Scheduling a delay between different surgeons' cases in the same operating room on the same day using upper prediction bounds for case durations

Association of surgeons' gender with elective surgical lists in the State of Florida is explained by differences in mean operative caseloads

BACKGROUND

A recent publication reported that at three hospitals within one academic health system, female surgeons received less surgical block time than male surgeons, suggesting potential gender-based bias in operating room scheduling. We examined this observation's generalizability.

METHODS

Our cross-sectional retrospective cohort study of State of Florida administrative data included all 4,176,551 ambulatory procedural encounters and inpatient elective surgical cases performed January 2017 through December 2019 by 8875 surgeons (1830 female) at all 609 non-federal hospitals and ambulatory surgery centers. There were 1,509,190 lists of cases (i.e., combinations of the same surgeon, facility, and date). Logistic regression adjusted for covariables of decile of surgeon's quarterly cases, surgeon's specialty, quarter, and facility.

RESULTS

Selecting randomly a male and a female surgeons' quarter, for 66% of selections, the male surgeon performed more cases (P < .0001). Without adjustment for quarterly caseloads, lists comprised one case for 44.2% of male and 54.6% of female surgeons (difference 10.4%, P < .0001). A similar result held for lists with one or two cases (difference 9.1%, P < .0001). However, incorporating quarterly operative caseloads, the direction of the observed difference between male and female surgeons was reversed both for case lists with one (-2.1%, P = .03) or one or two cases (-1.8%, P = .05).

CONCLUSIONS

Our results confirm the aforementioned single university health system results but show that the differences between male and female surgeons in their lists were not due to systematic bias in operating room scheduling (e.g., completing three brief elective cases in a week on three different workdays) but in their total case numbers. The finding that surgeons performing lists comprising a single case were more often female than male provides a previously unrecognized reason why operating room managers should help facilitate the workload of surgeons performing only one case on operative (anesthesia) workdays.

Average and longest expected treatment times for ultraviolet light disinfection of rooms

BACKGROUND

Planning Ultraviolet-C (UV-C) disinfection of operating rooms (ORs) is equivalent to scheduling brief OR cases. The study purpose was evaluation of methods for predicting surgical case duration applied to treatment times for ORs and hospital rooms.

METHODS

Data used were disinfection times with a 3-tower UV-C disinfection system in N=700 rooms each with ≥100 completed treatments.

RESULTS

The coefficient of variation of mean treatment duration among rooms was 19.6% (99% confidence interval [CI] 18.2%-21.0%); pooled mean 18.3 minutes among the 133,927 treatments. The 50^th percentile of coefficients of variation among treatments of the same room was 27.3% (CI 26.3%-28.4%), comparable to variabilities in durations of surgical procedures. The ratios of the 90^th percentile to mean differed among rooms. Log-normal distributions had poor fits for 33% of rooms. Combining results, we calculated 90% upper prediction limits for treatment times by room using a distribution-free method (e.g., third longest of preceding 29 durations). This approach was suitable because, once UV-C disinfection started, the median difference between the duration estimated by the system and actual time was 1 second.

CONCLUSIONS

Times for disinfection should be listed as treatment of a specific room (e.g., "UV-C main OR16"), not generically (e.g., "UV-C"). For estimating disinfection time after single surgical cases, use distribution-free upper prediction limits, because of considerable proportional variabilities in duration.

Obtaining and Modeling Variability in Travel Times From Off-Site Satellite Clinics to Hospitals and Surgery Centers for Surgeons and Proceduralists Seeing Office Patients in the Morning and Performing a To-Follow List of Cases in the Afternoon

BACKGROUND

Hospitals achieve growth in surgical caseload primarily from the additive contribution of many surgeons with low caseloads. Such surgeons often see clinic patients in the morning then travel to a facility to do 1 or 2 scheduled afternoon cases. Uncertainty in travel time is a factor that might need to be considered when scheduling the cases of to-follow surgeons. However, this has not been studied. We evaluated variability in travel times within a city with high traffic density.

