Home Medicine The effect of the immunoassay curve fitting routine on bias in troponin
Article
Licensed
Unlicensed Requires Authentication

The effect of the immunoassay curve fitting routine on bias in troponin

  • Tony Badrick EMAIL logo , Greg Ward and Peter Hickman
Published/Copyright: October 26, 2022
Clinical Chemistry and Laboratory Medicine (CCLM)
From the journal Clinical Chemistry and Laboratory Medicine (CCLM) Volume 61 Issue 2

Abstract

Objectives

Unlike many dose-response curves used in clinical chemistry, the immunoassay curve used to quantitate measurands is often sigmoidal rather than linear. Consequently, a more complex curve fitting model is required. Various models are available, but they can introduce bias, and there can be little awareness of why this error can be introduced.

Content

These curve-fitting models include those based on the law of mass-action, empirical models such as splines or linearization models such as the log/logit function. All these models involve assumptions, which can introduce bias as the dose-response curve is ‘forced’ to fit or minimize the distance between the standard concentration points to the theoretical curve. The most common curve fitting model is the four or five parameter model, which uses four or five parameters to fit a sigmoidal curve to a set of standard points.

Summary and outlook

Measurement of cardiac troponin is an important element in establishing a diagnosis of acute myocardial infarction. We use troponin, a cardiac biomarker, to demonstrate the potential effect of the bias that the curve fit could introduce. Troponin is used for both rule-in and rule-out decisions at different concentrations and at either end of the dose-response curve. The curve fitting process can cause lot-to-lot reagent (and calibrator) variation in immunoassay. However, laboratory staff need to be aware of this potential source of error and why it occurs. Understanding how the error occurs leads to a greater awareness of the importance of validating new reagent/calibrator assessment using patient samples with concentrations at crucial decision points.

Keywords: bias; data analysis; error; immunoassay
Corresponding author: Tony Badrick, Royal College of Pathologists of Australasia Quality Assurance Programs, St Leonards, Sydney, NSW, Australia, E-mail:

  1. Research funding: None declared.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Competing interests: Authors state no conflict of interest.

  4. Informed consent: Not applicable.

  5. Ethical approval: Not applicable.

References

1. Spiess, AN, Feig, C, Ritz, C. Highly accurate sigmoidal fitting of real-time PCR data by introducing a parameter for asymmetry. BMC Bioinf 2008;9:1–12. https://doi.org/10.1186/1471-2105-9-221.Search in Google Scholar PubMed PubMed Central

2. Baird, JK. A generalized statement of the law of mass action. J Chem Educ 1999;76:1146–50. https://doi.org/10.1021/ed076p1146.Search in Google Scholar

3. Fernandez, AA, Stevenson, GW, Abraham, GE, Chiamori, NY. Interrelations of the various mathematical approaches to radioimmunoassay. Clin Chem 1983;29:284–9. https://doi.org/10.1093/clinchem/29.2.284.Search in Google Scholar

4. Davies, C. Principles of competitive and immunometric assays (including ELISA). In: Wild, D, editor The immunoassay handbook, 4th ed. Amsterdam: Elsevier; 2013:29–59 pp.10.1016/B978-0-08-097037-0.00004-XSearch in Google Scholar

5. Sotnikov, DV, Zherdev, AV, Dzantiev, BB. Mathematical modeling of bioassays. Biochemistry (Moscow) 2017;82:1744–66. https://doi.org/10.1134/s0006297917130119.Search in Google Scholar PubMed

6. Dudley, RA, Edwards, P, Ekins, RP, Finney, DJ, McKenzie, IG, Raab, GM, et al.. Guidelines for immunoassay data processing. Clin Chem 1985;31:1264–71. https://doi.org/10.1093/clinchem/31.8.1264.Search in Google Scholar

7. Plikaytis, BD, Turner, SH, Gheesling, LL, Carlone, GM. Comparisons of standard curve-fitting methods to quantitate Neisseria meningitidis group A polysaccharide antibody levels by enzyme-linked immunosorbent assay. J Clin Microbiol 1991;29:1439–46. https://doi.org/10.1128/jcm.29.7.1439-1446.1991.Search in Google Scholar PubMed PubMed Central

