Prediction of the time to complete a series of surgical cases to avoid OR overutilization

ORAHS 2010

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

Agenda

1. Objectives

2. Introduction

3. Methods

4. Results

5. Discussion

6. Conclusions

ORAHS 2010

1. Objectives

ORAHS 2010

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

ORAHS 2010

2. Introduction

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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

ORAHS 2010

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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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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Lognormal approximation

Most authors agree that the lognormal distribution is adequate to represent surgical times

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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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3. Methods

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Data: surgeries

We studied 6,090 cases performed by 9 different cardiovascular surgeons between January 1st, 2004 and January 30th, 2009 at St. Michael’s Hospital, located in Toronto, Ontario, Canada

Cases were grouped clinically into 13 different categories

Coronary artery bypass graft surgery (CABG) accounted for 63.33% of the cases

1. Aortic plus mitral valve replacement/repair

2. Aortic valve replacement/repair 3. Aortic valve replacement/repair plus

CABG 4. Ascending aorta plus aortic valve

replacement/repair or CABG 5. Ascending aorta repair 6. CABG x1 x2 x3 7. CABG x4 x5 x6 8. Chest re-opening/closure 9. Complex 10. Major procedure (with

cardiopulmonary bypass) 11. Minor procedure 12. Mitral valve replacement/repair 13. Mitral valve replacement/repair plus

CABG

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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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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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Validation

We selected a schedule composed of 2 CABGs performed by the same surgeon (256 historical records)

We obtained the probability distribution of this schedule using our methodology

We then simulated 1 million schedule durations

Finally we compared the simulated ones with the real durations

Percventile FW Real Min %

PC_5 6.46 6.75 -17.47 -4.31

PC_10 6.79 7.00 -12.45 -2.96

PC_15 7.02 7.17 -8.55 -1.99

PC_20 7.21 7.33 -7.33 -1.67

PC_25 7.38 7.42 -2.47 -0.55

PC_30 7.53 7.50 1.56 0.35

PC_35 7.67 7.75 -5.03 -1.08

PC_40 7.80 7.83 -1.91 -0.41

PC_45 7.93 8.00 -3.91 -0.81

PC_50 8.07 8.08 -0.97 -0.20

PC_55 8.20 8.25 -2.93 -0.59

PC_60 8.34 8.42 -4.70 -0.93

PC_65 8.48 8.50 -1.04 -0.20

PC_66_66 8.53 8.50 1.96 0.39

PC_70 8.64 8.67 -1.78 -0.34

PC_75 8.81 8.75 3.36 0.64

PC_80 9.00 9.08 -5.17 -0.95

PC_85 9.23 9.50 -16.46 -2.89

PC_90 9.52 9.83 -18.96 -3.21

PC_95 9.96 10.25 -17.15 -2.79

Differences

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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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Lognormal distribution of the schedule

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4. Results

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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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Prediction of the total duration

0.19 hrs 0.59 hrs

Average 2nd tertile cut-off point

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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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5. Discussion

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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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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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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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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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6. Conclusions

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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)

ORAHS 2010

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