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An improved method for analysis of interrupted time series (ITS) data: accounting for patient heterogeneity using weighted analysis

  • Joycelyne Ewusie ORCID logo , Joseph Beyene , Lehana Thabane , Sharon E. Straus and Jemila S. Hamid EMAIL logo
Published/Copyright: September 2, 2021
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The International Journal of Biostatistics
From the journal The International Journal of Biostatistics Volume 18 Issue 2

Abstract

Interrupted time series (ITS) design is commonly used to evaluate the impact of interventions in healthcare settings. Segmented regression (SR) is the most commonly used statistical method and has been shown to be useful in practical applications involving ITS designs. Nevertheless, SR is prone to aggregation bias, which leads to imprecision and loss of power to detect clinically meaningful differences. The objective of this article is to present a weighted SR method, where variability across patients within the healthcare facility and across time points is incorporated through weights. We present the methodological framework, provide optimal weights associated with data at each time point and discuss relevant statistical inference. We conduct extensive simulations to evaluate performance of our method and provide comparative analysis with the traditional SR using established performance criteria such as bias, mean square error and statistical power. Illustrations using real data is also provided. In most simulation scenarios considered, the weighted SR method produced estimators that are uniformly more precise and relatively less biased compared to the traditional SR. The weighted approach also associated with higher statistical power in the scenarios considered. The performance difference is much larger for data with high variability across patients within healthcare facilities. The weighted method proposed here allows us to account for the heterogeneity in the patient population, leading to increased accuracy and power across all scenarios. We recommend researchers to carefully design their studies and determine their sample size by incorporating heterogeneity in the patient population.

Keywords: heteroskedasticity; interrupted time series; method comparison; simulation study; weighted segmented regression
Corresponding author: Jemila S. Hamid, Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada; Children’s Hospital of Eastern Ontario, Ottawa, ON, Canada, E-mail:

  1. Author contribution: JEE conceived and designed the study, analyzed and interpreted the data, and drafted the manuscript. JSH conceived and designed the study and drafted the manuscript. JB, LT and SS helped with critical revision of the manuscript for important intellectual content. All authors read and approved the final manuscript.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

Appendix
Table A.1:

Bias for segmented regression and for weighted segmented regression with small, moderate and large variance heterogeneity.

Change in Level, with order of magnitude 10−3
Sample size* Small variance Moderate variance Large variance
SR wSR SR wSR SR wSR
10 0.71 1.37 1.39 1.89 0.34 3.61
30 −0.19 −0.11 −0.38 −0.08 −1.88 −0.14
50 −0.38 −0.24 −0.68 −0.27 −0.74 −0.53
70 −0.56 −0.46 −0.99 −0.67 −2.09 −0.79
100 −0.05 −0.04 −0.10 −0.04 −0.66 −0.19
Change in Trend, with order of magnitude 10−3
10 −0.01 0.06 −0.02 0.10 0.12 0.28
30 −0.01 −0.01 −0.02 −0.01 −0.02 −0.05
50 −0.02 −0.01 −0.03 −0.001 −0.06 0.04
70 −0.01 −0.01 0.02 0.01 0.06 0.01
100 −0.01 −0.01 0.01 0.01 0.02 0.02

  1. *sample size refers to the expected sample size per timepoint

  2. SR: Segmented regression, wSR: Weighted Segmented Regression

Table A.2:

Mean squared error for segmented regression and for weighted segmented regression with small, moderate and large variance heterogeneity.

