Review Articles

Interval estimation for minimal clinically important difference and its classification error via a bootstrap scheme

Zehua Zhou ,

a Department of Biostatistics, School of Public Health and Health Professions, State University of New York at Buffalo, Buffalo, NY, USA

Jiwei Zhao ,

a Department of Biostatistics, School of Public Health and Health Professions, State University of New York at Buffalo, Buffalo, NY, USA

Melissa Kluczynski

b Department of Orthopaedics, Jacobs School of Medicine and Biomedical Sciences, State University of New York at Buffalo, Buffalo, NY, USA

Pages | Received 23 Jul. 2021, Accepted 23 Jul. 2021, Published online: 23 Jul. 2021,
  • Abstract
  • Full Article
  • References
  • Citations


With the improved knowledge on clinical relevance and more convenient access to the patient-reported outcome data, clinical researchers prefer to adopt minimal clinically important difference (MCID) rather than statistical significance as a testing standard to examine the effectiveness of certain intervention or treatment in clinical trials. A practical method to determining the MCID is based on the diagnostic measurement. By using this approach, the MCID can be formulated as the solution of a large margin classification problem. However, this method only produces the point estimation, hence lacks ways to evaluate its performance. In this paper, we introduce an m-out-of-n bootstrap approach which provides the interval estimations for MCID and its classification error, an associated accuracy measure for performance assessment. A variety of extensive simulation studies are implemented to show the advantages of our proposed method. Analysis of the chondral lesions and meniscus procedures (ChAMP) trial is our motivating example and is used to illustrate our method.