METHODS

We used the Google Distance Matrix application programming interface to prospectively determine driving times incorporating current traffic conditions at 5-minute intervals between 9:00 AM and 4:55 PM during the first 4 months of 2018 between 4 pairs of clinics and hospitals in the University of Miami health system. Travel time distributions were modeled using lognormal and Burr distributions and compared using the absolute and signed differences for the median and the 0.9 quantile. Differences were evaluated using 2-sided, 1-group t tests and Wilcoxon signed-rank tests. We considered 5-minute signed differences between the distributions as managerially relevant.

RESULTS

For the 80 studied combinations of origin-to-destination pairs (N = 4), day of week (N = 5), and the hour of departure between 10:00 AM and 1:55 PM (N = 4), the maximum difference between the median and 0.9 quantile travel time was 8.1 minutes. This contrasts with the previously published corresponding difference between the median and the 0.9 quantile of 74 minutes for case duration. Travel times were well fit by Burr and lognormal distributions (all 160 differences of medians and of 0.9 quantiles <5 minutes; P < .001). For each of the 4 origin-destination pairs, travel times at 12:00 PM were a reasonable approximation to travel times between the hours of 10:00 AM and 1:55 PM during all weekdays.

CONCLUSIONS

During mid-day, when surgeons likely would travel between a clinic and an operating room facility, travel time variability is small compared to case duration prediction variability. Thus, afternoon operating room scheduling should not be restricted because of concern related to unpredictable travel times by surgeons. Providing operating room managers and surgeons with estimated travel times sufficient to allow for a timely arrival on 90% of days may facilitate the scheduling of additional afternoon cases especially at ambulatory facilities with substantial underutilized time.

Event-based knowledge elicitation of operating room management decision-making using scenarios adapted from information systems data

Background

No systematic process has previously been described for a needs assessment that identifies the operating room (OR) management decisions made by the anesthesiologists and nurse managers at a facility that do not maximize the efficiency of use of OR time. We evaluated whether event-based knowledge elicitation can be used practically for rapid assessment of OR management decision-making at facilities, whether scenarios can be adapted automatically from information systems data, and the usefulness of the approach.

Methods

A process of event-based knowledge elicitation was developed to assess OR management decision-making that may reduce the efficiency of use of OR time. Hypothetical scenarios addressing every OR management decision influencing OR efficiency were created from published examples. Scenarios are adapted, so that cues about conditions are accurate and appropriate for each facility (e.g., if OR 1 is used as an example in a scenario, the listed procedure is a type of procedure performed at the facility in OR 1). Adaptation is performed automatically using the facility's OR information system or anesthesia information management system (AIMS) data for most scenarios (43 of 45). Performing the needs assessment takes approximately 1 hour of local managers' time while they decide if their decisions are consistent with the described scenarios. A table of contents of the indexed scenarios is created automatically, providing a simple version of problem solving using case-based reasoning. For example, a new OR manager wanting to know the best way to decide whether to move a case can look in the chapter on "Moving Cases on the Day of Surgery" to find a scenario that describes the situation being encountered.

Results

Scenarios have been adapted and used at 22 hospitals. Few changes in decisions were needed to increase the efficiency of use of OR time. The few changes were heterogeneous among hospitals, showing the usefulness of individualized assessments.

Conclusions

Our technical advance is the development and use of automated event-based knowledge elicitation to identify suboptimal OR management decisions that decrease the efficiency of use of OR time. The adapted scenarios can be used in future decision-making.

Influence of procedure classification on process variability and parameter uncertainty of surgical case durations

BACKGROUND

Predictive variability of operating room (OR) times influences decision making on the day of surgery including when to start add-on cases, whether to move a case from one OR to another, and where to assign relief staff. One contributor to predictive variability is process variability, which arises among cases of the same procedure(s). Another contributor is parameter uncertainty, which is caused by small sample sizes of historical data.

METHODS

Process variability was quantified using absolute percentage errors of surgeons' bias-corrected estimates of OR time. The influence of procedure classification on process variability was studied using a dataset of 61,353 cases, each with 1 to 5 scheduled and actual Current Procedural Terminology (CPT) codes (i.e., a standardized vocabulary). Parameter uncertainty's sensitivity to sample size was quantified by studying ratios of 90% prediction bounds to medians. That studied dataset of 65,661 cases was used previously to validate a Bayesian method to calculate 90% prediction bounds using combinations of surgeons' scheduled estimates and historical OR times.

