1. Prediction of the Time to Complete a Series of Surgical
Cases to Avoid Cardiac Operating Room Overutilization*
Rene Alvarez, MEng
Centre for Research in Healthcare Engineering, Department of
Mechanical and Industrial Engineering at the University of Toronto
St. Michael’s Hospital, Toronto, ON, Canada
Richard Bowry, MB BS FRCA
St. Michael’s Hospital, Toronto, ON, Canada
Faculty of Medicine, University of Toronto
Michael Carter, PhD
Centre for Research in Healthcare Engineering, Department of
Mechanical and Industrial Engineering at the University of Toronto
* Accepted for publication in the Canadian Journal of Anesthesia
Editor: Donald R. Miller, M.D.
Reviewer: Franklin Dexter, M.D., PhD
ORAHS 2010

2. Agenda
1. Objectives
2. Introduction
3. Methods
4. Results
5. Discussion
6. Conclusions
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3. 1. Objectives
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4. Objective
 We present a methodology to accurately
estimate the time to complete a series of
surgical cases in a single cardiac OR to
avoid overutilization when:
 the first case starts on time
 there are no add-on cases
 block time was calculated to match the typical OR
workload
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5. 2. Introduction
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6. OR Efficiency
 Efficient OR utilization must account for the cost of
both underutilized and overutilized OR hours
 From the accounting perspective, the staffing
expense during scheduled hours is a sunk cost so
the savings for finishing cases early is effectively
zero
 A “zero tolerance for overtime” policy may be too
rigid
 Therefore, OR efficiency has two competing
priorities:
 using all available time to perform cases
 control overutilization
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7. Overutilization
 If for a single OR we assume that:
1. the first case starts on time
2. there are no add-on cases
3. block time was calculated to match the typical OR
workload
 Then, overutilization in that OR can be
minimized by accurately estimating the
time required to complete the each case
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8. How to estimate surgery duration?
a. Surgeons’ estimation
b. Average time using historical data
c. Historical data combined with the surgeon’s
own estimate
d. A linear prediction model that combined
objective factors with the surgeons’
estimate of operative time
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9. Lognormal approximation
 Most authors agree that the lognormal
distribution is adequate to represent surgical
times
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10. How to sum these random times?
 Alvarez et al. (ORAHS 2008) suggested a
methodology based on the Fenton-
Wilkinson Approximation
 The Fenton-Wilkinson approach:
 gives an accurate estimate particularly in the tail of
the cumulative distribution function
 offers a closed-form solution for approximating the
underlying parameters to the lognormal distribution
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11. 3. Methods
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12. Data: surgeries
 We studied 6,090 cases 1. Aortic plus mitral valve
performed by 9 different replacement/repair
cardiovascular surgeons 2. Aortic valve replacement/repair
between January 1st, 2004 3. Aortic valve replacement/repair plus
CABG
and January 30th, 2009 at 4. Ascending aorta plus aortic valve
St. Michael’s Hospital, replacement/repair or CABG
located in Toronto, Ontario, 5. Ascending aorta repair
Canada 6. CABG x1 x2 x3
7. CABG x4 x5 x6
 Cases were grouped 8. Chest re-opening/closure
clinically into 13 different 9. Complex
categories 10. Major procedure (with
cardiopulmonary bypass)
 Coronary artery bypass
11. Minor procedure
graft surgery (CABG) 12. Mitral valve replacement/repair
accounted for 63.33% of 13. Mitral valve replacement/repair plus
the cases CABG
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13. Data: turnover times
 We collected data during a five month
period (January 2009-May 2009)
 The average turnover time was 0.50 hours,
with a standard deviation of 0.23 hours
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14. Lognormal distribution fit
 We fitted three parameter lognormal distributions
to surgical times and turnover times
 To study the lognormal goodness of fit we:
 conducted Kolmogorov-Smirnov tests, and
 performed two graphical analyses:
1. comparison of time histograms against the fitted lognormal
distributions
2. probability plots to compare both the real data quantiles
against the lognormal ones
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15. Validation
Differences
Percventile FW Real Min %
 We selected a schedule PC_5 6.46 6.75 -17.47 -4.31
composed of 2 CABGs PC_10
PC_15
6.79
7.02
7.00
7.17
-12.45
-8.55
-2.96
-1.99
performed by the same PC_20 7.21 7.33 -7.33 -1.67
surgeon (256 historical PC_25 7.38 7.42 -2.47 -0.55
records)
PC_30 7.53 7.50 1.56 0.35
PC_35 7.67 7.75 -5.03 -1.08
 We obtained the probability PC_40
PC_45
7.80
7.93
7.83
8.00
-1.91
-3.91
-0.41
-0.81
distribution of this schedule PC_50 8.07 8.08 -0.97 -0.20
using our methodology PC_55 8.20 8.25 -2.93 -0.59
PC_60 8.34 8.42 -4.70 -0.93
 We then simulated 1 million PC_65 8.48 8.50 -1.04 -0.20
schedule durations PC_66_66 8.53 8.50 1.96 0.39
PC_70 8.64 8.67 -1.78 -0.34
 Finally we compared the PC_75 8.81 8.75 3.36 0.64
simulated ones with the PC_80
PC_85
9.00
9.23
9.08
9.50
-5.17
-16.46
-0.95
-2.89
real durations PC_90 9.52 9.83 -18.96 -3.21
PC_95 9.96 10.25 -17.15 -2.79
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16. Estimators for schedule duration
1. The “estimated average duration of the schedule”
calculated as the sum of the average surgical times
and turnover times in the schedule
 this “empirical average” is equivalent to the mean value of
the lognormal probability distribution of the schedule
duration.
