Mathematical modelling and simulation for planning critical care capacity

Merging of two level-1 trauma centers in Amsterdam: premerger demand in integrated acute trauma care

PURPOSE

Availability of adequate and appropriate trauma care is essential. A merger of two Dutch academic level-1 trauma centers is upcoming. However, in the literature, volume effects after a merger are inconclusive. This study aimed to examine the premerger demand for level-1 trauma care on integrated acute trauma care and evaluate the expected demand on the system.

METHODS

A retrospective observational study was conducted between 1-1-2018 and 1-1-2019 in two level-1 trauma centers in the Amsterdam region using data derived from the local trauma registries and electronic patient records. All trauma patients presented at both centers' Emergency Departments (ED) were included. Patient- and injury characteristics and data concerning all prehospital and in-hospital-delivered trauma care were collected and compared. Pragmatically, the demand for trauma care in the post-merger setting was considered a sum of care demand for both centers.

RESULTS

In total, 8277 trauma patients were presented at both EDs, 4996 (60.4%) at location A and 3281 (39.6%) at location B. Overall, 462 patients were considered severely injured patients (Injury Severity Score ≥ 16). In total, 702 emergency surgeries (< 24 h) were performed, and 442 patients were admitted to the ICU. The sum care demand of both centers resulted in a 167.4% increase in trauma patients and a 151.1% increase in severely injured patients. Moreover, on 96 occasions annually, two or more patients within the same hour would require advanced trauma resuscitation by a specialized team or emergency surgery.

CONCLUSION

A merger of two Dutch level-1 trauma centers would, in this scenario, result in a more than 150% increase in the post-merger setting's demand for integrated acute trauma care.

Flow-Sizing Critical Care Resources

OBJECTIVES

To describe the factors affecting critical care capacity and how critical care organizations (CCOs) within academic centers in the U.S. flow-size critical care resources under normal operations, strain, and surge conditions.

DATA SOURCES

PubMed, federal agency and American Hospital Association reports, and previous CCO survey results were reviewed.

STUDY SELECTION

Studies and reports of critical care bed capacity and utilization within CCOs and in the United States were selected.

DATA EXTRACTION

The Academic Leaders in the Critical Care Medicine Task Force established regular conference calls to reach a consensus on the approach of CCOs to "flow-sizing" critical care services.

DATA SYNTHESIS

The approach of CCOs to "flow-sizing" critical care is outlined. The vertical (relation to institutional resources, e.g., space allocation, equipment, personnel redistribution) and horizontal (interdepartmental, e.g., emergency department, operating room, inpatient floors) integration of critical care delivery (ICUs, rapid response) for healthcare organizations and the methods by which CCOs flow-size critical care during normal operations, strain, and surge conditions are described. The advantages, barriers, and recommendations for the rapid and efficient scaling of critical care operations via a CCO structure are explained. Comprehensive guidance and resources for the development of "flow-sizing" capability by a CCO within a healthcare organization are provided.

CONCLUSIONS

We identified and summarized the fundamental principles affecting critical care capacity. The taskforce highlighted the advantages of the CCO governance model to achieve rapid and cost-effective "flow-sizing" of critical care services and provide recommendations and resources to facilitate this capability. The relevance of a comprehensive approach to "flow-sizing" has become particularly relevant in the wake of the latest COVID-19 pandemic. In light of the growing risks of another extreme epidemic, planning for adequate capacity to confront the next critical care crisis is urgent.

A systematic review of the prediction of hospital length of stay: Towards a unified framework

Hospital length of stay of patients is a crucial factor for the effective planning and management of hospital resources. There is considerable interest in predicting the LoS of patients in order to improve patient care, control hospital costs and increase service efficiency. This paper presents an extensive review of the literature, examining the approaches employed for the prediction of LoS in terms of their merits and shortcomings. In order to address some of these problems, a unified framework is proposed to better generalise the approaches that are being used to predict length of stay. This includes the investigation of the types of routinely collected data used in the problem as well as recommendations to ensure robust and meaningful knowledge modelling. This unified common framework enables the direct comparison of results between length of stay prediction approaches and will ensure that such approaches can be used across several hospital environments. A literature search was conducted in PubMed, Google Scholar and Web of Science from 1970 until 2019 to identify LoS surveys which review the literature. 32 Surveys were identified, from these 32 surveys, 220 papers were manually identified to be relevant to LoS prediction. After removing duplicates, and exploring the reference list of studies included for review, 93 studies remained. Despite the continuing efforts to predict and reduce the LoS of patients, current research in this domain remains ad-hoc; as such, the model tuning and data preprocessing steps are too specific and result in a large proportion of the current prediction mechanisms being restricted to the hospital that they were employed in. Adopting a unified framework for the prediction of LoS could yield a more reliable estimate of the LoS as a unified framework enables the direct comparison of length of stay methods. Additional research is also required to explore novel methods such as fuzzy systems which could build upon the success of current models as well as further exploration of black-box approaches and model interpretability.