8. Rodbard, D, Frazier, GF. Statistical analysis of radioligand assay data. Methods Enzymol 1975;37:3–22. https://doi.org/10.1016/s0076-6879(75)37003-1.Search in Google Scholar PubMed

9. Findlay, JW, Dillard, RF. Appropriate calibration curve fitting in ligand binding assays. AAPS J 2007;9:E260–7. https://doi.org/10.1208/aapsj0902029.Search in Google Scholar PubMed PubMed Central

10. Cumberland, WN, Fong, Y, Yu, X, Defawe, O, Frahm, N, De Rosa, S. Nonlinear calibration model choice between the four and five-parameter logistic models. J Biopharm Stat 2015;25:972–83. https://doi.org/10.1080/10543406.2014.920345.Search in Google Scholar PubMed PubMed Central

11. Eggers, KM, Venge, P, Lindahl, B, Lind, L. Cardiac troponin I levels measured with a high-sensitive assay increase over time and are strong predictors of mortality in an elderly population. J Am Coll Cardiol 2013;61:1906–13. https://doi.org/10.1016/j.jacc.2012.12.048.Search in Google Scholar PubMed

12. Thygesen, K, Alpert, JS, Jaffe, AS, Chaitman, BR, Bax, JJ, Morrow, DA, et al.. Fourth universal definition of myocardial infarction (2018). J Am Coll Cardiol 2018;72:2231–64. https://doi.org/10.1016/j.jacc.2018.08.1038.Search in Google Scholar PubMed

13. Gottschalk, PG, Dunn, JR. The five-parameter logistic: a characterization and comparison with the four-parameter logistic. Anal Biochem 2005;343:54–65. https://doi.org/10.1016/j.ab.2005.04.035.Search in Google Scholar PubMed

14. Rodbard, D. Statistical quality control and routine data processing for radioimmunoassays and immunoradiometric assays. Clin Chem 1974;20:1255–70. https://doi.org/10.1093/clinchem/20.10.1255.Search in Google Scholar

15. Raab, G. Comparison of logistic and a mass action curve for radioimmunoassy data. Clin Chem 1983;29:1757–61. https://doi.org/10.1093/clinchem/29.10.1757.Search in Google Scholar

16. Wold, S. Spline functions in data analysis. Technometrics 1974;16:1–11. https://doi.org/10.1080/00401706.1974.10489142.Search in Google Scholar

17. Pollock, D. Smoothing with cubic splines. In: Pollock, D, editor Signal processing and its applications, handbook of time series analysis, signal processing, and dynamics. San Diego, USA: Academic Press; 1999:293–322 pp.10.1016/B978-012560990-6/50013-0Search in Google Scholar

18. Kirkham, K, Hunter, W. Radioimmunoassay methods, 1st ed. Edinburgh: Churchill Livingston; 1971.Search in Google Scholar

19. Täljedal, IB, Wold, S. Fit of some analytical functions to insulin radio-immunoassay standard curves. Biochem J 1970;119:139–43.10.1042/bj1190139Search in Google Scholar PubMed PubMed Central

20. Hayes, R, Goswitz, F, Murphy, B. Radioisotopes in medicine: in vitro studies (Proceedings). Symposium. Oak Ridge: U.S. Atomic Energy Commission, Division of Technical Information; 1968:753 p.Search in Google Scholar

21. Rodbard, D, Hutt, D. Statistical analysis of radioimmunoassays and immunoradiometric (labelled antibody) assays: a generalized weighted, iterative, least-square method for logistic curve fitting. International Atomic Energy Agency, Vienna (Austria). Proc Ser 2 1973;1:165–89.Search in Google Scholar

22. Berkson, J. Application of the logistic function to bio-assay. J Am Stat Assoc 1944;39:357–65. https://doi.org/10.2307/2280041.Search in Google Scholar

23. Prentice, R. A generalization of the probit and logit methods for dose response curves. Biometrics 1976;32:761–8. https://doi.org/10.2307/2529262.Search in Google Scholar

