The handling of missing data in trial-based economic evaluations: should data be multiply imputed prior to longitudinal linear mixed-model analyses?

Ângela Jornada Ben, Johanna M van Dongen, Mohamed El Alili, Martijn W Heymans, Jos W R Twisk, Janet L MacNeil-Vroomen, Maartje de Wit, Susan E M van Dijk, Teddy Oosterhuis, Judith E Bosmans
Author Information
  1. Ângela Jornada Ben: Department of Health Sciences, Faculty of Science, Vrije Universiteit Amsterdam, Amsterdam Public Health Research Institute, Van der Boechorststraat 7, 1081 BT, Amsterdam, The Netherlands. a.jornadaben@vu.nl. ORCID
  2. Johanna M van Dongen: Department of Health Sciences, Faculty of Science, Vrije Universiteit Amsterdam, Amsterdam Public Health Research Institute, Van der Boechorststraat 7, 1081 BT, Amsterdam, The Netherlands.
  3. Mohamed El Alili: Department of Health Sciences, Faculty of Science, Vrije Universiteit Amsterdam, Amsterdam Public Health Research Institute, Van der Boechorststraat 7, 1081 BT, Amsterdam, The Netherlands.
  4. Martijn W Heymans: Department of Epidemiology and Data Science, Amsterdam UMC, Amsterdam Public Health Research Institute, Amsterdam, The Netherlands.
  5. Jos W R Twisk: Department of Epidemiology and Data Science, Amsterdam UMC, Amsterdam Public Health Research Institute, Amsterdam, The Netherlands.
  6. Janet L MacNeil-Vroomen: Section of Geriatrics, Department of Internal Medicine, Amsterdam Public Health Research Institute, Amsterdam UMC, University of Amsterdam, Amsterdam, The Netherlands.
  7. Maartje de Wit: Department of Medical Psychology, Amsterdam UMC, Vrije Universiteit, Amsterdam Public Health Research Institute, Amsterdam, The Netherlands.
  8. Susan E M van Dijk: Department of Health Sciences, Faculty of Science, Vrije Universiteit Amsterdam, Amsterdam Public Health Research Institute, Van der Boechorststraat 7, 1081 BT, Amsterdam, The Netherlands.
  9. Teddy Oosterhuis: Netherlands Society of Occupational Medicine (NVAB), Utrecht, The Netherlands.
  10. Judith E Bosmans: Department of Health Sciences, Faculty of Science, Vrije Universiteit Amsterdam, Amsterdam Public Health Research Institute, Van der Boechorststraat 7, 1081 BT, Amsterdam, The Netherlands.

Abstract

INTRODUCTION: For the analysis of clinical effects, multiple imputation (MI) of missing data were shown to be unnecessary when using longitudinal linear mixed-models (LLM). It remains unclear whether this also applies to trial-based economic evaluations. Therefore, this study aimed to assess whether MI is required prior to LLM when analyzing longitudinal cost and effect data.
METHODS: Two-thousand complete datasets were simulated containing five time points. Incomplete datasets were generated with 10, 25, and 50% missing data in follow-up costs and effects, assuming a Missing At Random (MAR) mechanism. Six different strategies were compared using empirical bias (EB), root-mean-squared error (RMSE), and coverage rate (CR). These strategies were: LLM alone (LLM) and MI with LLM (MI-LLM), and, as reference strategies, mean imputation with LLM (M-LLM), seemingly unrelated regression alone (SUR-CCA), MI with SUR (MI-SUR), and mean imputation with SUR (M-SUR).
RESULTS: For costs and effects, LLM, MI-LLM, and MI-SUR performed better than M-LLM, SUR-CCA, and M-SUR, with smaller EBs and RMSEs as well as CRs closers to nominal levels. However, even though LLM, MI-LLM and MI-SUR performed equally well for effects, MI-LLM and MI-SUR were found to perform better than LLM for costs at 10 and 25% missing data. At 50% missing data, all strategies resulted in relatively high EBs and RMSEs for costs.
CONCLUSION: LLM should be combined with MI when analyzing trial-based economic evaluation data. MI-SUR is more efficient and can also be used, but then an average intervention effect over time cannot be estimated.