Balancing scarce hospital resources during the COVID-19 pandemic using discrete-event simulation

COVID-19 has disrupted healthcare operations and resulted in large-scale cancellations of elective surgery. Hospitals throughout the world made life-altering resource allocation decisions and prioritised the care of COVID-19 patients. Without effective models to evaluate resource allocation strategies encompassing COVID-19 and non-COVID-19 care, hospitals face the risk of making sub-optimal local resource allocation decisions. A discrete-event-simulation model is proposed in this paper to describe COVID-19, elective surgery, and emergency surgery patient flows. COVID-19-specific patient flows and a surgical patient flow network were constructed based on data of 475 COVID-19 patients and 28,831 non-COVID-19 patients in Addenbrooke's hospital in the UK. The model enabled the evaluation of three resource allocation strategies, for two COVID-19 wave scenarios: proactive cancellation of elective surgery, reactive cancellation of elective surgery, and ring-fencing operating theatre capacity. The results suggest that a ring-fencing strategy outperforms the other strategies, regardless of the COVID-19 scenario, in terms of total direct deaths and the number of surgeries performed. However, this does come at the cost of 50% more critical care rejections. In terms of aggregate hospital performance, a reactive cancellation strategy prioritising COVID-19 is no longer favourable if more than 7.3% of elective surgeries can be considered life-saving. Additionally, the model demonstrates the impact of timely hospital preparation and staff availability, on the ability to treat patients during a pandemic. The model can aid hospitals worldwide during pandemics and disasters, to evaluate their resource allocation strategies and identify the effect of redefining the prioritisation of patients.

Intensive Care Unit Bed Utilization and Head Injury Burden in a Resource-Poor Setting

INTRODUCTION

In high-income countries (HICs), the intensive care unit (ICU) bed density is approximately 20-32 beds/100 000 population compared with countries in sub-Saharan Africa, like Malawi, with an ICU bed density of 0.1 beds/100 000 population. We hypothesize that the ICU bed utilization in Malawi will be high.

METHODS

This is an observational study at a tertiary care center in Malawi from August 2016 to May 2018. Variables used to evaluate ICU bed utilization include ICU length of stay (LOS), bed occupancy rates (average daily ICU census/number of ICU beds), bed turnover (total number of admissions/number of ICU beds), and turnover intervals (number of ICU bed days/total number of admissions - average ICU LOS).

RESULTS

494 patients were admitted to the ICU during the study period. The average LOS during the study period was 4.8 ± 6.0 days. Traumatic brain injury patients had the most extended LOS (8.7 ± 6.8 days) with a 49.5% ICU mortality. The bed occupancy rate per year was 74.7%. The calculated bed turnover was 56.5 persons treated per bed per year. The average turnover interval, defined as the number of days for a vacant bed to be occupied by the successive patient admission, was 1.63 days.

CONCLUSION

Despite the high burden of critical illness, the bed occupancy rates, turn over days, and turnover interval reveal significant underutilization of the available ICU beds. ICU bed underutilization may be attributable to the absence of an admission and discharge protocols. A lack of brain death policy further impedes appropriate ICU utilization.

Prediction of mortality in Intensive Care Units: a multivariate feature selection

CONTEXT

The critical nature of patients in Intensive Care Units (ICUs) demands intensive monitoring of their vital signs as well as highly qualified professional assistance. The combination of these needs makes ICUs very expensive, which requires investment to be prioritized. Administrative issues emerge, and health institutions face dilemmas such as: "How many beds should an ICU provide to serve the population, at the lowest costs" and "Which is the most critical body information to monitor in an ICU?". Due to financial and ethical implications, these judgments require technical and precise knowledge. Decisions have usually relied on clinical scores, like the APACHE (Acute Physiology And Chronic Health Evaluation) and SOFA (Sequential Organ Failure Assessment) scores, which are imprecise and outdated. The popularization of machine learning techniques has shed some light on the topic as a way to renew score purposes. In 2012, the PhysioNet/Computing in Cardiology launched the Challenge - ICU Patients. This Challenge aimed to stimulate the development of techniques to predict mortality in ICUs. Based on biometric and physiological features collected from patients, the participants predicted the patient's death risk by using their classifiers. Several participants achieved results that were better than the results produced by the SOFA and the APACHE scores; the prediction levels were ≈54%, which is weak.

