Skip to main content

Inverse optimization on hierarchical networks: an application to breast cancer clinical pathways

Health Care Management Science (2022)Cite this article

Abstract

Clinical pathways are standardized processes that outline the steps required for managing a specific disease. However, patient pathways often deviate from clinical pathways. Measuring the concordance of patient pathways to clinical pathways is important for health system monitoring and informing quality improvement initiatives. In this paper, we develop an inverse optimization-based approach to measuring pathway concordance in breast cancer, a complex disease. We capture this complexity in a hierarchical network that models the patient’s journey through the health system. A novel inverse shortest path model is formulated and solved on this hierarchical network to estimate arc costs, which are used to form a concordance metric to measure the distance between patient pathways and shortest paths (i.e., clinical pathways). Using real breast cancer patient data from Ontario, Canada, we demonstrate that our concordance metric has a statistically significant association with survival for all breast cancer patient subgroups. We also use it to quantify the extent of patient pathway discordances across all subgroups, finding that patients undertaking additional clinical activities constitute the primary driver of discordance in the population.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

References

  1. Ahuja RK, Orlin JB (2001) Inverse optimization. Oper Res 49(5):771–783

    Article  Google Scholar 

  2. Ahuja RK, Orlin JB (2002) Combinatorial algorithms for inverse network flow problems. Networks: Int J 40(4):181–187

    Article  Google Scholar 

  3. American Cancer Society (2021) How common is breast cancer? https://www.cancer.org/cancer/breast-cancer/about/how-common-is-breast-cancer.html. Accessed: May 2022

  4. Aswani A, Shen ZJ, Siddiq A (2018) Inverse optimization with noisy data. Oper Res 66 (3):870–892

    Article  Google Scholar 

  5. Babier A, Chan TC, Lee T, Mahmood R, Terekhov D (2021) An ensemble learning framework for model fitting and evaluation in inverse linear optimization. Informs J Optim 3(2):119–138

    Article  Google Scholar 

  6. Bergin RJ, Thomas RJ, Whitfield K, White V (2020) Concordance between optimal care pathways and colorectal cancer care: identifying opportunities to improve quality and reduce disparities. J Eval Clin Pract 26(3):918–926

    Article  Google Scholar 

  7. Bertsimas D, Gupta V, Paschalidis IC (2015) Data-driven estimation in equilibrium using inverse optimization. Math Program 153(2):595–633

    Article  Google Scholar 

  8. Burton D, Toint PL (1992) On an instance of the inverse shortest paths problem. Math Program 53(1–3):45–61

    Article  Google Scholar 

  9. Burton D, Pulleyblank W, Toint PL (1997) The inverse shortest paths problem with upper bounds on shortest paths costs. In: Network optimization. Springer, pp 156–171

  10. Campbell H, Hotchkiss R, Bradshaw N, Porteous M (1998) Integrated care pathways. Bmj 316(7125):133–137

    Article  Google Scholar 

  11. Canadian Cancer Society (2021) Breast cancer in men. https://www.cancer.ca/en/cancer-information/cancer-type/breast/breast-cancer/breast-cancer-in-men/?region=on. Accessed: May 2022

  12. Cancer Care Ontario (2021) About cancer care ontario. https://www.cancercareontario.ca/en/cancer-care-ontario/about-us, Accessed: May 2022

  13. Cancer Care Ontario (2021) Breast cancer pathway map. https://www.cancercareontario.ca/en/pathway-maps/breast-cancer, Accessed: May 2022

  14. Cancer Care Ontario (2021) Ontario breast screening program (obsp). https://www.cancercareontario.ca/en/cancer-care-ontario/programs/screening-programs/ontario-breast-obsp, Accessed: May 2022

  15. Chan TC, Craig T, Lee T, Sharpe MB (2014) Generalized inverse multiobjective optimization with application to cancer therapy. Oper Res 62(3):680–695

    Article  Google Scholar 

  16. Chan TC, Lee T, Terekhov D (2019) Inverse optimization: closed-form solutions, geometry, and goodness of fit. Manag Sci 65(3):1115–1135

    Article  Google Scholar 

  17. Chan TC, Mahmood R, Zhu IY (2021) Inverse optimization: theory and applications. arXiv:210903920

  18. Chan TC, Eberg M, Forster K, Holloway C, Ieraci L, Shalaby Y, Yousefi N (2022) An inverse optimization approach to measuring clinical pathway concordance. Manag Sci 68(3):1882–1903

    Article  Google Scholar 

  19. Charlson ME, Pompei P, Ales KL, MacKenzie CR (1987) A new method of classifying prognostic comorbidity in longitudinal studies: development and validation. J Chronic Diseases 40(5):373–383

