In this article, we analyze a discrete‐time queue that is motivated from studying hospital inpatient flow management, where the customer count process captures the midnight inpatient census. The ...stationary distribution of the customer count has no explicit form and is difficult to compute in certain parameter regimes. Using the Stein's method framework, we identify a continuous random variable to approximate the steady‐state customer count. The continuous random variable corresponds to the stationary distribution of a diffusion process with state‐dependent diffusion coefficients. We characterize the error bounds of this approximation under a variety of system load conditions—from lightly loaded to heavily loaded. We also identify the critical role that the service rate plays in the convergence rate of the error bounds. We perform extensive numerical experiments to support the theoretical findings and to demonstrate the approximation quality. In particular, we show that our approximation performs better than those based on constant diffusion coefficients when the number of servers is small, which is relevant to decision making in a single hospital ward.
One key factor contributing to emergency department (ED) overcrowding is prolonged waiting time for admission to inpatient wards, also known as ED boarding time. To gain insights into reducing this ...waiting time, we study operations in the inpatient wards and their interface with the ED. We focus on understanding the effect of inpatient discharge policies and other operational policies on the time-of-day waiting time performance, such as the fraction of patients waiting longer than six hours in the ED before being admitted. Based on an empirical study at a Singaporean hospital, we propose a novel stochastic processing network with the following characteristics to model inpatient operations: (1) A patient's service time in the inpatient wards depends on that patient's admission and discharge times and length of stay. The service times capture a two-time-scale phenomenon and are not independent and identically distributed. (2) Pre-and post-allocation delays model the extra amount of waiting caused by secondary bottlenecks other than bed unavailability, such as nurse shortage. (3) Patients waiting for a bed can overflow to a nonprimary ward when the waiting time reaches a threshold, where the threshold is time dependent. We show, via simulation studies, that our model is able to capture the inpatient flow dynamics at hourly resolution and can evaluate the impact of operational policies on both the daily and time-of-day waiting time performance. In particular, our model predicts that implementing a hypothetical policy can eliminate excessive waiting for those patients who request beds in mornings. This policy incorporates the following components: a discharge distribution with the first discharge peak between 8 A.M. and 9 A.M. and 26% of patients discharging before noon, and constant-mean allocation delays throughout the day. The insights gained from our model can help hospital managers to choose among different policies to implement depending on the choice of objective, such as to reduce the peak waiting in the morning or to reduce daily waiting time statistics.
One of the most important decisions a hospitalist makes at the intersection of cost and quality of care is when to discharge a patient from the hospital. Keeping patients longer (shorter) increases ...(decreases) overcrowding and hospital costs but also decreases (increases) readmission risk. Here a long-run average cost optimization problem for determining on each day who and how many patients to discharge is developed. The authors combined structural properties of the model with an analytical solution for a special cost structure to approximately solve the high-dimensional Markov decision process. This transformed the originally intractable problem into a simple univariate optimization problem that can be solved efficiently yet allowed capture of time nonstationarity and fully heterogeneous inpatient populations, where each patient has a personalized risk trajectory. Moreover, the authors took one step beyond theory and implemented their discharge decision support tool in a partner hospital. For the tool to be properly parametrized and implementable, the authors developed a model to predict readmission risk as a function of length of stay that integrated several statistical methods in a novel manner. The resulting implementation was described as a showcase, demonstrating the tool’s applicability for integration with general hospital data systems and workflows.
When to discharge a patient plays an important role in hospital patient flow management and the quality of care and patient outcomes. In this work, we develop and implement a data-integrated decision support framework to aid hospitals in managing the delicate balance between readmission risk at discharge and ward congestion. We formulate a large-scale Markov decision process (MDP) that integrates a personalized readmission prediction model to dynamically prescribe both how many and which patients to discharge on each day. Because of patient heterogeneity and the fact that length of stay is not memoryless, the MDP has the curse of dimensionality. We leverage structural properties and an analytical solution for a special cost setting to transform the MDP into a univariate optimization; this leads to a novel, efficient dynamic heuristic. Furthermore, for our decision framework to be implementable in practice, we build a unified prediction model that integrates several statistical methods and provides key inputs to the decision framework; existing off-the-shelf readmission prediction models alone could not adequately parametrize our decision support. Through extensive counterfactual analyses, we demonstrate the value of our discharge decision tool over our partner hospital’s historical discharge behavior. We also obtain generalizable insights by applying the tool to a broad range of hospital types through a high-fidelity simulation. Last, we showcase an implementation of our tool at our partner hospital to demonstrate broader applicability through our framework’s
plug-and-play
design for integration with general hospital data systems and workflows.
