA. Being rational about (im)precision: A statement from the Biochemistry Subcommittee of the Joint European Society of Cardiology/American College of Cardiology Foundation/American Heart Association/World Heart Federation Task Force for the Definition of Myocardial Infarction. Clin Chem 2010;56:941- 3.
- Thygesen K, Mair J, Katus H, et al. Recommendations for the use of cardiac troponin measurement in acute cardiac care. Eur Heart J 2010; 31:2197–206
- Eggers KM, Jaffe AS, Venge P, Lindahl B. Clinical implications of the change of cardiac troponin I levels in patients with acute chest pain — An evaluation with respect to the Universal Definition of Myocardial Infarction. Clin Chim Acta 2011;41:291–7
- Apple FS, Pearce LA, Smith SW, Kaczmarek JM, Murakami MM. Role of monitoring changes in sensitive cardiac troponin I assay results for early diagnosis of myocardial infarction and prediction of risk of adverse events. Clin Chem 2009;55:930-7
- Westgard JO. Nothing but the Truth Manual. Madison, WI, Westgard QC, 2004
- Fraser CG. Biological Variation: From Principles to Practice. Washington, DC, AACC Press, 2001 [6th printing, 2010]
- Fraser CG. Are scientific statements the scientific truth? See: www.westgard.com/are-scientific-statements-the-scientific-truth.htm
- Fraser CG. Data on biological variation: essential prerequisites for introducing new procedures? Clin Chem 1994;40:1671-3
- Wu AHB, Lu QA, Todd J, Moecks J, Wians F. Short- and long-term biological variation in cardiac troponin I measured with a high-sensitivity assay: implications for clinical practice. Clin Chem 2009;55:52-8
- Aakre KM, Sandberg S. Can changes in troponin results be useful in diagnosing myocardial infarction. Clin Chem 2010;56:1047-9
- Fraser CG. Biological variation data for setting quality specifications. See: www.westgard.com/biological-variation-data-for-setting-quality-specifications.htm
- Fokkema MR, Herrmann Z, Muskiet FAJ, Moecks J. Reference change values for brain natriuretic peptides revisited. Clin Chem 2006;52:1602–3
- Vasile VC, Saenger AK, Kroning JM, Jaffe AS. Biological and analytical variability of a novel high-sensitivity cardiac troponin T assay. Clin Chem 2010;56:1086–90
- Fraser CG. Quality specifications for B-type natriuretic peptides. Clin Chem 2005;51:1307-922

### About Callum G. Fraser

Callum G Fraser PhD is Senior Advisor to the Scottish Bowel Screening Programme, Honorary Professor in the University of Dundee, and Honorary Consultant Clinical Biochemist to NHS Tayside, Scotland. He has published much on the setting of analytical quality specifications and the interpretation of laboratory data, and is author of Biological Variation: From Principles to Practice, Washington, AACC, 2001.Professor Callum G Fraser

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