  1. Bickel, P., Götze, F., & van Zwet, W. (1997). Resampling fewer than n observations: Gains, losses, and remedies for losses. Statistica Sinica7, 1–31. [Web of Science ®], [Google Scholar]
  2. Bisson, L. J., Kluczynski, M. A., Wind, W. M., Fineberg, M. S., Bernas, G. A., Rauh, M. A., … Zhao, J. (2017). Patient outcomes after observation versus debridement of unstable chondral lesions during partial meniscectomy. The Journal of Bone and Joint Surgery99, 1078–1085. doi: 10.2106/JBJS.16.00855 [Crossref][Web of Science ®], [Google Scholar]
  3. Bisson, L. J., Kluczynski, M. A., Wind, W. M., Fineberg, M. S., Bernas, G. A., Rauh, M. A., … Zhao, J. (2018). How does the presence of unstable chondral lesions affect patient outcomes after partial meniscectomy? The ChAMP randomized controlled trial. The American Journal of Sports Medicine46, 590–597. doi: 10.1177/0363546517744212 [Crossref][Web of Science ®], [Google Scholar]
  4. Bisson, L., Phillips, P., Matthews, J., Zhou, Z., Zhao, J., Wind, W., Fineberg, M., Bernas, G., Rauh, M., Marzo, J. and Kluczynski, M. (2019). Association Between Bone Marrow Lesions, Chondral Lesions, and Pain in Patients Without Radiographic Evidence of Degenerative Joint Disease Who Underwent Arthroscopic Partial Meniscectomy. Orthopaedic Journal of Sports Medicine, 7(3), 2325967119830381. doi: 10.1177/2325967119830381 [Crossref][Web of Science ®], [Google Scholar]
  5. Cook, C. E. (2008). Clinimetrics corner: The minimal clinically important change score (MCID): A necessary pretense. Journal of Manual & Manipulative Therapy16, 82E–83E. doi: 10.1179/jmt.2008.16.4.82E [Taylor & Francis Online], [Google Scholar]
  6. Efron, B. (1979). Bootstrap methods: Another look at the jackknife. The Annals of Statistics7, 1–26. doi: 10.1214/aos/1176344552 [Crossref][Web of Science ®], [Google Scholar]
  7. Erdogan, B. D., Leung, Y. Y., Pohl, C., Tennant, A., & Conaghan, P. G. (2016). Minimal clinically important difference as applied in rheumatology: An OMERACT Rasch Working Group systematic review and critique. The Journal of Rheumatology43, 194–202. doi: 10.3899/jrheum.141150 [Crossref][Web of Science ®], [Google Scholar]
  8. Hedayat, A., Wang, J., & Xu, T. (2015). Minimum clinically important difference in medical studies. Biometrics71, 33–41. doi: 10.1111/biom.12251 [Crossref][Web of Science ®], [Google Scholar]
  9. Jaeschke, R., Singer, J., & Guyatt, G. H. (1989). Measurement of health status: Ascertaining the minimal clinically important difference. Controlled Clinical Trials10, 407–415. doi: 10.1016/0197-2456(89)90005-6 [Crossref], [Google Scholar]
  10. Kimeldorf, G., & Wahba, G. (1971). Some results on Tchebycheffian spline functions. Journal of Mathematical Analysis and Applications33, 82–95. doi: 10.1016/0022-247X(71)90184-3 [Crossref][Web of Science ®], [Google Scholar]
  11. Kluczynski, M. A., Marzo, J. M., Wind, W. M., Fineberg, M. S., Bernas, G. A., M. A. Rauh, … Bisson, L. J. (2017). The effect of body mass index on clinical outcomes in patients without radiographic evidence of degenerative joint disease after arthroscopic partial meniscectomy. Arthroscopy: The Journal of Arthroscopic & Related Surgery33, 2054–2063. [Web of Science ®], [Google Scholar]
  12. Laber, E. B., & Murphy, S. A. (2011). Adaptive confidence intervals for the test error in classification. Journal of the American Statistical Association106, 904–913. doi: 10.1198/jasa.2010.tm10053 [Taylor & Francis Online][Web of Science ®], [Google Scholar]
  13. McGlothlin, A. E., & Lewis, R. J. (2014). Minimal clinically important difference: Defining what really matters to patients. JAMA312, 1342–1343. doi: 10.1001/jama.2014.13128 [Crossref][Web of Science ®], [Google Scholar]
  14. Shao, J. (1994). Bootstrap sample size in nonregular cases. Proceedings of the American Mathematical Society122, 1251–1262. doi: 10.1090/S0002-9939-1994-1227529-8 [Crossref][Web of Science ®], [Google Scholar]
  15. Shao, J. (1996). Bootstrap model selection. Journal of the American Statistical Association91, 655–665. doi: 10.1080/01621459.1996.10476934 [Taylor & Francis Online][Web of Science ®], [Google Scholar]
  16. Thi Hoai An, L., & Dinh Tao, P. (1997). Solving a class of linearly constrained indefinite quadratic problems by DC algorithms. Journal of Global Optimization11, 253–285. doi: 10.1023/A:1008288411710 [Crossref][Web of Science ®], [Google Scholar]
  17. Ware, J. E., Jr, & Sherbourne, C. D. (1992). The MOS 36-item short-form health survey (SF-36): I. Conceptual framework and item selection. Medical Care30, 473–483. doi: 10.1097/00005650-199206000-00002 [Crossref][Web of Science ®], [Google Scholar]
  18. Wright, A., Hannon, J., Hegedus, E. J., & Kavchak, A. E. (2012). Clinimetrics corner: A closer look at the minimal clinically important difference (MCID). Journal of Manual & Manipulative Therapy20, 160–166. doi: 10.1179/2042618612Y.0000000001 [Taylor & Francis Online], [Google Scholar]
  19. Xu, Y., Yu, M., Zhao, Y.-Q., Li, Q., Wang, S., & Shao, J. (2015). Regularized outcome weighted subgroup identification for differential treatment effects. Biometrics71, 645–653. doi: 10.1111/biom.12322 [Crossref][Web of Science ®], [Google Scholar]

Articles from other publishers

Zehua Zhou, Jiwei Zhao, Leslie J. Bisson. (2020) Estimation of data adaptive minimal clinically important difference with a nonconvex optimization procedure. Statistical Methods in Medical Research 29:3, pages 879-893.