BACKGROUND:In previous studies, hospitals’ operating room (OR) schedules were influenced markedly by decisions made within a few days of surgery. At an academic hospital, 46% of ORs had their last ...case scheduled or changed within 1 working day of surgery, and a private hospital had 64%. Many of these changes were for patients who were admitted before surgery (i.e., inpatient cases). In this study, we investigate the impact on OR productivity of how cases are scheduled within 1 working day before the day of surgery.
METHODS:We consider the case-scheduling choice between 2 ORs. We compare 3 scheduling policiesBest Fit Descending, Worst Fit Descending, and Worst Fit Ascending. “Descending” strategies consider new cases from longest to shortest, whereas “Ascending” considers new cases from shortest to longest. Best Fit schedules each new case into the OR with sufficient but the least remaining underutilized OR time for the case. Worst Fit does the same but with the most remaining time. For our application, Best Fit chooses a later start time, whereas Worst Fit chooses an earlier start time. In our computational model, cases are of 2 possible durations, brief or long. Case cancellation is incorporated explicitly, and the number of new cases to schedule depends on the current number of scheduled cases in each OR, both new from previous studies. The number of cases in each OR is modeled as a Markov chain, evolving between 2 periods, corresponding to 1 day and 0 days before the day of surgery. For each scheduling policy, we evaluate the mean overutilized OR time and productivity. Our sensitivity analyses cover many cancellation rates, arrival settings, case durations, and initial conditions (i.e., how cases are scheduled into the 2 ORs preceding 1 workday before the day of surgery).
RESULTS:Best Fit Descending and Worst Fit Descending achieved almost the same overutilized time and productivity. Worst Fit Ascending caused greater overutilized time (as much as 6.6 minutes more per OR) and thus lesser productivity (as much as 1.6% less) compared with Best Fit Descending or Worst Fit Descending. When the staff were scheduled for less time than the optimal allocated OR time, there were nearly the same differences between the staff productivity resulting from the use of Worst Fit Ascending rather than Worst Fit Descending or Best Fit Descending.
CONCLUSIONS:Scheduling office decision making within 1 day before surgery should be based on statistical forecasts of expected total OR workload (i.e., forecasts that include the addition of non-elective cases and the subtraction of cases that cancel). As long as a case is not scheduled into overutilized time when less overutilized time could be achieved in another OR, and cases are considered in descending sequence of scheduled durations, the differences in overutilized time and productivity among the scheduling policies are small. Cognitive bias in staff scheduling causes a significant reduction in productivity, but the differences among scheduling policies are nearly the same as when there is no bias.
We analyze a time-varying
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queueing system. The arrival process is periodic Poisson. The service time of a customer has components in different time scales: length of stay ...(LOS) in days and departure time (
h
dis
) in hours. This queueing system has been used to study patient flows from the emergency department (ED) to hospital inpatient wards. In that setting, the LOS of a patient is simply the number of days she spends in a ward, and her departure time
h
dis
is the discharge hour on the day of her discharge.
We develop a new analytical framework that can perform exact analysis on this novel queueing system. This framework has two steps: first analyze the midnight customer count process and obtain its stationary distribution, then analyze the time-dependent customer count process to compute various performance measures. We also develop approximation tools that can significantly reduce the computational time. In particular, via Stein’s method, we derive explicit expressions to approximate the stationary distribution of the midnight count. We provide error bounds for these approximations and numerically demonstrate that they are remarkably accurate for systems with various sizes and load conditions. Our theoretical and numerical analysis have produced a number of insights that can be used to improve hospital inpatient flow management. We find that the LOS term affects the overnight wait caused by the mismatch between daily arrivals and discharges, whereas the
h
dis
term affects the intraday wait caused by the nonsynchronization between the arrival and discharge time patterns. Thus, reducing LOS or increasing capacity can impact the daily average performance significantly; shifting the discharge timing to earlier times of a day can alleviate the peak congestion in the morning and mainly affects the time-dependent performance.
The e-companion is available at
https://doi.org/10.1287/opre.2016.1566
.
We performed a descriptive study of operating room (OR) case scheduling within 1 week of the day of surgery.