24. Ritchie, DG, Nickerson, JM, Fuller, GM. Two simple programs for the analysis of data from enzyme-linked immunosorbent (ELISA) assays on a programmable desk-top calculator. Anal Biochem 1981;110:281–90. https://doi.org/10.1016/0003-2697(81)90193-7.Search in Google Scholar PubMed

25. Xiang, Y, Donley, J, Seletskaia, E, Shingare, S, Kamerud, J, Gorovits, B. A simple approach to determine a curve fitting model with a correct weighting function for calibration curves in quantitative ligand binding assays. AAPS J 2018;20:1–10. https://doi.org/10.1208/s12248-018-0208-7.Search in Google Scholar PubMed

26. Healy, MJ. Statistical analysis of radioimmunoassay data. Biochem J 1972;130:207–10. https://doi.org/10.1042/bj1300207.Search in Google Scholar PubMed PubMed Central

27. Finney, DJ. Bioassay and the practice of statistical inference. Int Stat Rev 1979;47:1. https://doi.org/10.2307/1403201.Search in Google Scholar

28. Rodbard, D, Munson, P, DeLean, A. Improved curve-fitting, parallelism testing, characterization of sensitivity and specificity, and optimization for radioligand assays. Radioimmunoassay Relat Proced Med 1975;1:469–504.Search in Google Scholar

29. Ricketts, JH, Head, GA. A five-parameter logistic equation for investigating asymmetry of curvature in baroreflex studies. Am J Physiol Regul Integr Comp Physiol 1999;277:441–54. https://doi.org/10.1152/ajpregu.1999.277.2.R441.Search in Google Scholar PubMed

30. Cox, KL. Immunoassay development, optimization and validation flow chart. ImmunoAssay Methods 2011;(Md):1–38.Search in Google Scholar

31. Azadeh, M, Gorovits, B, Kamerud, J, MacMannis, S, Safavi, A, Sailstad, J, et al.. Calibration curves in quantitative ligand binding assays: recommendations and best practices for preparation, design, and editing of calibration curves. AAPS J 2018;20:22. https://doi.org/10.1208/s12248-017-0159-4.Search in Google Scholar PubMed

32. Nisbet, JA, Owen, JA, Ward, GE. A comparison of five curve-fitting procedures in radioimmunoassay. Ann Clin Biochem 1986;23:694–8. https://doi.org/10.1177/000456328602300612.Search in Google Scholar PubMed

33. Raab, G. Estimation of a variance function, with application to immunoassay. Appl Stat 1981;30:32–40. https://doi.org/10.2307/2346655.Search in Google Scholar

34. Rodbard, D, Lenox, R, Wray, H, Ramseth, D. Statistical characterization of the random errors in the radioimmunoassay dose-response variable. Clin Chem 1976;22:350–8. https://doi.org/10.1093/clinchem/22.3.350.Search in Google Scholar

35. Finney, ADJ, Phillips, P. The form and estimation of a variance function, with particular reference to radioimmunoassay. Appl Stat 1977;26:312–20. https://doi.org/10.2307/2346972.Search in Google Scholar

36. Finney, D. Statistical methods in biological assays, 3rd ed. London: Charles Griffin; 1978.Search in Google Scholar

37. Gottschalk, P, Dunn, J. Bio-Plex suspension array system fitting Brendan’s five-parameter logistic curve. Hercules, California, USA: BioRad Laboratories; 1994.Search in Google Scholar

38. Motulsky, HJ, Ransnas, LA. Fitting curves to data using nonlinear regression: a practical and nonmathematical review. FASEB J 1987;1:365–74. https://doi.org/10.1096/fasebj.1.5.3315805.Search in Google Scholar

39. Bursa, F. Complications of fitting 4PL and 5PL models to bioassay data – Quantics Biostatistics [Internet]. Quantics Biostatistics; 2017. https://www.quantics.co.uk/blog/complications-fitting-4pl-5pl-models-bioassay-data/ [Cited 16 Nov 2020].Search in Google Scholar