Change in Level, with order of magnitude 10−2
Sample size* Small variance Moderate variance Large variance
SR wSR SR wSR SR wSR
10 15.12 18.93 66.69 50.08 155.93 89.58
30 4.77 3.75 20.86 10.05 48.63 18.04
50 2.69 2.06 11.81 5.54 27.58 9.95
70 2.00 1.49 8.74 3.91 20.38 6.94
100 1.37 1.01 6.02 2.69 14.07 4.81
Change in Trend, with order of magnitude 10−3
10 0.75 0.92 3.29 2.46 7.68 4.43
30 0.22 0.18 0.99 0.47 2.30 0.83
50 0.14 0.10 0.61 0.28 1.43 0.51
70 0.09 0.07 0.41 0.19 0.95 0.34
100 0.07 0.05 0.29 0.13 0.67 0.24

  1. *sample size refers to the expected sample size per timepoint

  2. SR: Segmented regression, wSR: Weighted Segmented Regression

References

1. Albu, JB, Sohler, N, Li, R, Li, X, Young, E, Gregg, EW, et al.. An interrupted time series analysis to determine the effect of an electronic health record-based intervention on appropriate screening for type 2 diabetes in urban primary care clinics in New York city. Diabetes Care 2017;40:1058–64. https://doi.org/10.2337/dc16-2133.Search in Google Scholar PubMed PubMed Central

2. Aregawi, M, Malm, KL, Wahjib, M, Kofi, O, Allotey, N-K, Yaw, PN, et al.. Effect of anti-malarial interventions on trends of malaria cases, hospital admissions and deaths, 2005–2015, Ghana. Malar J 2017;16:177. https://doi.org/10.1186/s12936-017-1828-6.Search in Google Scholar PubMed PubMed Central

3. Berrevoets, MAH, Pot, JHLW, Houterman, AE, Dofferhoff, ATSM, Nabuurs-Franssen, MH, Fleuren, HWHA, et al.. An electronic trigger tool to optimise intravenous to oral antibiotic switch: a controlled, interrupted time series study. Antimicrob Resist Infect Contr 2017;6:81. https://doi.org/10.1186/s13756-017-0239-3.Search in Google Scholar PubMed PubMed Central

4. Bond, SE, Adhikari, S, Miyakis, S, Boutlis, CS, Yeo, WW, Batterham, MJ, et al.. Outcomes of multisite antimicrobial stewardship programme implementation with a shared clinical decision support system. J Antimicrob Chemother 2017;14:14. https://doi.org/10.1007/s40274-017-3991-y.Search in Google Scholar

5. Gutacker, N, Bloor, K, Cookson, R, Gale, CP, Maynard, A, Pagano, D, et al.. Hospital surgical volumes and mortality after coronary artery bypass grafting: using international comparisons to determine a safe threshold. Health Serv Res 2017;52:863–78. https://doi.org/10.1111/1475-6773.12508.Search in Google Scholar PubMed PubMed Central

6. Marti, IR, Allepuz, A, Palomar, GR, Font, FO, Cera, MS. Impact of an intervention on the prescription of aliskiren after new evidence on safety reported. Pharmacoepidemiol Drug Saf 2017;26:91–6. https://doi.org/10.1002/pds.4136.Search in Google Scholar PubMed

7. Taylor, JE, McDonald, SJ, Earnest, A, Buttery, J, Fusinato, B, Hovenden, S, et al.. A quality improvement initiative to reduce central line infection in neonates using checklists. Eur J Pediatr 2017;176:639–46. https://doi.org/10.1007/s00431-017-2888-x.Search in Google Scholar PubMed

8. Balkhi, B, Seoane-Vazquez, E, Rodriguez-Monguio, R. Osteoporosis drugs marketed in the United States: generic competition, pricing structure, and dispersion among payers. Int J Technol Assess Health Care 2016;32:385–92. https://doi.org/10.1017/s0266462316000623.Search in Google Scholar

9. Bobo, WV, Epstein, RA, Hayes, RM, Shelton, RC, Hartert, TV, Mitchel, E, et al.. The effect of regulatory advisories on maternal antidepressant prescribing, 1995–2007: an interrupted time series study of 228,876 pregnancies. Arch Womens Ment Health 2014 Feb;17:17–26.10.1007/s00737-013-0383-6Search in Google Scholar PubMed PubMed Central