Keywords

References

  1. J Clin Epidemiol. 2013 Sep;66(9):1022-8 [PMID: 23790725]
  2. J Physiother. 2017 Jul;63(3):144-153 [PMID: 28668558]
  3. Qual Life Res. 2005 Aug;14(6):1523-32 [PMID: 16110932]
  4. Stat Med. 2019 Jan 30;38(2):210-220 [PMID: 30207407]
  5. Br Med Bull. 2010;96:5-21 [PMID: 21037243]
  6. Value Health. 2021 May;24(5):699-706 [PMID: 33933239]
  7. Qual Life Res. 2015 Apr;24(4):805-15 [PMID: 25471286]
  8. Health Econ. 2022 Jun;31(6):1276-1287 [PMID: 35368119]
  9. Stat Med. 2018 Jun 30;37(14):2252-2266 [PMID: 29682776]
  10. Health Econ. 2004 May;13(5):405-15 [PMID: 15127421]
  11. J R Stat Soc Ser A Stat Soc. 2020 Feb;183(2):607-629 [PMID: 34385761]
  12. BMC Med Res Methodol. 2018 Dec 12;18(1):168 [PMID: 30541455]
  13. Stat Methods Med Res. 1999 Mar;8(1):3-15 [PMID: 10347857]
  14. Med Decis Making. 2007 Jul-Aug;27(4):471-90 [PMID: 17641141]
  15. BMC Health Serv Res. 2021 May 19;21(1):475 [PMID: 34011337]
  16. J R Stat Soc Ser A Stat Soc. 2009 Jan;172(1):3-20 [PMID: 20585409]
  17. J Health Serv Res Policy. 2005 Apr;10(2):97-102 [PMID: 15831192]
  18. Health Econ. 2021 Dec;30(12):3138-3158 [PMID: 34562295]
  19. Stat Med. 2011 Feb 20;30(4):377-99 [PMID: 21225900]
  20. Med Decis Making. 2012 Jan-Feb;32(1):209-20 [PMID: 21610256]
  21. PLoS One. 2017 Aug 1;12(8):e0181023 [PMID: 28763451]
  22. Diabet Med. 2018 Feb;35(2):214-222 [PMID: 29150861]
  23. Psychol Methods. 2001 Dec;6(4):330-51 [PMID: 11778676]
  24. Expert Rev Pharmacoecon Outcomes Res. 2014 Apr;14(2):221-33 [PMID: 24625040]
  25. Comput Stat Data Anal. 2010 Mar 1;54(3):790-801 [PMID: 20526424]
  26. Pharmacoeconomics. 2014 Dec;32(12):1157-70 [PMID: 25069632]
  27. BMJ. 2009 Jun 29;338:b2393 [PMID: 19564179]
  28. Health Econ. 2000 Oct;9(7):623-30 [PMID: 11103928]
  29. Eur Spine J. 2012 Jul;21(7):1290-300 [PMID: 22258622]
  30. Int J Technol Assess Health Care. 2007 Fall;23(4):480-7 [PMID: 17937837]
  31. Stat Methods Med Res. 2018 Sep;27(9):2610-2626 [PMID: 28034175]
  32. Pharmacoecon Open. 2017 Jun;1(2):79-97 [PMID: 29442336]
  33. Ann Transl Med. 2016 Jan;4(1):9 [PMID: 26855945]
  34. Clin Trials. 2014 Oct;11(5):590-600 [PMID: 24902924]
  35. BMC Med Res Methodol. 2014 Jun 05;14:75 [PMID: 24903709]
  36. Springerplus. 2013 May 14;2(1):222 [PMID: 23853744]
  37. Health Econ. 2004 May;13(5):461-75 [PMID: 15127426]
  38. Health Econ. 2012 Feb;21(2):187-200 [PMID: 22223561]
  39. Health Econ. 2010 Mar;19(3):316-33 [PMID: 19378353]
  40. Stat Med. 2019 May 20;38(11):2074-2102 [PMID: 30652356]
  41. J Clin Epidemiol. 2012 Jun;65(6):686-95 [PMID: 22459429]
  42. Pharmacoeconomics. 2020 Nov;38(11):1247-1261 [PMID: 32729091]
  43. BMJ. 2011 Apr 07;342:d1548 [PMID: 21474510]
  44. BMC Med Res Methodol. 2019 Jul 3;19(1):136 [PMID: 31269898]

Grants

  1. 2019075/MdB/EdB/Amsterdam Public Health Research Institute
  2. 2019/Amsterdam Public Health Research Institute

MeSH Term

Humans
Cost-Benefit Analysis
Linear Models
Computer Simulation

Word Cloud

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