40. Sadler, WA. Imprecision profiling. Clin Biochem Rev 2008;29(1 Suppl):S33–6.Search in Google Scholar

41. Rocke, D, Jones, G. Optimal design for ELISA and other forms of immunoassay. Technometrics 1997;39:162–70. https://doi.org/10.2307/1270904.Search in Google Scholar

42. Karpinski, K. Optimality assessment in the enzyme-linked immunosorbent assay (ELISA). Biometrics 1990;46:381–90. https://doi.org/10.2307/2531443.Search in Google Scholar

43. Gottschalk, PG, Dunn, JR. Determining the error of dose estimates and minimum and maximum acceptable concentrations from assays with nonlinear dose – response curves. Comput Methods Progr Biomed 2005;80:204–15. https://doi.org/10.1016/j.cmpb.2005.08.003.Search in Google Scholar PubMed

44. Dunn, J, Wild, D. Calibration curve fitting. In: The immunoassay handbook. Oxford, UK: Elsevier Ltd; 2013:323–36 pp.10.1016/B978-0-08-097037-0.00022-1Search in Google Scholar

45. Koerbin, G, Potter, JM, Abhayaratna, WP, Telford, RD, Badrick, T, Apple, FS, et al.. Longitudinal studies of cardiac troponin I in a large cohort of healthy children. Clin Chem 2012;58:1665–72. https://doi.org/10.1373/clinchem.2012.192054.Search in Google Scholar PubMed

46. Koerbin, G, Tate, J, Potter, JM, Cavanaugh, J, Glasgow, N, Hickman, PE. Characterisation of a highly sensitive troponin I assay and its application to a cardio-healthy population. Clin Chem Lab Med 2012;50:871–8. https://doi.org/10.1515/cclm-2011-0540.Search in Google Scholar PubMed

47. Chapman, A, Mills, N. A single blood test to rule out acute coronary syndrome. Heart 2018;104:632–3. https://doi.org/10.1136/heartjnl-2017-312269.Search in Google Scholar PubMed PubMed Central

48. Chapman, AR, Mills, NL. High-sensitivity cardiac troponin and the early rule out of myocardial infarction: time for action. Heart 2020;106:955–7. https://doi.org/10.1136/heartjnl-2020-316811.Search in Google Scholar PubMed PubMed Central

49. Hickman, PE, Koerbin, G, Badrick, T, Oakman, C, Potter, JM. The importance of low level QC for high sensitivity troponin assays. Clin Biochem 2018;58:60–3. https://doi.org/10.1016/j.clinbiochem.2018.05.007.Search in Google Scholar PubMed

50. Thygesen, K, Alpert, JS, Jaffe, AS, Chaitman, BR, Bax, JJ, Morrow, DA, et al.. Fourth universal definition of myocardial infarction. Circulation 2018;138:e618–51. https://doi.org/10.1161/CIR.0000000000000617.Search in Google Scholar PubMed

51. Saraph, JV, Benson, PG, Schroeder, RP. An instrument for measuring the critical factors of quality management. Decis Sci J 1989;20:810–29. https://doi.org/10.1111/j.1540-5915.1989.tb01421.x.Search in Google Scholar

52. Hickman, PE, Koerbin, G, Potter, JM, Abhayaratna, WP. Statistical considerations for determining high-sensitivity cardiac troponin reference intervals. Clin Biochem 2017;50:502–5. https://doi.org/10.1016/j.clinbiochem.2017.02.022.Search in Google Scholar PubMed

53. Herman, DS, Kavsak, PA, Greene, DN. Variability and error in cardiac troponin testing: an ACLPS critical review. Am J Clin Pathol 2017;148:281–95. https://doi.org/10.1093/ajcp/aqx066.Search in Google Scholar PubMed

54. Potomac, W, Diercks, DB. Using high sensitivity troponins to rule out acute coronary syndrome and lower admission rates. Cardiol Rev 2019;27:314–21. https://doi.org/10.1097/crd.0000000000000275.Search in Google Scholar PubMed