OBJECTIVES

Here, we investigate the reasons that led to these results as a means to ground our solution. Then, we propose alternative practices in an attempt to improve the results. Our main goal is to improve the prediction of mortality in ICUs by using the same data employed during the 2012 PhysioNet Challenge. Our specific objectives are (i) to simplify the problem by reducing the dimensionality; (ii) to reduce the uncontrolled variance, and (iii) to make classifiers less dependent on the training set.

METHODS

Accordingly, we propose a methodology based on extensive steps, including sample filter and data normalization. To select features and to reduce the intra-group variance, we employ multivariate data analysis by using Principal Component Analysis, Factor Analysis, Spectral Clustering, and Tukey's HSD Test, recursively. After that, we use machine learning techniques to create classifiers according to different methods. We evaluate our results with the same metrics proposed by the 2012 PhysioNet Challenge.

RESULTS

For classifiers constructed and tested by using independent datasets, our best classifier was a linear SVM, which provided results of ≈0.73. These results were significantly better than the ≈0.54 achieved in previous work at >99% confidence interval. Furthermore, our approach only demanded twelve features, which was consistently smaller than the number of features required by the previous approaches.

CONCLUSION

Our results indicated that our approach presented: (a) higher performance to predict death risks (+20%); (b) smaller dependence on the training set; and (c) lower costs for ICU monitoring (few features). Besides the better prediction power, our approach also demanded lower costs for implementation and a more extensive range of potential ICUs. Future studies should employ our proposal to investigate the possibility of including some physiological features that were not available for the 2012 PhysioNet Challenge.

[Model for a threshold of daily rate reduction of COVID-19 cases to avoid hospital collapse in Chile]

Using a mathematical model, we explore the problem of availability versus overdemand of critical hospital processes (e.g., critical beds) in the face of a steady epidemic expansion such as is occurring from the COVID-19 pandemic. In connection with the statistics of new cases per day, and the assumption of maximum quota, the dynamics associated with the variables number of hospitalized persons (critical occupants) and mortality in the system are explored. A parametric threshold condition is obtained, which involves a parameter associated with the minimum daily effort for not collapsing the system. To exemplify, we include some simulations for the case of Chile, based on a parameter of effort to be sustained with the purpose of lowering the daily infection rate.

A decision support simulation model for bed management in healthcare

PURPOSE

In order to provide access to care in a timely manner, it is necessary to effectively manage the allocation of limited resources. such as beds. Bed management is a key to the effective delivery of high quality and low-cost healthcare. The purpose of this paper is to develop a discrete event simulation to assist in planning and staff scheduling decisions.

DESIGN/METHODOLOGY/APPROACH

A discrete event simulation model was developed for a hospital system to analyze admissions, patient transfer, length of stay (LOS), waiting time and queue time. The hospital system contained 50 beds and four departments. The data used to construct the model were from five years of patient records and contained information on 23,019 patients. Each department's performance measures were taken into consideration separately to understand and quantify the behavior of departments individually, and the hospital system as a whole. Several scenarios were analyzed to determine the impact on reducing the number of patients waiting in queue, waiting time and LOS of patients.

FINDINGS

Using the simulation model, it was determined that reducing the bed turnover time by 1 h resulted in a statistically significant reduction in patient wait time in queue. Further, reducing the average LOS by 10 h results in statistically significant reductions in the average patient wait time and average patient queue. A comparative analysis of department also showed considerable improvements in average wait time, average number of patients in queue and average LOS with the addition of two beds.

ORIGINALITY/VALUE

This research highlights the applicability of simulation in healthcare. Through data that are often readily available in bed management tracking systems, the operational behavior of a hospital can be modeled, which enables hospital management to test the impact of changes without cost and risk.

POLICY: A novel modelling technique to predict resource -requirements in critical care - a case study

Modelling is an under-used tool in the NHS operationally; this is primarily due to a lack of familiarity, but also due to the complex nature of the healthcare system, lack of sufficiently detailed data, and difficulties trying to distil the heterogeneity of individual patient experience into manageable groups.  This paper describes a model of patient flow and resource use on the critical care unit at Bradford Royal Infirmary, -produced using a novel technique which helps avoid these issues by using genuine routinely collected historical data in lieu of trying to model individual patients. This has had -unexpected benefits in terms of engagement with the model as it is much easier to justify its validity when it is based directly on real people.  Going forward, we will use this approach to model an entire hospital.