2. The second tertile cut-off point of the lognormal
distribution obtained using Alvarez et al. (ORAHS
2008) methodology
 the time taken for 2/3 of cases to be completed
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17. Lognormal distribution of the schedule
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18. 4. Results
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19. Simultaneous schedule tracking
 June-August 2009
 138 scheduled blocks
 43 blocks were excluded due to last minute
changes to the schedule resulting in
unpredicted delays or case cancellations
 95 schedules were analyzed
 42 (44.2%) comprised two sequential
coronary artery bypass graft (1 to 3
bypasses) surgeries
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20. Prediction of the total duration
Average 2nd tertile cut-off point
0.19 hrs 0.59 hrs
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21. Overtime
 37 (39.95%) schedules with overtime
 average overtime was 65.81 minutes
 standard deviation 50.33 minutes
 range from 5 minutes to 170 minutes
 The estimated average
 predicted 44 overrun schedules
 32 overran
 The second tertile cut-off point
 predicted 61 overrun schedules
 35 overran
 26 false predictions in total:
 the real duration of the schedule was on average located at the
26.67% percentile point (standard deviation 17.53%).
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22. 5. Discussion
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23. Lognormal fit
 Graphical analyses and computer
simulation validate the lognormal
distribution even in those cases where the
p-value of the traditional goodness of fit
test rejects it
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24. Average
 We validated the use of the average
duration of a series of surgical cases and
turnover times to estimate total schedule
duration
 We found the average value to be located
between the 51% and 53% percentile
points for 74.74% of the cases
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25. Overtime prediction capacity
 Our results suggest that neither the
estimated average nor the second tertile
cut-off points alone are able to predict the
need for overtime without considerable
false positive results
 As suggested by Alvarez et al. (ORAHS
2008) the combined use of the estimated
average schedule duration and the second
tertile cut-off point may help limit overtime
expense
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26. Cancellations
 An analysis of the cancellation data, where
the second case was cancelled due to
insufficient time, showed that most of the
first cases exceeded the second tertile cut-
off point
 This is an expected effect of lognormal
distributed operating times and cannot be
prevented using this methodology
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27. 6. Conclusions
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28. Decision rule
 Approve an schedule only when the second
tertile cut-off point is less or equal the
block time length plus an “acceptable
overtime” (e.g. 30 minutes for an 8 hours
block time)
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29. Prediction of the Time to Complete a Series of Surgical
Cases to Avoid Cardiac Operating Room Overutilization*
Rene Alvarez, MEng
Centre for Research in Healthcare Engineering, Department of
Mechanical and Industrial Engineering at the University of Toronto
St. Michael’s Hospital, Toronto, ON, Canada
Richard Bowry, MB BS FRCA
St. Michael’s Hospital, Toronto, ON, Canada
Faculty of Medicine, University of Toronto
Michael Carter, PhD
Centre for Research in Healthcare Engineering, Department of
Mechanical and Industrial Engineering at the University of Toronto
* Accepted for publication in the Canadian Journal of Anesthesia
Editor: Donald R. Miller, M.D.
Reviewer: Franklin Dexter, M.D., PhD
ORAHS 2010