55. Latini, R, Masson, S, Anand, IS, Missov, E, Carlson, M, Vago, T, et al.. Prognostic value of very low plasma concentrations of troponin T in patients with stable chronic heart failure. Circulation 2007;116:1242–9. https://doi.org/10.1161/circulationaha.106.655076.Search in Google Scholar PubMed

56. Parsonage, WA, Tate, JR, Greenslade, JH, Hammett, CJ, Ungerer, JPJ, Pretorius, CJ, et al.. Effect of recalibration of the hs-TnT assay on diagnostic performance. Clin Chem Lab Med 2014;52:25–7. https://doi.org/10.1515/cclm-2013-0490.Search in Google Scholar PubMed

57. Hickman, PE, Lindahl, B, Cullen, L, Koerbin, G, Tate, J, Potter, JM. Decision limits and the reporting of cardiac troponin: meeting the needs of both the cardiologist and the ED physician. In: Critical reviews in clinical laboratory sciences. London, UK: Informa Healthcare; 2015, 52:28–44 pp.10.3109/10408363.2014.972497Search in Google Scholar PubMed

Received: 2022-07-07
Accepted: 2022-10-11
Published Online: 2022-10-26
Published in Print: 2023-01-27

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. Standardization and harmonization in laboratory medicine: not only for clinical chemistry measurands
  4. Mini Review
  5. The effect of the immunoassay curve fitting routine on bias in troponin
  6. Opinion Papers
  7. An overview of the most important preanalytical factors influencing the clinical performance of SARS-CoV-2 antigen rapid diagnostic tests (Ag-RDTs)
  8. Time to address quality control processes applied to antibody testing for infectious diseases
  9. Perspectives
  10. Definition and application of performance specifications for measurement uncertainty of 23 common laboratory tests: linking theory to daily practice
  11. The gaps between the new EU legislation on in vitro diagnostics and the on-the-ground reality
  12. General Clinical Chemistry and Laboratory Medicine
  13. Second-generation Elecsys cerebrospinal fluid immunoassays aid diagnosis of early Alzheimer’s disease
  14. Evaluation of the interchangeability between the new fully-automated affinity chrome-mediated immunoassay (ACMIA) and the Quantitative Microsphere System (QMS) with a CE-IVD-certified LC-MS/MS assay for therapeutic drug monitoring of everolimus after solid organ transplantation
  15. Quantitative detection of anti-PLA2R antibodies targeting different epitopes and its clinical application in primary membranous nephropathy
  16. Reference Values and Biological Variations
  17. A zlog-based algorithm and tool for plausibility checks of reference intervals
  18. Harmonization of indirect reference intervals calculation by the Bhattacharya method
  19. Red blood cell parameters in early childhood: a prospective cohort study
  20. Cancer Diagnostics
  21. Association of circulating free and total oxysterols in breast cancer patients
  22. Effect of short-term storage of blood samples on gene expression in lung cancer patients
  23. Infectious Diseases
  24. Operation Moonshot: rapid translation of a SARS-CoV-2 targeted peptide immunoaffinity liquid chromatography-tandem mass spectrometry test from research into routine clinical use
  25. Seroprevalence of SARS-CoV-2 antibodies in Italy in newborn dried blood spots
  26. Positivization time of a COVID-19 rapid antigen self-test predicts SARS-CoV-2 viral load: a proof of concept
  27. New insights into SARS-CoV-2 Lumipulse G salivary antigen testing: accuracy, safety and short TAT enhance surveillance
  28. Preanalytical stability of SARS-CoV-2 anti-nucleocapsid antibodies
  29. Prognostic value of procalcitonin in cancer patients with coronavirus disease 2019
  30. 24/7 workflow for bloodstream infection diagnostics in microbiology laboratories: the first step to improve clinical management
  31. Diagnostic performance of machine learning models using cell population data for the detection of sepsis: a comparative study
  32. Diagnostic value of procalcitonin, hypersensitive C-reactive protein and neutrophil-to-lymphocyte ratio for bloodstream infections in pediatric tumor patients
  33. Letters to the Editor
  34. Pseudohyponatremia: interference of hyperglycemia on indirect potentiometry
  35. Ligand binding assay-related underestimation of 25-hydroxyvitamin D in pregnant women exaggerates the prevalence of vitamin D insufficiency
  36. Urokinase-type plasminogen activator soluble receptor (suPAR) assay in clinical routine: evaluation one year after its introduction in the high automation corelab of the A. Gemelli hospital
  37. Is this a true lambda free light chain?
  38. Effect of various blood collection tubes on serum lithium and other electrolytes: our perspective from a tertiary healthcare institute
https://doi.org/10.1515/cclm-2022-0657
Keywords for this article
bias; data analysis; error; immunoassay

