Skip to main content
SpringerLink
Log in

Statistical Analysis—Measurement Error

  • Chapter
  • First Online:
Clinical Applications of Artificial Intelligence in Real-World Data

  • 539 Accesses

Abstract

An important aspect of data quality when conducting clinical analyses using real-world data is how variables in the data have been recorded or measured. The discrepancy between an observed value and the true value is called measurement error (also known as noise in the artificial intelligence and machine learning literature) and can have consequences for your analyses in all kinds of contexts. To properly assess the potential impact of measurement error it is essential to understand the relationship between the true and observed variables as well as the goal of the analysis and how it will be implemented in practice. Commonly, measurement error is distinguished as being classical, Berkson, systematic and/or differential. While it is clear that measurement error can have far-reaching consequences on analyses, the effect can differ depending on whether analyses are descriptive, explanatory or predictive. Validation studies can inform the estimation and characterization of measurement error as well as provide crucial information for correction methods that are available in several statistical programming languages such as SAS, R and Python.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Algan G, Ulusoy I. Label noise types and their effects on deep learning. 2020. ArXiv: https://arxiv.org/abs/2003.10471

  2. Bauldry S, Bollen KA, Adair LS. Evaluating measurement error in readings of blood pressure for adolescents and young adults. Blood Press. 2015;24:96–102. https://doi.org/10.3109/08037051.2014.986952.

    Article  Google Scholar 

  3. Boeschoten L, Oberski D, De Waal T. Estimating classification errors under edit restrictions in composite survey-register data using multiple imputation latent class modelling (MILC). J Off Stat. 2017;33:921–62. https://doi.org/10.1515/jos-2017-0044.

    Article  Google Scholar 

  4. Boeschoten L, van Kesteren E-J, Bagheri A, Oberski DL. Achieving fair inference using error-prone outcomes. Int J Interact Multimed Artif Intell. 2021;6:9. https://doi.org/10.9781/ijimai.2021.02.007.

    Article  Google Scholar 

  5. Boudreau DM, Daling JR, Malone KE, et al. A validation study of patient interview data and pharmacy records for antihypertensive, statin, and antidepressant medication use among older women. Am J Epidemiol. 2004;159:308–17. https://doi.org/10.1093/aje/kwh038.

    Article  Google Scholar 

  6. Brakenhoff TB, Mitroiu M, Keogh RH, et al. Measurement error is often neglected in medical literature: a systematic review. J Clin Epidemiol. 2018;98:89–97. https://doi.org/10.1016/j.jclinepi.2018.02.023.

    Article  Google Scholar 

  7. Brakenhoff TB, van Smeden M, Visseren FLJ, Groenwold RHH. Random measurement error: why worry? An example of cardiovascular risk factors. PLoS ONE. 2018;13: e0192298. https://doi.org/10.1371/journal.pone.0192298.

    Article  Google Scholar 

  8. Buonaccorsi JP. Measurement error: models, methods, and applications. New York: Chapman and Hall/CRC; 2010.

    Book  MATH  Google Scholar 

  9. Carroll RJ, Ruppert D, Stefanski LA, Crainiceanu CM. Measurement error in nonlinear models: a modern perspective. 2nd ed. New York: Chapman and Hall/CRC; 2006.

    Book  MATH  Google Scholar 

  10. Carroll RJ, Spiegelman CH, Lan KKG, et al. On errors-in-variables for binary regression models. Biometrika. 1984;71:19–25. https://doi.org/10.1093/biomet/71.1.19.

    Article  MathSciNet  MATH  Google Scholar 

  11. Carroll RJ, Stefanski LA. Approximate quasi-likelihood estimation in models with surrogate predictors. J Am Stat Assoc. 1990;85:652–63. https://doi.org/10.1080/01621459.1990.10474925.

    Article  MathSciNet  Google Scholar 

  12. Ching T, Himmelstein DS, Beaulieu-Jones BK, et al. Opportunities and obstacles for deep learning in biology and medicine. J R Soc Interface. 2018;15:20170387. https://doi.org/10.1098/rsif.2017.0387.

    Article  Google Scholar 

  13. Cole SR, Chu H, Greenland S. Multiple-imputation for measurement-error correction. Int J Epidemiol. 2006;35:1074–81. https://doi.org/10.1093/ije/dyl097.

    Article  Google Scholar 

  14. Cook JR, Stefanski LA. Simulation-extrapolation estimation in parametric measurement error models. J Am Stat Assoc. 1994;89:1314–28. https://doi.org/10.1080/01621459.1994.10476871.