10. Pow, JL, Baumeister, AA, Hawkins, MF, Cohen, AS, Garand, JC. Deinstitutionalization of American public hospitals for the mentally ill before and after the introduction of antipsychotic medications. Harv Rev Psychiatry 2015;23:176–87.10.1097/HRP.0000000000000046Search in Google Scholar PubMed

11. Yang, C, Shen, Q, Cai, W, Zhu, W, Li, Z, Wu, L, et al.. Impact of the zero-markup drug policy on hospitalisation expenditure in western rural China: an interrupted time series analysis. Trop Med Int Health 2017;22:180–6. https://doi.org/10.1111/tmi.12817.Search in Google Scholar PubMed

12. Shadish, WR, Cook, TD, Campbell, DT. Experimental and quasi-experimental designs for generalized causal inference. Wadsworth Cengage learning; 2002.Search in Google Scholar

13. Ramsay, CR, Matowe, L, Grilli, R, Grimshaw, JM, Thomas, RE. Interrupted time series designs in health technology assessment: lessons from two systematic reviews of behavior change strategies. Int J Technol Assess Health Care 2003;19:613–23. https://doi.org/10.1017/s0266462303000576.Search in Google Scholar PubMed

14. Langford, BJ, Seah, J, Chan, A, Downing, M, Johnstone, J, Matukas, LM. Antimicrobial stewardship in the microbiology lab: impact of selective susceptibility reporting on ciprofloxacin utilization and gram-negative susceptibility in a hospital setting. J Clin Microbiol 2016;54:2343–7.10.1128/JCM.00950-16Search in Google Scholar PubMed PubMed Central

15. Ewusie, JE, Soobiah, C, Blondal, E, Beyene, J, Thabane, L, Hamid, JS. Methods, applications and challenges in the analysis of interrupted time series data: A scoping review. J Multidiscip Healthc 2020;13:411.10.2147/JMDH.S241085Search in Google Scholar PubMed PubMed Central

16. Ansari, F, Gray, K, Nathwani, D, Phillips, G, Ogston, S, Ramsay, C, et al.. Outcomes of an intervention to improve hospital antibiotic prescribing: interrupted time series with segmented regression analysis. J Antimicrob Chemother 2003;52:842–8. https://doi.org/10.1093/jac/dkg459.Search in Google Scholar PubMed

17. Gebski, V, Ellingson, K, Edwards, J, Jernigan, J, Kleinbaum, D. Modelling interrupted time series to evaluate prevention and control of infection in healthcare. Epidemiol Infect 2012;140:2131–41. https://doi.org/10.1017/s0950268812000179.Search in Google Scholar PubMed PubMed Central

18. Kastner, M, Sawka, AM, Hamid, J, Chen, M, Thorpe, K, Chignell, M, et al.. A knowledge translation tool improved osteoporosis disease management in primary care: an interrupted time series analysis. Implement Sci 2014;9:109. https://doi.org/10.1186/s13012-014-0109-9.Search in Google Scholar PubMed PubMed Central

19. Michielutte, R, Shelton, B, Paskett, ED, Tatum, CM, Velez, R. Use of an interrupted time-series design to evaluate a cancer screening program. Health Educ Res 2000;15:615–23. https://doi.org/10.1093/her/15.5.615.Search in Google Scholar PubMed

20. Taljaard, M, McKenzie, JE, Ramsay, CR, Grimshaw, JM. The use of segmented regression in analysing interrupted time series studies: an example in pre-hospital ambulance care. Implement Sci 2014;9:77. https://doi.org/10.1186/1748-5908-9-77.Search in Google Scholar PubMed PubMed Central

21. Liu, B, Moore, JE, Almaawiy, U, Chan, W-H, Khan, S, Ewusie, J, et al.. Outcomes of Mobilisation of Vulnerable Elders in Ontario (MOVE ON): a multisite interrupted time series evaluation of an implementation intervention to increase patient mobilisation. Age Ageing 2017;47:112–9. https://doi.org/10.1093/ageing/afx128.Search in Google Scholar PubMed PubMed Central