The data used were from the case scheduling and transaction audit tables of a hospital's ...anesthesia and OR information management systems. Each change to a scheduled case in the OR information system was captured in an audit table, including the date and time when the change was made. The timestamps allowed reconstruction of the elective OR schedule for each date of surgery at preceding dates (e.g., 2 workdays ahead). The sample size was n = 17 consecutive 4-week periods. The allocated OR time, for each combination of service and day of the week, was the number of hours that minimized the inefficiency of use of OR time, a weighted combination of the hours of underutilized OR time and the more expensive hours of overutilized OR time. Data are reported as mean ±SE.
(1) The percentage of OR date combinations with at least 1 add-on case was 24.1% ± 0.3%. The most recent addition of a case to an OR occurred 1 working day before surgery for 22.3% ± 0.4% of OR date combinations. At least half (51.5% ± 0.5%) of ORs had its last case scheduled or changed within 2 working days of surgery. In addition, when allocated OR time was filled and the service scheduled additional case(s), the median time ahead when each such case was scheduled was 2.2 ± 0.2 workdays. Thus, managers can productively focus on the day of surgery starting 2 working days before surgery. (2) Once allocated time was full, the ratio of the net additional cases scheduled to the total number performed was 1.2% ± 0.6%. However, 11.1% ± 1.7% of the total were additional cases. Thus, schedulers should rely on the allocated time to be predictive of the actual (net) workload that will occur in the future, on the day of surgery. (3) For service and day combinations for which 2 working days ahead the scheduled hours exceeded the allocated hours, there was no significant net increase in minutes of cases scheduled (P = 0.79), unlike when the scheduled hours were less than allocated (P < 0.0001). Thus, additional hours of cases scheduled within the same number of workdays are heterogeneous both within and among services based on the prior hours of cases scheduled.
Planning anesthesia assignments, ORs to target, etc., can be done productively starting 2 working days ahead of surgery. There are so many changes to the OR schedule those last 2 workdays that anesthesia groups should be engaged with the scheduling office during that period. The primary predictor of additional net hours of cases to be scheduled is the difference between the allocated (i.e., forecasted) OR time and the hours scheduled so far.
At the onset of the COVID‐19 pandemic, hospitals were in dire need of data‐driven analytics to provide support for critical, expensive, and complex decisions. Yet, the majority of analytics being ...developed were targeted at state‐ and national‐level policy decisions, with little availability of actionable information to support tactical and operational decision‐making and execution at the hospital level. To fill this gap, we developed a multi‐method framework leveraging a parsimonious design philosophy that allows for rapid deployment of high‐impact predictive and prescriptive analytics in a time‐sensitive, dynamic, data‐limited environment, such as a novel pandemic. The product of this research is a workload prediction and decision support tool to provide mission‐critical, actionable information for individual hospitals. Our framework forecasts time‐varying patient workload and demand for critical resources by integrating disease progression models, tailored to data availability during different stages of the pandemic, with a stochastic network model of patient movements among units within individual hospitals. Both components employ adaptive tuning to account for hospital‐dependent, time‐varying parameters that provide consistently accurate predictions by dynamically learning the impact of latent changes in system dynamics. Our decision support system is designed to be portable and easily implementable across hospital data systems for expeditious expansion and deployment. This work was contextually grounded in close collaboration with IU Health, the largest health system in Indiana, which has 18 hospitals serving over one million residents. Our initial prototype was implemented in April 2020 and has supported managerial decisions, from the operational to the strategic, across multiple functionalities at IU Health.
The gap between medical research on diagnostic testing and clinical workflow can lead to rejection of valuable medical research in a busy clinical environment due to increased workloads, or rejection ...of medical research in the laboratory that may be valuable in practice due to a misunderstanding of the system‐level benefits of the new test. This has implications for research organizations, diagnostic test manufacturers, and hospital managers among others. To bridge this gap, we develop a Markov decision process (MDP) from which we create “adoption regions” that specify the combination of test characteristics medical research must achieve for the test to be feasible for adoption in practice. To address the curse of dimensionality from patient risk stratification, we develop a decomposition algorithm along with structural properties that shed light on which patients and when a new diagnostic test should be used. In a case study of a partner Emergency Department, we show that the conventional myopic medical criterion can lead to poor decision making in both research development and clinical practice. In particular, we find that specificity—long a secondary consideration and often overlooked in the research process—is, in fact, the key to effective implementation of new tests into clinical environments. This myopic approach can lead to overvaluing or undervaluing new medical research. This mismatch is accentuated when a simple (current) policy is used to integrate research into the clinical environment compared with our MDP’s policy—poor implementation of a new test can also lead to unnecessary rejection. Our framework provides easily interpretable guidelines for medical research development and clinical adoption decisions that can guide medical research as to which test characteristics to focus on to improve the chances of adoption.