    Article  MATH  Google Scholar 

  15. Delate T, Jones AE, Clark NP, Witt DM. Assessment of the coding accuracy of warfarin-related bleeding events. Thromb Res. 2017;159:86–90. https://doi.org/10.1016/j.thromres.2017.10.004.

    Article  Google Scholar 

  16. Ferrari P, Friedenreich C, Matthews CE. The role of measurement error in estimating levels of physical activity. Am J Epidemiol. 2007;166:832–40. https://doi.org/10.1093/aje/kwm148.

    Article  Google Scholar 

  17. Freedman LS, Commins JM, Willett W, et al. Evaluation of the 24-hour recall as a reference instrument for calibrating other self-report instruments in nutritional cohort studies: evidence from the validation studies pooling project. Am J Epidemiol. 2017;186:73–82. https://doi.org/10.1093/aje/kwx039.

    Article  Google Scholar 

  18. Freedman LS, Schatzkin A, Midthune D, Kipnis V. Dealing with dietary measurement error in nutritional cohort studies. JNCI J Natl Cancer Inst. 2011;103:1086–92. https://doi.org/10.1093/jnci/djr189.

    Article  Google Scholar 

  19. Frenay B, Verleysen M. Classification in the presence of label noise: a survey. IEEE Trans Neural Netw Learn Syst. 2014;25:845–69. https://doi.org/10.1109/TNNLS.2013.2292894.

    Article  MATH  Google Scholar 

  20. Fuller WA. Measurement error models. New York: John Wiley & Sons; 1987.

    Book  MATH  Google Scholar 

  21. Gianfrancesco MA, Tamang S, Yazdany J, Schmajuk G. Potential biases in machine learning algorithms using electronic health record data. JAMA Intern Med. 2018;178:1544. https://doi.org/10.1001/jamainternmed.2018.3763.

    Article  Google Scholar 

  22. Goldman GT, Mulholland JA, Russell AG, et al. Impact of exposure measurement error in air pollution epidemiology: effect of error type in time-series studies. Environ Health. 2011;10:61. https://doi.org/10.1186/1476-069X-10-61.

    Article  Google Scholar 

  23. Gravel CA, Platt RW. Weighted estimation for confounded binary outcomes subject to misclassification. Stat Med. 2018;37:425–36. https://doi.org/10.1002/sim.7522.

    Article  MathSciNet  Google Scholar 

  24. Guolo A. Robust techniques for measurement error correction: a review. Stat Methods Med Res. 2008;17:555–80. https://doi.org/10.1177/0962280207081318.

    Article  MathSciNet  Google Scholar 

  25. Gupta S, Gupta A. Dealing with noise problem in machine learning data-sets: a systematic review. Procedia Comput Sci. 2019;161:466–74. https://doi.org/10.1016/j.procs.2019.11.146.

    Article  Google Scholar 

  26. Gustafson P. Measurement error and misclassification in statistics and epidemiology: impacts and bayesian adjustments. CRC Press (2003)

    Google Scholar 

  27. Gyorkos TW, Frappier-Davignon L, Dick Maclean J, Viens P. Effect of screening and treatment on imported intestinal parasite infections: results from a randomized, Controlled Trial. Am J Epidemiol. 1989;129:753–61. https://doi.org/10.1093/oxfordjournals.aje.a115190

  28. Gyorkos TW, Genta RM, Viens P, Maclean JD. Seroepidemiology of Strongyloides infection in the Southeast Asian refugee population in. Canada. Am. J. Epidemiol. 1990;257–64

    Google Scholar 

  29. Hardin JW, Schmiediche H, Carroll RJ. The regression-calibration method for fitting generalized linear models with additive measurement error. Stata J Promot Commun Stat Stata. 2003;3:361–72. https://doi.org/10.1177/1536867X0400300406.

    Article  Google Scholar 

  30. Hardin JW, Schmiediche H, Carroll RJ. The simulation extrapolation method for fitting generalized linear models with additive measurement error. Stata J Promot Commun Stat Stata. 2003;3:373–85. https://doi.org/10.1177/1536867X0400300407.

    Article  Google Scholar 

  31. He W, Xiong J, Yi GY, SIMEX R package for accelerated failure time models with covariate measurement error. J Stat Softw. 2012;46:1–14. https://doi.org/10.18637/jss.v046.c01

  32. Hui SL, Walter SD. Estimating the error rates of diagnostic tests. Biometrics. 1980;36:167–71. https://doi.org/10.2307/2530508.

    Article  MATH  Google Scholar 

  33. Jiang T, Gradus JL, Lash TL, Fox MP. Addressing measurement error in random forests using quantitative bias analysis. Am J Epidemiol. 2021. https://doi.org/10.1093/aje/kwab010.