22. Hanson, CC, Randolph, GD, Erickson, JA, Mayer, CM, Bruckel, JT, Harris, BD, et al.. A reduction in cardiac arrests and duration of clinical instability after implementation of a paediatric rapid response system. BMJ Qual Saf 2009;18:500–4.10.1136/qshc.2007.026054Search in Google Scholar PubMed

23. Jandoc, R, Burden, AM, Mamdani, M, Lévesque, LE, Cadarette, SM. Interrupted time series analysis in drug utilization research is increasing: systematic review and recommendations. J Clin Epidemiol 2015;68:950–6. https://doi.org/10.1016/j.jclinepi.2014.12.018.Search in Google Scholar PubMed

24. Carter, R, Quesnel-Vallée, A, Plante, C, Gamache, P, Lévesque, J-F. Effect of family medicine groups on visits to the emergency department among diabetic patients in Quebec between 2000 and 2011: a population-based segmented regression analysis. BMC Fam Pract 2016;17:23. https://doi.org/10.1186/s12875-016-0422-2.Search in Google Scholar PubMed PubMed Central

25. Dayer, MJ, Jones, S, Prendergast, B, Baddour, LM, Lockhart, PB, Thornhill, MH. Incidence of infective endocarditis in England, 2000-13: a secular trend, interrupted time-series analysis. Lancet 2015;385:1219–28. https://doi.org/10.1016/s0140-6736(14)62007-9.Search in Google Scholar

26. Graves, AJ, Kozhimannil, KB, Kleinman, KP, Wharam, JF. The association between high-deductible health plan transition and contraception and birth rates. Health Serv Res 2016;51:187–204. https://doi.org/10.1111/1475-6773.12326.Search in Google Scholar PubMed PubMed Central

27. Walley, AY, Ziming, X, Holly, HH, Emily, Q, Maya, D-S, Amy, S-A, et al.. Opioid overdose rates and implementation of overdose education and nasal naloxone distribution in Massachusetts: interrupted time series analysis. Br Med J 2013;346:f174. https://doi.org/10.1136/bmj.f174.Search in Google Scholar PubMed PubMed Central

28. Bussieres, AE, Sales, AE, Ramsay, T, Hilles, SM, Grimshaw, JM. Impact of imaging guidelines on X-ray use among American provider network chiropractors: interrupted time series analysis. Spine J 2014;14:1501–9. https://doi.org/10.1016/j.spinee.2013.08.051.Search in Google Scholar PubMed

29. Buyle, F, Vogelaers, D, Peleman, R, Maele, GV, Robays, H. Implementation of guidelines for sequential therapy with fluoroquinolones in a Belgian hospital. Pharm World Sci 2010;32:404–10. https://doi.org/10.1007/s11096-010-9384-y.Search in Google Scholar PubMed

30. Judge, A, Wallace, G, Prieto-Alhambra, D, Arden, NK, Edwards, CJ. Can the publication of guidelines change the management of early rheumatoid arthritis? An interrupted time series analysis from the United Kingdom. Rheumatology 2015;54:2244–8. https://doi.org/10.1093/rheumatology/kev268.Search in Google Scholar PubMed

31. Jiang, M, Hughes, DR, Duszak, R. Screening mammography rates in the Medicare population before and after the 2009 US Preventive Services Task Force guideline change: an interrupted time series analysis. Wom Health Issues 2015;25:239–45. https://doi.org/10.1016/j.whi.2015.03.002.Search in Google Scholar PubMed

32. Mackie, AS, Liu, W, Savu, A, Marelli, AJ, Kaul, P. Infective endocarditis hospitalizations before and after the 2007 American Heart Association prophylaxis guidelines. Can J Cardiol 2016;32:942–8. https://doi.org/10.1016/j.cjca.2015.09.021.Search in Google Scholar PubMed

