Skip to main content
Log in

Estimating Procedure Times for Surgeries by Determining Location Parameters for the Lognormal Model

  • Published:
Health Care Management Science Aims and scope Submit manuscript

Abstract

We present an empirical study of methods for estimating the location parameter of the lognormal distribution. Our results identify the best order statistic to use, and indicate that using the best order statistic instead of the median may lead to less frequent incorrect rejection of the lognormal model, more accurate critical value estimates, and higher goodness-of-fit. Using simulation data, we constructed and compared two models for identifying the best order statistic, one based on conventional nonlinear regression and the other using a data mining/machine learning technique. Better surgical procedure time estimates may lead to improved surgical operations.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A.M. Epstein, US teaching hospitals in the evolving health care system, JAMA 273 (1995) 1203–1207.

    Google Scholar 

  2. D.A. Redelmeier and V.R. Fuchs, Hospital expenditures in the United States and Canada, New England Journal of Medicine 328 (1993) 772–778.

    Google Scholar 

  3. American Hospital Association, Ambulatory Surgery Trendlines (Society for Ambulatory Care Professionals, Chicago, 1994).

    Google Scholar 

  4. F.D. Moore, Surgical streams in the flow of health care financing, The role of surgery in national expenditures: What costs are controllable? Ann. Surg. 201 (1985) 132–141.

    Google Scholar 

  5. H. Beaulieu, J.A. Ferland, B. Gendron and P. Michelon, A mathematical programming approach for scheduling physicians in the emergency room, Health Care Management Science 3 (2000) 193–200.

    Google Scholar 

  6. M.W. Carter and S.D. Lapierre, Scheduling emergency room physicians, Health Care Management Science 4 (2001) 347–360.

    Google Scholar 

  7. E. Litvak and M.C. Long, Cost and quality under managed care: Irreconcilable differences? American Journal of Managed Care 6 (2000).

  8. M.L. McManus, M.C. Long, A. Cooper, J. Mandell, D.M. Berwick, M. Pagano and E. Litvak, Variability in surgical caseload and access to intensive care services, Anesthesiology 98 (2003) 1491–1496.

    Google Scholar 

  9. T.M. Wickizer, Effect of hospital utilization review on medical expenditures in selected diagnostic areas: An exploratory study, American Journal of Public Health 81 (1991) 482–484.

    Google Scholar 

  10. F. Dexter, R.H. Epstein and H.M. Marsh, A statistical analysis of weekday operating room anesthesia group staffing costs at nine independently managed surgical suites, Anesthesia and Analgesia 92 (2001) 1493–1498.

    Google Scholar 

  11. F. Dexter and R.D. Traub, Sequencing cases in the operating room: Predicting whether one surgical case will last longer than another, Anesthesia and Analgesia 90 (2000) 975–979.

    Google Scholar 

  12. F. Dexter, R.D. Traub and A. Macario, How to release allocated operating room time to increase efficiency: Predicting which surgical service will have the most underutilized operating room time, Anesthesia and Analgesia 96 (2003) 507–512.

    Google Scholar 

  13. S.D. Lapierre, C. Batson and S. McCaskey, Improving on-time performance in health care organizations: A case study, Health Care Management Science 2 (1999) 27–34.

    Google Scholar 

  14. F. Dexter, A. Macario, R.D. Traub, M. Hopwood and D.A. Lubarsky, An operating room scheduling strategy to maximize the use of operating room block time: Computer simulation of patient scheduling and survey of patients' preferences for surgical waiting time, Anesthesia and Analgesia 89 (1999) 7–20.

    Google Scholar 

  15. J.T. Blake, F. Dexter and J. Donald, Operating room managers' use of integer programming for assigning block time to surgical groups: A case study, Anesthesia and Analgesia 94 (2002) 143–148.

    Google Scholar 

  16. J.T. Blake and J. Donald, Mount Sinai hospital uses integer programming to allocate operating room time, Interfaces 32 (2002) 66–73.

    Google Scholar 

  17. F. Dexter and A. Macario, Changing allocations of operating room time from a system based on historical utilization to one where the aim is to schedule as many surgical cases as possible, Anesthesia and Analgesia 94 (2002) 1272–1279.

    Google Scholar 

  18. F. Dexter, A. Macario and R.D. Traub, Which algorithm for scheduling add-on elective cases maximizes operating room utilization? Use of bin packing algorithms and fuzzy constraints in operating room management, Anesthesiology 91 (1999) 1491–1500.