    Article  Google Scholar 

  20. Cheng K, Chan C, Wong R, Leung K, Mui J, Chui W, Cheung E (2012) Integrated care pathway for the personalized care programme for patients with severe mental illness in hong kong. Int J Care Pathways 16(3):72–75

    Article  Google Scholar 

  21. Cox D (1971) Regression models and life-tables (with discussion). J R Stat Soc 34(2):187–220

    Google Scholar 

  22. van Dam PA, Verheyden G, Sugihara A, Trinh XB, Van Der Mussele H, Wuyts H, Verkinderen L, Hauspy J, Vermeulen P, Dirix L (2013) A dynamic clinical pathway for the treatment of patients with early breast cancer is a tool for better cancer care: implementation and prospective analysis between 2002–2010. World J Surg Oncol 11(1):70

    Article  Google Scholar 

  23. De Bleser L, Depreitere R, WAELE KD, Vanhaecht K, Vlayen J, Sermeus W (2006) Defining pathways. J Nurs Manag 14(7):553–563

    Article  Google Scholar 

  24. Esfahani PM, Shafieezadeh-Abadeh S, Hanasusanto GA, Kuhn D (2018) Data-driven inverse optimization with imperfect information. Math Program 167(1):191–234

    Article  Google Scholar 

  25. Faragó A, Szentesi Á, Szviatovszki B (2003) Inverse optimization in high-speed networks. Discret Appl Math 129(1):83–98

    Article  Google Scholar 

  26. Forster K, Tsang K, Li S, Ieraci L, Murray P, Woltman K, Chmelnitsky D, Holloway C, Kennedy E (2020) Can concordance between actual care received and a pathway map be measured on a population level in ontario? A pilot study. Curr Oncol 27(1):e27

    Article  Google Scholar 

  27. Heuberger C (2004) Inverse combinatorial optimization: a survey on problems, methods, and results. J Comb Optim 8(3):329–361

    Article  Google Scholar 

  28. Ishwaran H, Kogalur UB, Blackstone EH, Lauer MS et al (2008) Random survival forests. Annals Appl Stat 2(3):841–860

    Article  Google Scholar 

  29. Karunakaran M, Barreto SG, Singh MK, Kapoor D, Chaudhary A (2020) Deviations from a clinical pathway post pancreatoduodenectomy predict 90-day unplanned re-admission. Future Oncol 16 (24):1839–1849

    Article  Google Scholar 

  30. Keshavarz A, Wang Y, Boyd S (2011) Imputing a convex objective function. In: 2011 IEEE International symposium on intelligent control (ISIC), IEEE, pp 613–619

  31. van de Klundert J, Gorissen P, Zeemering S (2010) Measuring clinical pathway adherence. J Biomed Inform 43(6):861–872

    Article  Google Scholar 

  32. Ontario Health (Cancer Care Ontario) (2017) Pathway Map Development Methodology. Tech. rep.

  33. Panella M, Marchisio S, Di Stanislao F (2003) Reducing clinical variations with clinical pathways: do pathways work? Int J Qual Health Care 15(6):509–521

    Article  Google Scholar 

  34. Quan H, Sundararajan V, Halfon P, Fong A, Burnand B, Luthi JC, Saunders LD, Beck CA, Feasby TE, Ghali WA (2005) Coding algorithms for defining comorbidities in icd-9-cm and icd-10 administrative data. Med Care 43(11):1130–1139

    Article  Google Scholar 

  35. Rotter T, Kinsman L, James EL, Machotta A, Gothe H, Willis J, Snow P, Kugler J (2010) Clinical pathways: effects on professional practice, patient outcomes, length of stay and hospital costs. Cochrane database of systematic reviews (3)

  36. Rotter T, Kinsman L, James E, Machotta A, Willis J, Snow P, Kugler J (2012) The effects of clinical pathways on professional practice, patient outcomes, length of stay, and hospital costs: Cochrane systematic review and meta-analysis. Eval Health Prof 35(1):3–27

    Article  Google Scholar 

  37. Schmidt I, Thor J, Davidson T, Nilsson F, Carlsson C (2018) The national program on standardized cancer care pathways in Sweden: observations and findings halfway through. Health Policy 122(9):945–948

    Article  Google Scholar 

  38. Troutt MD, Pang WK, Hou SH (2006) Behavioral estimation of mathematical programming objective function coefficients. Manag Sci 52(3):422–434

    Article  Google Scholar 

  39. Vanounou T, Pratt W, Fischer JE, Vollmer Jr CM, Callery MP (2007) Deviation-based cost modeling: a novel model to evaluate the clinical and economic impact of clinical pathways. J Am Coll Surg 204(4):570–579