RESULTS

(1) Process variability differed significantly among 11 groups of surgical specialty and case urgency (P < 0.0001). For example, absolute percentage errors exceeded the overall median of 22% for 57% of urgent spine surgery cases versus 42% of elective spine surgery cases. (2) Process variability was not increased when scheduled and actual CPTs differed (P = 0.23 without and P = 0.47 with stratification based on the 11 groups), because most differences represented known (planned) options inherent to procedures. (3) Process variability was not associated with incidence of procedures (P = 0.79), after excluding cataract surgery, a procedure with high relative variability. (4) Parameter uncertainty from uncommon procedures (0-2 historical cases) accounted for essentially all of the uncertainty in decisions dependent on estimates of OR times. The Bayesian method moderated the effect of small sample sizes on uncertainty in estimates of OR times. In contrast, from prior work, the use of broad categories of procedures reduces parameter uncertainty but at the expense of increased process variability.

CONCLUSIONS

For procedures with few historic data, the Bayesian method allows for effective case duration prediction, permitting use of detailed procedure descriptions. Although fine resolution of scheduling procedures increases the chance of performed procedure(s) differing from scheduled procedure(s), this does not increase process variability. Future studies need both to address differences in process variability among specialties and accept the limitation that findings from one may not apply to others.

Prediction of surgery times and scheduling of operation theaters in ophthalmology department

This paper presents the framework for forecasting the surgery time by taking into account the surgical environment in an ophthalmology department (experience of surgeon in years, experience of anesthetist in years, staff experience in years, type of anesthesia etc.). The estimation of surgery times is done using three techniques, such as the Adaptive Neuro Fuzzy Inference Systems (ANFIS), Artificial Neural Networks (ANN) and Multiple Linear Regression Analysis (MLRA) and the results of estimation accuracy were compared. Though the developed framework is general, it is illustrated for three ophthalmologic surgeries such as the cataract surgery, corneal transplant surgery and Oculoplastic surgery. The framework is validated by using data obtained from a local hospital. It is hypothesized that by accurately knowing the surgery times, one can schedule the operations optimally resulting in the efficient utilization of the operating rooms. This increase in the efficiency is demonstrated through computer simulations of the operating theater.

A Psychological Basis for Anesthesiologists’ Operating Room Managerial Decision-Making on the Day of Surgery

BACKGROUND

We investigated whether, without prompting, anesthesiologists tend to make managerial decisions to increase the clinical work per unit time of the sites to which they are assigned during their scheduled time present. Although a sound basis for decision-making involving individual ORs, the heuristic is often suboptimal economically when applied to decisions involving multiple ORs.

METHODS

Two studies were performed at one hospital. 1) A retrospective analysis was made of anesthesiologists' managerial decisions when caring for sequential lists of patients. 2) Patients' and surgeons' waiting on nights and weekends were studied before/after education on optimal decision-making.

RESULTS

1) Anesthesiologists' decisions resulted in an increase in their clinical work per unit time, not a reduction in patient waiting. 2) Paradoxically, such efforts on nights and weekends caused increased patient and surgeon waiting. Decisions were unchanged after education on a different way to assign cases.

CONCLUSIONS

In a companion article, we showed that clinicians tended to make decisions that increased the clinical work per unit time at each moment in each OR, even when doing so resulted in an increase in overutilized OR time, higher staffing costs, unpredictable work hours, and/or mandatory overtime. The current studies show that such efforts to work fast cannot be explained as a consequence of efforts to reduce surgeon and patient waiting. Rather, the heuristic followed is consistent with increasing one's personal clinical work per unit time at one's assigned anesthetizing location.