    Google Scholar 

  19. J. Zhou, F. Dexter, A. Macario and D.A. Lubarsky, Relying solely on historical surgical times to estimate accurately future surgical times is unlikely to reduce the average length of time cases finish late, Journal of Clinical Anesthesiology 11 (1999) 601–605.

    Google Scholar 

  20. A. Macario and F. Dexter, Estimating the duration of a case when the surgeon has not recently scheduled the procedure at the surgical suite, Anesthesia and Analgesia 89 (1999) 1241–1245.

    Google Scholar 

  21. D.P. Strum, J.H. May and L.G. Vargas, Modeling the uncertainty of surgical procedure times: Comparison of log-normal and normal models, Anesthesiology 92 (2000) 1160–1167.

    Google Scholar 

  22. J.H. May, D.P. Strum and Vargas, Fitting the lognormal distribution to surgical procedure times, Decision Sciences 31 (2000) 129–148.

    Google Scholar 

  23. N.L. Johnson, S. Kotz and N. Balakrishnan, Continuous Univariate Distributions, Vol. 1, 2nd Ed. (Wiley, New York, 1994) pp. 222–235.

    Google Scholar 

  24. N. Balakrishnan and A.C. Cohen, Order Statistics and Inference: Estimation Methods (Academic Press, Boston, 1991).

    Google Scholar 

  25. H.L. Harter and N. Balakrishnan, CRC Handbook of Tables for the Use of Order Statistics in Estimation (CRC Press, Boca Raton, 1996).

    Google Scholar 

  26. K. Muralidhar and S.H. Zanakis, A simple minimum-bias percentile estimator of the location parameter for the gamma, weibull, and lognormal distributions, Decision Sciences 23 (1992) 862–879.

    Google Scholar 

  27. S.D. Dubey, Some percentile estimators for Weibull parameters, Technometrics 9 (1967) 119–129.

    Google Scholar 

  28. D.G. Dannenbring, Procedures for estimating optimal solution values for large combinatorial problems, Management Science 23 (1977) 1273–1283.

    Google Scholar 

  29. D.P. Strum, L.G. Vargas and J.H. May, Surgical subspeciality block utilization and capacity planning: A minimal cost analysis model, Anesthesiology 90 (1999) 1176–1185.

    Google Scholar 

  30. R.B. D'Agostino, Tests for the normal distribution, in: Goodness-of-Fit Techniques, eds. R.B. D'Agostino and M.A. Stephens (Marcel Dekker, New York, 1986) pp. 367–419.

    Google Scholar 

  31. X.H. Zhou, Estimation of the log-normal mean [In Process Citation], Statistics Medicine 17 (1998) 2251–2264.

    Google Scholar 

  32. P. Bratley, B.L. Fox and L.E. Schrage, A Guide to Simulation, 2nd Ed. (Springer, New York, 1987) pp. 131–135.

    Google Scholar 

  33. U.S. Karmarkar, A robust forecasting technique for inventory and leadtime management, Journal of Operations Management 12 (1994) 45–54.

    Google Scholar 

  34. J. Zhou and F. Dexter, Method to assist in the scheduling of add-on surgical cases-upper prediction bounds for surgical case durations based on the log-normal distribution, Anesthesiology 89 (1998) 1228–1232.

    Google Scholar 

  35. Rulequest, Cubist, Release 1.06a (Computer Software), Rulequest Research Pty Ltd.: St. Ives, NSW, Australia (1999).

  36. D.P. Strum, A.R. Sampson, J.H. May and L.G. Vargas, Surgeon and type of anesthesia predict variability in surgical procedure times, Anesthesiology 92 (2000) 1454–1466.

    Google Scholar 

  37. E.S. Pearson, R.B. D'Agostino and K.O. Bowman, Tests for departure from normality: Comparison of powers, Biometrika 64 (1977) 231–246.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jerrold H. May.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Spangler, W.E., Strum, D.P., Vargas, L.G. et al. Estimating Procedure Times for Surgeries by Determining Location Parameters for the Lognormal Model. Health Care Management Science 7, 97–104 (2004). https://doi.org/10.1023/B:HCMS.0000020649.78458.98

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:HCMS.0000020649.78458.98

Navigation