    Article  Google Scholar 

  34. Joseph L, Gyorkos TW, Coupal L. Bayesian estimation of disease prevalence and the parameters of diagnostic tests in the absence of a gold standard. Am J Epidemiol. 1995;141:263–72. https://doi.org/10.1093/oxfordjournals.aje.a117428.

    Article  Google Scholar 

  35. Karimi D, Dou H, Warfield SK, Gholipour A. Deep learning with noisy labels: exploring techniques and remedies in medical image analysis. Med Image Anal. 2020;65: 101759. https://doi.org/10.1016/j.media.2020.101759.

    Article  Google Scholar 

  36. Keogh RH, Shaw PA, Gustafson P, et al. STRATOS guidance document on measurement error and misclassification of variables in observational epidemiology: Part 1—Basic theory and simple methods of adjustment. Stat Med. 2020;39:2197–231. https://doi.org/10.1002/sim.8532.

    Article  MathSciNet  Google Scholar 

  37. https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8531

    Article  MathSciNet  MATH  Google Scholar 

  38. Lash TL, Fox MP, MacLehose RF, et al. Good practices for quantitative bias analysis. Int J Epidemiol. 2014;43:1969–85. https://doi.org/10.1093/ije/dyu149.

    Article  Google Scholar 

  39. Lederer W, Küchenhoff H. A short introduction to the SIMEX and MCSIMEX. Newsl R Proj. 2006;6(4):26–31.

    Google Scholar 

  40. Liao X, Zucker DM, Li Y, Spiegelman D. Survival analysis with error-prone time-varying covariates: a risk set calibration approach. Biometrics. 2011;67:50–8. https://doi.org/10.1111/j.1541-0420.2010.01423.x.

    Article  MathSciNet  MATH  Google Scholar 

  41. Lim S, Wyker B, Bartley K, Eisenhower D. Measurement error of self-reported physical activity levels in New York City: assessment and correction. Am J Epidemiol. 2015;181:648–55. https://doi.org/10.1093/aje/kwu470.

    Article  Google Scholar 

  42. Luijken K, Groenwold RHH, Calster BV, et al. Impact of predictor measurement heterogeneity across settings on the performance of prediction models: a measurement error perspective. Stat Med. 2019;38:3444–59. https://doi.org/10.1002/sim.8183.

    Article  MathSciNet  Google Scholar 

  43. Luijken K, Wynants L, van Smeden M, et al. Changing predictor measurement procedures affected the performance of prediction models in clinical examples. J Clin Epidemiol. 2020;119:7–18. https://doi.org/10.1016/j.jclinepi.2019.11.001.

    Article  Google Scholar 

  44. McCaffrey DF, Griffin BA, Almirall D, et al. A tutorial on propensity score estimation for multiple treatments using generalized boosted models. Stat Med. 2013;32:3388–414. https://doi.org/10.1002/sim.5753.

    Article  MathSciNet  Google Scholar 

  45. Murray RP, Connett JE, Lauger GG, Voelker HT. Error in smoking measures: effects of intervention on relations of cotinine and carbon monoxide to self-reported smoking. The Lung Health Study Research Group. Am J Public Health. 1993;83:1251–7. https://doi.org/10.2105/AJPH.83.9.1251.

    Article  Google Scholar 

  46. Nab L, Groenwold RHH., Welsing PMJ, van Smeden M. Measurement error in continuous endpoints in randomised trials: problems and solutions. Stat Med. 2019;38:5182–96. https://doi.org/10.1002/sim.8359.

  47. Nab L, van Smeden M, de Mutsert R, et al. Sampling strategies for internal validation samples for exposure measurement error correction: a study of visceral adipose tissue measures replaced by waist circumference measures. Am J Epidemiol Kwab. 2021a;114. https://doi.org/10.1093/aje/kwab114

  48. Nab L, van Smeden M, Keogh RH, Groenwold RHH. mecor: An R package for measurement error correction in linear regression models with a continuous outcome. Comput Methods Programs Biomed. 2021b;208:

    Google Scholar 

  49. Nicholson B, Sheng VS, Zhang J. Label noise correction and application in crowdsourcing. Expert Syst Appl. 2016;66:149–62. https://doi.org/10.1016/j.eswa.2016.09.003.

    Article  Google Scholar 

  50. Nigam N, Dutta T, Gupta HP. Impact of noisy labels in learning techniques: a survey. In: Kolhe ML, Tiwari S, Trivedi MC, Mishra KK, editors. Advances in Data and Information Sciences. Singapore: Springer; 2020. p. 403–11.