A three-phase approach for operating theatre schedules

In this paper we develop a three-phase, hierarchical approach for the weekly scheduling of operating rooms. This approach has been implemented in one of the surgical departments of a public hospital located in Genova (Genoa), Italy. Our aim is to suggest an integrated way of facing surgical activity planning in order to improve overall operating theatre efficiency in terms of overtime and throughput as well as waiting list reduction, while improving department organization. In the first phase we solve a bin packing-like problem in order to select the number of sessions to be weekly scheduled for each ward; the proposed and original selection criterion is based upon an updated priority score taking into proper account both the waiting list of each ward and the reduction of residual ward demand. Then we use a blocked booking method for determining optimal time tables, denoted Master Surgical Schedule (MSS), by defining the assignment between wards and surgery rooms. Lastly, once the MSS has been determined we use the simulation software environment Witness 2004 in order to analyze different sequencings of surgical activities that arise when priority is given on the basis of a) the longest waiting time (LWT), b) the longest processing time (LPT) and c) the shortest processing time (SPT). The resulting simulation models also allow us to outline possible organizational improvements in surgical activity. The results of an extensive computational experimentation pertaining to the studied surgical department are here given and analyzed.

A Simple Method for Deciding When Patients Should Be Ready on the Day of Surgery Without Procedure-Specific Data

BACKGROUND

Deciding when patients should arrive for same-day-admission or ambulatory surgery is a problem at many hospitals and surgery centers. Although staff can often start cases earlier than scheduled, the potential start times are not known when each case is scheduled. Patient availability must therefore be balanced against patient waiting times and fasting times. Knowing the earliest time that a case might begin, given its scheduled start time, provides a rational basis for telling patients when to report for surgery and when to refrain from eating or drinking before their procedure.

METHODS

We describe and validate a simple method for determining the earliest possible start time for a case, with only a 5% probability that staff would be able to start the case even earlier. Calculations use nonparametric methods to determine the 0.05 lower prediction bound for the start time of a case, using historical values for the scheduled and actual start times of cases performed by the same surgical suite/surgical service/day of the week combination as the case of interest. Information is not needed regarding the preceding cases performed in the same operating room. No patient or surgeon identifiable information is used.

RESULTS

We use results from earlier studies to provide a derivation and theoretical justification for these methods. New data confirm the validity of the results obtained and show that the required calculations are easy to implement. Individualized patient instructions can be accessed via a public website without disclosing confidential information.

CONCLUSIONS

We have developed a simple method for determining when patients should be ready on the day of surgery based on the start times of historical cases performed by the same surgical suite/surgical service/day of the week combination as the case of interest.

Visualizing the demand for various resources as a function of the master surgery schedule: a case study

This paper presents a software system that visualizes the impact of the master surgery schedule on the demand for various resources throughout the rest of the hospital. The master surgery schedule can be seen as the engine that drives the hospital. Therefore, it is very important for decision makers to have a clear image on how the demand for resources is linked to the surgery schedule. The software presented in this paper enables schedulers to instantaneously view the impact of, e.g., an exchange of two block assignments in the master surgery schedule on the expected resource consumption pattern. A case study entailing a large Belgian surgery unit illustrates how the software can be used to assist in building better surgery schedules.

Estimating the duration of common elective operations: implications for operating list management

Over-running operating lists are known to be a common cause of cancellation of operations on the day of surgery. We investigated whether lists were overbooked because surgeons were optimistic in their estimates of the time that operations would take to complete. We used a questionnaire to assess the estimates of total operation time of 22 surgeons, 35 anaesthetists and 16 senior nursing staff for 31 common, general surgical and urological procedures. The response rate was 66%. We found no difference between the estimates of these three groups of staff, or between these estimates and times obtained from theatre computer records (p = 0.722). We then applied the average of the surgeons' estimates prospectively to 50 consecutive published surgical lists. Surgical estimates were very accurate in predicting the actual duration of the list (r2= 0.61; p < 0.001), but were poor at booking the list to within its scheduled duration: 50% of lists were predictably overbooked, 50% over-ran their scheduled time, and 34% of lists suffered a cancellation. We suggest that using the estimates of operating times to plan lists would reduce the incidence of predictable over-runs and cancellations.