33. Harrington, M, Velicer, WF. Comparing visual and statistical analysis in single-case studies using published studies. Multivariate Behav Res 2015;50:162–83. https://doi.org/10.1080/00273171.2014.973989.Search in Google Scholar PubMed PubMed Central

34. Gillings, D, Makuc, D, Siegel, E. Analysis of interrupted time series mortality trends: an example to evaluate regionalized perinatal care. Am J Publ Health 1981;71:38–46. https://doi.org/10.2105/ajph.71.1.38.Search in Google Scholar PubMed PubMed Central

35. Shardell, M, Harris, AD, El-Kamary, SS, Furuno, JP, Miller, RP, Perencevich, EN. Statistical analysis and application of quasi experiments to antimicrobial resistance intervention studies. Clin Infect Dis 2007;45:901–7. https://doi.org/10.1086/521255.Search in Google Scholar PubMed

36. Sen, A, Srivastava, M. Regression analysis: theory, methods, and applications. Springer Science, Business Media; 2012.Search in Google Scholar

37. Draper, NR, Smith, H. Applied regression analysis. John Wiley & Sons; 2014, vol 326.Search in Google Scholar

38. Gilstein, CZ, Leamer, EE. The set of weighted regression estimates. J Am Stat Assoc 1983;78:942–8. https://doi.org/10.1080/01621459.1983.10477044.Search in Google Scholar

39. Tsai, C-L, Wu, X. Diagnostics in transformation and weighted regression. Technometrics 1990;32:315–22. https://doi.org/10.1080/00401706.1990.10484684.Search in Google Scholar

40. R Core Team. R: a language and environment for statistical computing; 2018. Available from: https://www.R-project.org/.Search in Google Scholar

41. Liu, B, Almaawiy, U, Moore, JE, Chan, W-H, Straus, SE, MOVE ON Team. Evaluation of a multisite educational intervention to improve mobilization of older patients in hospital: protocol for mobilization of vulnerable elders in Ontario (MOVE ON). Implement Sci 2013;8:76. https://doi.org/10.1186/1748-5908-8-76.Search in Google Scholar PubMed PubMed Central

Received: 2020-04-07
Revised: 2021-05-12
Accepted: 2021-08-05
Published Online: 2021-09-02

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/ijb-2020-0046
Keywords for this article
heteroskedasticity; interrupted time series; method comparison; simulation study; weighted segmented regression

Articles in the same Issue

  1. Frontmatter
  2. Research Articles
  3. Doubly robust adaptive LASSO for effect modifier discovery
  4. Increasing the efficiency of randomized trial estimates via linear adjustment for a prognostic score
  5. Review
  6. Review and comparison of treatment effect estimators using propensity and prognostic scores
  7. Research Articles
  8. Error rate control for classification rules in multiclass mixture models
  9. Regression trees and ensembles for cumulative incidence functions
  10. Causal inference under over-simplified longitudinal causal models
  11. Causal inference under interference with prognostic scores for dynamic group therapy studies
  12. Bayesian multi-response nonlinear mixed-effect model: application of two recent HIV infection biomarkers
  13. A Bayesian semiparametric accelerate failure time mixture cure model
  14. Quantifying the extent of visit irregularity in longitudinal data
  15. An improved method for analysis of interrupted time series (ITS) data: accounting for patient heterogeneity using weighted analysis
  16. A robust hazard ratio for general modeling of survival-times
  17. Penalized likelihood estimation of the proportional hazards model for survival data with interval censoring
  18. A parametric approach to relaxing the independence assumption in relative survival analysis
  19. The number of response categories in ordered response models
  20. A comparison of joint dichotomization and single dichotomization of interacting variables to discriminate a disease outcome
  21. Spike detection for calcium activity
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