    Chapter  Google Scholar 

  51. Nir G, Hor S, Karimi D, et al. Automatic grading of prostate cancer in digitized histopathology images: learning from multiple experts. Med Image Anal. 2018;50:167–80. https://doi.org/10.1016/j.media.2018.09.005.

    Article  Google Scholar 

  52. Nissen F, Morales DR, Mullerova H, et al. Validation of asthma recording in the clinical practice research datalink (CPRD). BMJ Open. 2017;7: e017474. https://doi.org/10.1136/bmjopen-2017-017474.

    Article  Google Scholar 

  53. Nitzan M, Slotki I, Shavit L. More accurate systolic blood pressure measurement is required for improved hypertension management: a perspective. Med Devices Auckl NZ. 2017;10:157–63. https://doi.org/10.2147/MDER.S141599.

    Article  Google Scholar 

  54. Pajouheshnia R, van Smeden M, Peelen LM, Groenwold RHH. How variation in predictor measurement affects the discriminative ability and transportability of a prediction model. J Clin Epidemiol. 2019;105:136–41. https://doi.org/10.1016/j.jclinepi.2018.09.001.

    Article  Google Scholar 

  55. Pot M, Kieusseyan N, Prainsack B. Not all biases are bad: equitable and inequitable biases in machine learning and radiology. Insights Imag. 2021;12:13. https://doi.org/10.1186/s13244-020-00955-7.

    Article  Google Scholar 

  56. Ratner A, Bach SH, Ehrenberg H, et al. Snorkel: rapid training data creation with weak supervision. Proc VLDB Endow Int Conf Very Large Data Bases 2017;11:269–282. https://doi.org/10.14778/3157794.3157797

  57. Ravì D, Wong C, Deligianni F, et al. Deep learning for health informatics. IEEE J Biomed Health Inform. 2017;21:4–21. https://doi.org/10.1109/JBHI.2016.2636665.

    Article  Google Scholar 

  58. Rosenbaum PR, Rubin DB. The central role of the propensity score in observational studies for causal effects. Biometrika. 1983;70:41–55.

    Article  MathSciNet  MATH  Google Scholar 

  59. Rosner B, Spiegelman D, Willett WC. Correction of logistic regression relative risk estimates and confidence intervals for measurement error: the case of multiple covariates measured with error. Am J Epidemiol. 1990;132:734–45. https://doi.org/10.1093/oxfordjournals.aje.a115715.

    Article  Google Scholar 

  60. Rosner B, Spiegelman D, Willett WC. Correction of logistic regression relative risk estimates and confidence intervals for random within-person measurement error. Am J Epidemiol. 1992;136:1400–13. https://doi.org/10.1093/oxfordjournals.aje.a116453.

    Article  Google Scholar 

  61. Rosseel, Y. lavaan: an R package for structural equation modeling. J Stat Softw. 2012;48:1–36. https://doi.org/10.18637/jss.v048.i02.

  62. Rothman KJ, Greenland S, Lash TL. Modern epidemiology. Wolters Kluwer Health/Lippincott Williams & Wilkins Philadelphia; 2008.

    Google Scholar 

  63. Sánchez BN, Budtz-Jørgensen E, Ryan LM, Hu H. Structural equation models. J Am Stat Assoc. 2005;100:1443–55. https://doi.org/10.1198/016214505000001005.

    Article  MATH  Google Scholar 

  64. Schnack, H. Bias, noise, and interpretability in machine learning. In: Machine Learning. Elsevier; 2020. p. 307–28

    Google Scholar 

  65. Schneeweiss S, Avorn J. A review of uses of health care utilization databases for epidemiologic research on therapeutics. J Clin Epidemiol. 2005;58:323–37. https://doi.org/10.1016/j.jclinepi.2004.10.012.

    Article  Google Scholar 

  66. Shanthini A, Vinodhini G, Chandrasekaran RM, Supraja P. A taxonomy on impact of label noise and feature noise using machine learning techniques. Soft Comput. 2019;23:8597–607. https://doi.org/10.1007/s00500-019-03968-7.

    Article  Google Scholar 

  67. Shaw PA, Deffner V, Keogh RH, et al. Epidemiologic analyses with error-prone exposures: review of current practice and recommendations. Ann Epidemiol. 2018;28:821–8. https://doi.org/10.1016/j.annepidem.2018.09.001.

    Article  Google Scholar 

  68. Shaw PA, Gustafson P, Carroll RJ, et al. STRATOS guidance document on measurement error and misclassification of variables in observational epidemiology: Part 2—More complex methods of adjustment and advanced topics. Stat Med. 2020;39:2232–63. https://doi.org/10.1002/sim.8531.