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. Standardization and harmonization in laboratory medicine: not only for clinical chemistry measurands
  4. Mini Review
  5. The effect of the immunoassay curve fitting routine on bias in troponin
  6. Opinion Papers
  7. An overview of the most important preanalytical factors influencing the clinical performance of SARS-CoV-2 antigen rapid diagnostic tests (Ag-RDTs)
  8. Time to address quality control processes applied to antibody testing for infectious diseases
  9. Perspectives
  10. Definition and application of performance specifications for measurement uncertainty of 23 common laboratory tests: linking theory to daily practice
  11. The gaps between the new EU legislation on in vitro diagnostics and the on-the-ground reality
  12. General Clinical Chemistry and Laboratory Medicine
  13. Second-generation Elecsys cerebrospinal fluid immunoassays aid diagnosis of early Alzheimer’s disease
  14. Evaluation of the interchangeability between the new fully-automated affinity chrome-mediated immunoassay (ACMIA) and the Quantitative Microsphere System (QMS) with a CE-IVD-certified LC-MS/MS assay for therapeutic drug monitoring of everolimus after solid organ transplantation
  15. Quantitative detection of anti-PLA2R antibodies targeting different epitopes and its clinical application in primary membranous nephropathy
  16. Reference Values and Biological Variations
  17. A zlog-based algorithm and tool for plausibility checks of reference intervals
  18. Harmonization of indirect reference intervals calculation by the Bhattacharya method
  19. Red blood cell parameters in early childhood: a prospective cohort study
  20. Cancer Diagnostics
  21. Association of circulating free and total oxysterols in breast cancer patients
  22. Effect of short-term storage of blood samples on gene expression in lung cancer patients
  23. Infectious Diseases
  24. Operation Moonshot: rapid translation of a SARS-CoV-2 targeted peptide immunoaffinity liquid chromatography-tandem mass spectrometry test from research into routine clinical use
  25. Seroprevalence of SARS-CoV-2 antibodies in Italy in newborn dried blood spots
  26. Positivization time of a COVID-19 rapid antigen self-test predicts SARS-CoV-2 viral load: a proof of concept
  27. New insights into SARS-CoV-2 Lumipulse G salivary antigen testing: accuracy, safety and short TAT enhance surveillance
  28. Preanalytical stability of SARS-CoV-2 anti-nucleocapsid antibodies
  29. Prognostic value of procalcitonin in cancer patients with coronavirus disease 2019
  30. 24/7 workflow for bloodstream infection diagnostics in microbiology laboratories: the first step to improve clinical management
  31. Diagnostic performance of machine learning models using cell population data for the detection of sepsis: a comparative study
  32. Diagnostic value of procalcitonin, hypersensitive C-reactive protein and neutrophil-to-lymphocyte ratio for bloodstream infections in pediatric tumor patients
  33. Letters to the Editor
  34. Pseudohyponatremia: interference of hyperglycemia on indirect potentiometry
  35. Ligand binding assay-related underestimation of 25-hydroxyvitamin D in pregnant women exaggerates the prevalence of vitamin D insufficiency
  36. Urokinase-type plasminogen activator soluble receptor (suPAR) assay in clinical routine: evaluation one year after its introduction in the high automation corelab of the A. Gemelli hospital
  37. Is this a true lambda free light chain?
  38. Effect of various blood collection tubes on serum lithium and other electrolytes: our perspective from a tertiary healthcare institute
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 30.12.2025 from https://www.degruyterbrill.com/document/doi/10.1515/cclm-2022-0657/html
Scroll to top button