IntroductionTotal knee and hip arthroplasty (TKA and THA, respectively) are the gold-standard treatment for end-stage arthritis of the hip and knee joints. These procedures are the first and second most frequently performed in the United States, excluding maternal and neonatal procedures [1]. In 2018, 1.3 million of these procedures were performed in the United States, a 21.9% increase from 2008 [1]. This number will continue to increase globally due to an aging population and the ongoing obesity pandemic [2,3]. The ubiquity of these procedures correlates strongly with their burden on health care systems globally. In the United States, approximately 5% of the gross domestic product is to care for musculoskeletal conditions [4,5]. Despite this spending, wait times for elective surgical procedures in OECD countries continue to increase, conferring extended periods of time with poor quality of life for TKA and THA patients [6,7]. For these reasons, there is a growing interest and research into improving the efficiency and cost-effectiveness of arthritis care [8,9].
Most research has focused purely on the prediction of duration of surgery (DOS) or the optimization of operating room scheduling, ignoring their inherent interrelation [10-14]. More recently, these approaches have been combined to plan post-surgical beds and plan emergency surgeries based on predicted priority with varying results [15,16]. DOS prediction models typically represent a large volume of varying procedures, spanning multiple surgical specialties with limited practical applications. Classic regression modeling in orthopedics has identified age, BMI, surgical procedure, primary or revision, and gender as important variables affecting DOS predictions [17,18]. Machine learning (ML) models have been applied to predict DOS for various surgeries [10,12,19-24]. However, in practice, mean time or surgeon-specific rolling mean time is typically used to generate schedules at the operational level.
Research evaluating the optimization of surgery scheduling has been performed using an average or a randomly sampled (typically from a lognormal distribution) DOS value prior to optimizing a schedule through integer linear programming based on either the multiple knapsack or job-shop scheduling problem [25-27]. Stochastic programming and distributionally robust optimization have also been attempted to mitigate the effects of an uncertain DOS, but these approaches assume a distribution of DOS rather than using specific features to aid in prediction [28].
To our knowledge, no prior work has combined patient-level DOS predictions with schedule optimization to create an optimized surgical schedule at the operational level. It is known that neural networks are strong predictors of DOS; however, their realizable improvements when implemented over various surgical schedule optimization problems, while performing simulations accounting for real-world constraints, remain unclear [23,24]. The primary aim of this paper was to determine if a 2-stage approach using an ML model for prediction of DOS paired with schedule optimization improves operating room overutilization or underutilization compared to using the mean DOS. Secondary objectives were to determine the effect of schedule granularity and length of surgeon waitlist on scheduling accuracy.
DiscussionThis paper compared 3 different scheduling optimization problems and evaluated a novel approach to surgical scheduling for TKAs and THAs using a combined 2-stage ML DOS prediction and optimization. There was no significant difference in operating room underutilization or overtime between the MSSP (one surgeon designated to one operating room per day) or Split (maximum of 2 surgeons designated for 1 operating room per day) optimization formulations. However, both performed significantly better than the Any (no limit on surgeons per operating room per day) formulation.
We believe this is due to the limitations of the predictions: underestimating the DOS of 1 case c being performed by surgeon h in room r can have cascading effects on another room r′ in which the same surgeon h is due to perform another surgery c′ at a later time. This causes additional overtime penalties for “Any,” something that the more restrictive “Split” and “MSSP” do not encounter. This is why, despite optimal solutions to “Any” being theoretically better than those of “Split,” they performed worse when simulated with the actual DOS.
Overall, the combined 2-stage approach significantly outperformed the current standard for scheduling cases, which is a case-specific mean surgery duration. This performance improvement was maintained across all schedule parameter combinations, including different schedule block granularity and different patient waitlist sizes considered. Despite this improvement, the 2-stage approach performed considerably worse than the hindsight schedule, highlighting the limitations of the current predictions that are based solely on preoperative patient data. Interestingly, there was no impact on overtime by varying schedule granularity or waitlist size; however, both of these impacted the amount of underutilization. The smaller waitlist size of 2 weeks of considered cases had a greater amount of underutilization, which was likely due to surgeons not having enough cases to fill their operating room time. Once a threshold was met at a 4-week pool of cases, there was no difference between groups. Also notable was the fact that when only considering a 2-week pool of cases, the Split optimization formulation outperformed MSSP, likely due to some surgeons not having enough cases to fill their time. Therefore, as the MSSP formulation is most practically implementable, it must be ensured that either the considered case pool is large enough or surgeons are allocated time when they have enough cases to fill an entire operating room day to avoid underutilization.