    Article  Google Scholar 

  40. Williams R, Buchan IE, Prosperi M, Ainsworth J (2014) Using string metrics to identify patient journeys through care pathways. In: AMIA Annual symposium proceedings, American medical informatics association, vol 2014, p 1208

  41. World Health Organization (2021) Breast cancer now most common form of cancer: who taking action. https://www.who.int/news/item/03-02-2021-breast-cancer-now-most-common-form-of-cancer-who-taking-action. Accessed: May 2022

  42. Xu S, Zhang J (1995) An inverse problem of the weighted shortest path problem. Japan J Ind Appl Math 12(1):47

    Article  Google Scholar 

  43. Yan H, Van Gorp P, Kaymak U, Lu X, Ji L, Chiau CC, Korsten HH, Duan H (2018) Aligning event logs to task-time matrix clinical pathways in bpmn for variance analysis. IEEE J Biomed Health Inform 22(2):311–317

    Article  Google Scholar 

  44. Yang C, Zhang J, Ma Z (1997) Inverse maximum flow and minimum cut problems. Optimization 40(2):147–170

    Article  Google Scholar 

  45. Zhang J, Cai MC (1998) Inverse problem of minimum cuts. Math Methods Oper Res 47 (1):51–58

    Article  Google Scholar 

  46. Zhang J, Ma Z (1996) A network flow method for solving some inverse combinatorial optimization problems. Optimization 37(1):59–72

    Article  Google Scholar 

  47. Zhang J, Ma Z, Yang C (1995) A column generation method for inverse shortest path problems. Zeitschrift für Oper Res 41(3):347–358

    Google Scholar 

  48. Zhao Q, Stettner A, Reznik E, Segrè D, Paschalidis IC (2015) Learning cellular objectives from fluxes by inverse optimization. In: 2015 IEEE 54th Annual conference on decision and control (CDC). IEEE, pp 1271–1276

Download references

Acknowledgements

The authors thank the Editor-in-Chief (Gregory S. Zaric), an anonymous associate editor, and three anonymous referees for their valuable comments and suggestions that significantly improved the paper. The authors also thank Grace Bannerman and Sarah Bastedo for their project management support. This study was conducted with the support of Ontario Health (Cancer Care Ontario) through funding provided by the Ontario Ministry of Health and funding from the Ontario Institute for Cancer Research. Parts of this material are based on data and information provided by Ontario Health (Cancer Care Ontario). The opinions, results, views, and conclusions reported in this publication are those of the authors and do not necessarily reflect those of Ontario Health (Cancer Care Ontario). No endorsement by Ontario Health (Cancer Care Ontario) is intended or should be inferred.

Author information

Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, Canada

    Timothy C. Y. Chan & Yusuf Shalaby

  2. Ontario Health (Cancer Care Ontario), Toronto, Ontario, Canada

    Katharina Forster, Steven Habbous, Claire Holloway & Luciano Ieraci

  3. Smith School of Business, Queen’s University, Kingston, Ontario, Canada

    Nasrin Yousefi

Authors
  1. Timothy C. Y. Chan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Katharina Forster
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Steven Habbous
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Claire Holloway
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Luciano Ieraci
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Yusuf Shalaby
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Nasrin Yousefi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nasrin Yousefi.

Ethics declarations

Conflict of Interests

The authors declare that they have no conflict of interest.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendices

Appendix A: Pathway requirements for subgroups 3-9

Table 8 Clinical pathway requirements for subgroup 3
Full size table
Table 9 Clinical pathway requirements for subgroup 4
Full size table
Table 10 Clinical pathway requirements for subgroup 5
Full size table
Table 11 Clinical pathway requirements for subgroup 6
Full size table
Table 12 Clinical pathway requirements for subgroup 7
Full size table
Table 13 Clinical pathway requirements for subgroup 8
Full size table
Table 14 Clinical pathway requirements for subgroup 9
Full size table

Appendix B: Supplementary figures and tables

Fig. 7
figure 7

Distribution of difference in concordance scores between a bootstrapped sample and the original model

Full size image
Table 15 Risk of mortality associated with concordance score (ω) for subgroups when patient data are swapped in model (4)
Full size table

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Chan, T.C.Y., Forster, K., Habbous, S. et al. Inverse optimization on hierarchical networks: an application to breast cancer clinical pathways. Health Care Manag Sci (2022). https://doi.org/10.1007/s10729-022-09599-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10729-022-09599-z

Keywords

  • Operations research
  • Inverse optimization
  • Hierarchical network
  • Clinical pathway concordance
  • Breast cancer
  • Survival analysis