Introduction When the hospital census is high, perioperative medical directors or operating room (OR) managers may need to consider postponing some surgical cases scheduled to be performed within the ...next three workdays. This scenario has arisen at hospitals in regions with large increases in admissions due to coronavirus disease 2019 (COVID-19). We compare summary measures for hospital length of stay (LOS) to guide the OR manager having to decide which cases may need to be postponed to ensure a sufficient reserve of available inpatient beds. Methods We studied the 1,201,815 ambulatory and 649,962 inpatient elective cases with a major therapeutic procedure performed during 2018 at all 412 non-federal hospitals in Florida. The data were sorted by the hospital, and then by procedure category. Statistical comparisons of LOS were made pairwise among all procedure categories with at least 100 cases at (the) each hospital, using the chi-square test (LOS ≤ 1 day versus LOS > 1 day), Student's t-test with unequal variances, and the Wilcoxon-Mann-Whitney test. The comparisons among the three tests then were repeated having sorted the data by procedure category and making statistical comparisons among all hospitals with at least 100 cases for the procedure category. Results Whether using a criterion for statistical significance of P < 0.05 or P < 0.01, and whether compared with Student's t-test with unequal variances or Wilcoxon-Mann-Whitney test, the chi-square test had greater odds (i.e., greater statistical power) to detect differences in LOS (all four with P
< 0.0001 and all 95% lower confidence limits for odds ratios ≥ 3.00). The findings were consistent when the data, first sorted by procedure category and then by probability distributions of LOS, were compared between hospitals (all P < 0.0001 and the 95% lower confidence limits for odds ratio ≥ 3.72). Conclusions For purposes of comparing procedure categories pairwise at the same hospital, there was no loss of information by summarizing the probability distributions using single numbers, the percentages of cases among patients staying longer than overnight. This finding substantially simplifies the mathematics for constructing dashboards or summaries of OR information system data to help the perioperative OR manager or medical director decide which cases may need to be postponed, when the hospital census is high, to provide a sufficient reserve of inpatient hospital beds.
When the hospital census is high, perioperative medical directors or operating room (OR) managers sometimes need to review with surgical departments as to which surgical cases scheduled to be ...performed within the next three days may need to be postponed. Although distributions of hospital length of stay (LOS) are highly skewed, a surprisingly effective summary measure is the percentage of patients previously undergoing the same category of procedure as that scheduled whose LOS was zero or one day. We evaluated how to forecast each hospital's percentage of cases with LOS of <2 days, segmented by category of surgical procedure. The large teaching hospital studied included several inpatient adult surgical suites, an ambulatory surgery center, and a pediatric surgical suite.
We included 98,540 cases in a training dataset to predict 24,338 cases in a test dataset. For each category of procedure, we calculated the cumulative count of cases among quarters, from the most recent quarter, second most recent quarter, and so forth up to the quarter resulting in at least 800 cases. If every quarter combined had fewer than 800 cases for a given category of procedure, we included all cases for that category. For each combination of category and quarter, we used the cumulative counts of cases and cases with LOS of <2 days, excluding the current quarter. Then, for each category of procedure, and for each of the preceding quarters included for the category, we used the cumulative counts to calculate the asymptotic standard error (SE) for the proportion of cases with LOS of <2 days. If all preceding quarters combined provided a sample size such that the estimated SE for the proportion exceeded 1.25%, we included all preceding quarters. The observed absolute percentage error was 0.76% (SE: 0.12%). This error was nearly 100-fold smaller than the percentage of cases to which it would be used (i.e., 0.76% versus 73.1% with LOS of <2 days). The principal weakness of the forecasting methodology was a small bias caused by a progressive reduction in the overall LOS over time. However, this bias is unlikely to be important for predicting cases’ LOS when the hospital census is high. When performing these time series calculations quarterly, a reasonable approach is to perform calculations of both case counts and SEs for each category of procedure. We recommend using the fewest historical quarters, starting with the most recent quarter, either with at least 800 cases or an estimated asymptotic SE for the estimated percentage no greater than 1.25%. Applying our methodology with local LOS data will allow OR managers to estimate the number of patients on the elective OR schedule each day who will be hospitalized for longer than overnight, facilitating communication and decision-making with surgical departments when census considerations constrain the ability to run a full surgical schedule.
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