Predicting Anesthesia Times for Diagnostic and Interventional Radiological Procedures

We studied anesthesia times for diagnostic and interventional radiology using anesthesia billing data and paper radiology logbooks. For computerized tomography and magnetic resonance imaging procedures, we tried to predict future anesthesia times by using historical anesthesia times classified by Current Procedural Terminology (CPT) codes. By this method, anesthesia times were estimated even less accurately than operating room cases. Computerized tomography and magnetic resonance imaging had many different CPT codes, most rare, and CPT codes reflected organs imaged, not scanning times. However, when, anesthesia times were estimated by expert judgment, face validity and accuracy were good. Lower and upper prediction bounds were also estimated from the expert estimates. For interventional radiology, predicting anesthesia times was challenging because few CPT codes accounted for most cases. Because interventional radiologists scheduled their elective cases into allocated time, the necessary goal was not to estimate the time to complete each case but rather the time to complete each day's entire series of elective cases including turnover times. We determined the time of day (e.g., 4 pm) up to when interventional radiology could schedule so that on 80% of days the anesthesia team finishes no later than a specified time (e.g., 6 pm). Both diagnostic and interventional radiology results were similarly less accurate when Version 9 of the International Classifications of Diseases' procedure codes was used instead of CPT.

Why can't my procedures start on time?

Despite OR practice improvements, approximately 50% of second or subsequent surgical procedures will not start on time because of procedure duration overruns caused by preceding procedures. Operating room scheduling that uses reliable historical data about specific surgeon and procedure combinations and computerized scheduling systems can minimize overruns. Statistical variability in procedure durations, however, implies that one-half of the procedures will run longer than the calculated mean, resulting in wait times for time-scheduled surgeons and their patients. Managers must understand the tradeoffs between the competing goals of surgical throughput and decreasing patient wait times in their efforts to optimize the OR schedule.

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

Many facilities allocate operating room (OR) time based on historical utilization of OR time. This assumes that there is a fixed amount of regularly scheduled OR time, called "block time". This "Fixed Hours" system does not apply to many surgical suites in the US. Most facilities make OR time available for all its surgeons' patients, even if cases are expected to finish after the end of block time. In this setting, OR time should be allocated to maximize OR efficiency, not historical utilization. Then, cases are scheduled either on "Any Workday" (i.e., date chosen by patient and surgeon) or within a reasonable time (e.g., "Four Weeks"). In this study, we used anesthesia billing data from two facilities to study statistical challenges in converting from a Fixed Hours to an Any Workday or Four Weeks patient scheduling system. We report relationships among the number of staffed ORs (i.e., first case of the day starts), length of the regularly scheduled OR workday, OR efficiency, OR staffing cost, and changes in services' OR allocations. These relationships determine the expected changes in each service's OR allocation, when a facility using Fixed Hours considers converting to the Any Workday or Four Weeks systems.

IMPLICATIONS

We investigated the complex relationships among the number of surgical services, number of staffed operating rooms (ORs), length of the regularly scheduled OR workday, efficiency of use of OR time, OR staffing cost, and changes in each services' allocated OR time.

How to schedule elective surgical cases into specific operating rooms to maximize the efficiency of use of operating room time

We considered elective case scheduling at hospitals and surgical centers at which surgeons and patients choose the day of surgery, cases are not turned away, and anesthesia and nursing staffing are adjusted to maximize the efficiency of use of operating room (OR) time. We investigated scheduling a new case into an OR by using two patient-scheduling rules: Earliest Start Time or Latest Start Time. By using several scenarios, we showed that the use of Earliest Start Time is rational economically at such facilities. Specifically, it maximizes OR efficiency when a service has nearly filled its regularly scheduled hours of OR time. However, Latest Start Time will perform better at balancing workload among services' OR time. We then used historical case duration data from two facilities in computer simulations to investigate the effect of errors in predicting case durations on the performance of these two heuristics. The achievable incremental reduction in overtime by having perfect information on case duration versus using historical case durations was only a few minutes per OR. The differences between Earliest Start Time and Latest Start Time were also only a few minutes per OR. We conclude that for facilities at which the goals are, in order of importance, safety, patient and surgeon access to OR time, and then efficiency, few restrictions need to be placed on patient scheduling to achieve an efficient use of OR time.

IMPLICATIONS

We showed how elective cases should be scheduled to maximize the efficiency of use of operating room time. The analysis applies to surgical suites at which surgeons and patients have access to operating room time every workday.