Errors in procedure length estimation by clinicians occur in approximately 75% of cases, with 32%‐50% of daily operating room schedules being underbooked and 37%‐42% overbooked [34,35]. This is compounded by the fact that less than 50% of operating time is spent doing surgery [34]. Booking based on a historical mean is more accurate than when estimated by the surgical team, though less accurate than traditional ML approaches [10,36-38]. Previous approaches using computing to improve surgical scheduling have included schedule optimization or ML to predict DOS in isolation [13,21,27,37,39,40]. Other approaches to scheduling operating room utilization include the use of surgeon-specific mean DOS or a surgeon case-specific rolling average time. To our knowledge, these have not been compared to an ML prediction-based approach. Due to the lack of surgeon-specific details included in the ACS NSQIP dataset, we could not assess the efficacy of these approaches in the present study.
The implementation of this predict-then-optimize scheduling approach would face several challenges in the real world. The MSSP optimization model is in line with current surgical scheduling practices at most hospitals. This formulation optimizes a specific surgeon’s waiting list, increasing their ability to accurately plan their day while ensuring a fair distribution of time (by operating room days) for each surgeon. However, attempting to implement the other optimization formulations (Split and Any) may be faced with resistance by end-users. Particularly, using the Any formulation, surgeons may have cases at the beginning and end of the day spread out across more days in a week. ML-predicted DOS has been trialed previously in operating room planning by one group that found a reduction in wait time between cases [41]. However, they generated the predicted DOS and evaluated the implications of that information over a single day, not considering other cases from the waitlist or optimizing the schedule based on the predicted DOS.
In addition to improving operating room utilization at the systems level, the present study has implications for surgeon-level daily planning. Accurate patient-specific DOS prediction and scheduling allow for more effective personal scheduling, including preoperative preparation, intraoperative workflow, and postoperative responsibilities. Accurate DOS predictions can assist surgeons in anticipating the need for ancillary support (eg, anesthesia, nursing, imaging) and have the potential to help decrease fatigue associated with unplanned overruns. When integrated into scheduling systems that allocate block time based on surgeon-specific waitlists (as in the MSSP formulation), this can enhance both surgeon efficiency and case throughput, aligning institutional resource allocation with the surgeon’s realistic operative capacity.
The generated models and optimization formulations have the ability to transform how elective operating room scheduling is performed. By developing models specific to each operation, this increases the accuracy of each model. Most previous research evaluating the effect of ML for DOS prediction has grouped multiple different procedures [21,37]. Using such models, the procedure performed would generally be the most important feature, diluting the effect of other important patient factors without using appropriate ML techniques. The potential for cost savings for hospitals, related to reduction in overtime costs and valuable underused operating room time, is high, but the main limitation lies in the accuracy of the DOS prediction. The predictive models for TKA and THA included 33 individual patient features. Improving the model with the use of operational factors from a specific institution would likely have a corresponding effect on the schedule results but would reduce the generalizability of the approach. Further improvements may also be made by directly integrating the downstream scheduling optimization problem into training the predictive ML model [42].
This work presents some limitations. First, the DOS prediction was restricted to preoperative patient factors, based on the availability of data elements in the ACS NSQIP database, limiting the prediction accuracy. This was evidenced by the large difference in schedule performance between the 2-stage method and the perfect, hindsight, schedule. Nevertheless, this approach to predicting DOS still yielded improved schedules as compared to using a surgery-specific mean time estimate. Second, the goal of our optimization problem was to maximize the utilization of the operating room; however, this may not be directly in line with the goals of all hospitals, as some institutions may have other priorities, such as maximizing the number of cases completed. This project only developed predictive models for primary TKA and THA procedures, which may have artificially lowered the potential effect size of using this approach, as these are relatively routine procedures with lower DOS variability. By generating more surgery-specific predictive models within orthopedic surgery or other specialties, the potential for this approach may be even larger. However, these results are more directly applicable to high-volume arthroplasty surgical centers. Additionally, this scheduling approach was a simplified proof-of-concept model that may not be applicable to more complex, real-world scheduling scenarios. For example, it did not consider downstream constraints, such as the number of recovery beds, ward beds, or available staff. This was not a concern at our local institution due to its relative efficiency as a high-volume arthroplasty center. However, this would need to be expanded upon in future work if this is to be practically implemented in less specialized centers. Finally, the Split and Any optimization problems were computationally intensive when considering a waiting list size of 2‐3 months of patients. This may be a consideration depending on institutional computational resources, which is worth noting when implementing a similar solution.
In conclusion, using ML patient-specific DOS predictions coupled with optimization was superior to elective scheduling based on a mean DOS metric over 3 different optimization problems with varying constraints and combinations of waitlist size and granularity. This generalizable approach suggests that improvements in hospital resource utilization are possible with the application of new computational methods, but the inclusion of institution-specific operational data may be considered to further improve predictions and scheduling. This has significant potential implications for health care systems struggling with pressures of rising costs and growing operative waitlists.