    Article  MathSciNet  Google Scholar 

  69. Sheppard L, Burnett RT, Szpiro AA, et al. Confounding and exposure measurement error in air pollution epidemiology. Air Qual Atmosphere Health. 2012;5:203–16. https://doi.org/10.1007/s11869-011-0140-9.

    Article  Google Scholar 

  70. Shmueli G. To Explain or to Predict? Stat Sci. 2010;25.https://doi.org/10.1214/10-STS330.

  71. Smedt TD, Merrall E, Macina D, et al. Bias due to differential and non-differential disease- and exposure misclassification in studies of vaccine effectiveness. PLoS ONE. 2018;13: e0199180. https://doi.org/10.1371/journal.pone.0199180.

    Article  Google Scholar 

  72. Stefanski LA. Unbiased estimation of a nonlinear function a normal mean with application to measurement err oorf models. Commun Stat - Theory Methods. 1989;18:4335–58. https://doi.org/10.1080/03610928908830159.

    Article  MATH  Google Scholar 

  73. Thiébaut ACM, Freedman LS, Carroll RJ, Kipnis V. Is It necessary to correct for measurement error in nutritional epidemiology? Ann Intern Med. 2007;146:65. https://doi.org/10.7326/0003-4819-146-1-200701020-00012.

    Article  Google Scholar 

  74. van Smeden M, Lash TL, Groenwold RHH. Reflection on modern methods: five myths about measurement error in epidemiological research. Int J Epidemiol. 2020;49:338–47. https://doi.org/10.1093/ije/dyz251.

    Article  Google Scholar 

  75. van der Wel MC, Buunk IE, van Weel C, et al. A novel approach to office blood pressure measurement: 30-minute office blood pressure vs daytime ambulatory blood pressure. Ann Fam Med. 2011;9:128–35. https://doi.org/10.1370/afm.1211.

    Article  Google Scholar 

  76. White JT, Fienen MN, Doherty JE. A python framework for environmental model uncertainty analysis. Environ Model Softw. 2016;85:217–28. https://doi.org/10.1016/j.envsoft.2016.08.017.

    Article  Google Scholar 

  77. Yu AYX, Quan H, McRae AD, et al. A cohort study on physician documentation and the accuracy of administrative data coding to improve passive surveillance of transient ischaemic attacks. BMJ Open. 2017;7: e015234. https://doi.org/10.1136/bmjopen-2016-015234.

    Article  Google Scholar 

  78. Zeger SL, Thomas D, Dominici F, et al. Exposure measurement error in time-series studies of air pollution: concepts and consequences. Environ Health Perspect. 2000;108:419–26. https://doi.org/10.1289/ehp.00108419.

    Article  Google Scholar 

  79. Zhu X, Wu X. Class noise vs. attribute noise: a quantitative study. Artif Intell Rev. 2004;22:177–210. https://doi.org/10.1007/s10462-004-0751-8.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Julius Clinical, Zeist, The Netherlands

    Timo B. Brakenhoff

  2. Julius Center for Health Sciences and Primary Care, UMC Utrecht, Utrecht University, Utrecht, The Netherlands

    Maarten van Smeden & Daniel L. Oberski

  3. Dept. Methodology & Statistics, Utrecht University, Utrecht, The Netherlands

    Daniel L. Oberski

Authors
  1. Timo B. Brakenhoff
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Maarten van Smeden
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Daniel L. Oberski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Timo B. Brakenhoff .

Editor information

Editors and Affiliations

  1. Amsterdam University Medical Center, University of Amsterdam, Amsterdam, The Netherlands

    Folkert W. Asselbergs

  2. Institute of Health Informatics, University College London, London, UK

    Spiros Denaxas

  3. Department of Data Science and Biostatistics, University Medical Center Utrecht (UMCU), Utrecht, The Netherlands

    Daniel L. Oberski

  4. Cedars-Sinai Medical Center, Los Angeles, CA, USA

    Jason H. Moore

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Brakenhoff, T.B., van Smeden, M., Oberski, D.L. (2023). Statistical Analysis—Measurement Error. In: Asselbergs, F.W., Denaxas, S., Oberski, D.L., Moore, J.H. (eds) Clinical Applications of Artificial Intelligence in Real-World Data. Springer, Cham. https://doi.org/10.1007/978-3-031-36678-9_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-36678-9_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-36677-2

  • Online ISBN: 978-3-031-36678-9

  • eBook Packages: MedicineMedicine (R0)

Publish with us

Policies and ethics

Search

Navigation