Simulation model of the relationship between cesarean section rates and labor duration

Cesarean delivery is the most common major abdominal surgery in many parts of the world, and it accounts for nearly one-third of births in the United States. For a patient who requires a C-section, allowing prolonged labor is not recommended because of the increased risk of infection. However, for a patient who is capable of a successful vaginal delivery, performing an unnecessary C-section can have a substantial adverse impact on the patient's future health. We develop two stochastic simulation models of the delivery process for women in labor; and our objectives are (i) to represent the natural progression of labor and thereby gain insights concerning the duration of labor as it depends on the dilation state for induced, augmented, and spontaneous labors; and (ii) to evaluate the Friedman curve and other labor-progression rules, including their impact on the C-section rate and on the rates of maternal and fetal complications. To use a shifted lognormal distribution for modeling the duration of labor in each dilation state and for each type of labor, we formulate a percentile-matching procedure that requires three estimated quantiles of each distribution as reported in the literature. Based on results generated by both simulation models, we concluded that for singleton births by nulliparous women with no prior complications, labor duration longer than two hours (i.e., the time limit for labor arrest based on the Friedman curve) should be allowed in each dilation state; furthermore, the allowed labor duration should be a function of dilation state.

Modeling the Length of Stay of Respiratory Patients in Emergency Department Using Coxian Phase-Type Distributions With Covariates

Variability and unpredictability are typical features of emergency departments (EDs) where patients randomly arrive with diverse conditions. Patient length of stay (LOS) represents the consumption level of hospital resources, and it is positively skewed and heterogeneous. Both accurate modeling of patient ED LOS and analysis of potential blocking causes are especially useful for patient scheduling and resource management. To tackle the uncertainty of ED LOS, this paper introduces two methods: statistical modeling and distribution fitting. The models are applied to 894 respiratory diseases patients data in the year 2014 from ED of a Chinese public tertiary hospital. Covariates recorded include patient region, gender, age, arrival time, arrival mode, triage category, and treatment area. A Coxian phase-type (PH) distribution model with covariates is proposed as an alternative method for modeling ED LOS. The expectation-maximization (EM) algorithm is used to implement parameter estimation. The results show that ED LOS data can be modeled well by the proposed models. Distributions of ED LOS differ significantly with respect to patients' gender, arrival mode, and treatment area. Using the fitted Coxian PH model will assist ED managers in identifying patients who are most likely to have an extreme ED LOS and in predicting the forthcoming workload for resources.

Operations research in intensive care unit management: a literature review

The intensive care unit (ICU) is a crucial and expensive resource largely affected by uncertainty and variability. Insufficient ICU capacity causes many negative effects not only in the ICU itself, but also in other connected departments along the patient care path. Operations research/management science (OR/MS) plays an important role in identifying ways to manage ICU capacities efficiently and in ensuring desired levels of service quality. As a consequence, numerous papers on the topic exist. The goal of this paper is to provide the first structured literature review on how OR/MS may support ICU management. We start our review by illustrating the important role the ICU plays in the hospital patient flow. Then we focus on the ICU management problem (single department management problem) and classify the literature from multiple angles, including decision horizons, problem settings, and modeling and solution techniques. Based on the classification logic, research gaps and opportunities are highlighted, e.g., combining bed capacity planning and personnel scheduling, modeling uncertainty with non-homogenous distribution functions, and exploring more efficient solution approaches.

Identifying seasonal and temporal trends in the pressures experienced by hospitals related to unscheduled care

BACKGROUND

As part of an electronic dashboard operated by Public Health Wales, senior managers at hospitals in Wales report daily "escalation" scores which reflect management opinion on the pressure a hospital is experiencing and ability to meet ongoing demand with respect to unscheduled care. An analysis was undertaken of escalation scores returned for 18 hospitals in Wales between the years 2006 and 2014 inclusive, with a view to identifying systematic temporal patterns in pressure experienced by hospitals in relation to unscheduled care.

METHODS

Exploratory data analysis indicated the presence of within-year cyclicity in average daily scores over all hospitals. In order to quantify this cyclicity, a Generalised Linear Mixed Model was fitted which incorporated a trigonometric function (sine and cosine) to capture within-year change in escalation. In addition, a 7-level categorical day of the week effect was fitted as well as a 3-level categorical Christmas holiday variable based on patterns observed in exploration of the raw data.

RESULTS

All of the main effects investigated were found to be statistically significant. Firstly, significant differences emerged in terms of overall pressure reported by individual hospitals. Furthermore, escalation scores were found to vary systematically within-year in a wave-like fashion for all hospitals (but not between hospitals) with the period of highest pressure consistently observed to occur in winter and lowest pressure in summer. In addition to this annual variation, pressure reported by hospitals was also found to be influenced by day of the week (low at weekends, high early in the working week) and especially low over the Christmas period but high immediately afterwards.

CONCLUSIONS

Whilst unpredictable to a degree, quantifiable pressure experienced by hospitals can be anticipated according to models incorporating systematic temporal patterns. In the context of finite resources for healthcare services, these findings could optimise staffing schedules and inform resource utilisation.

Forecasting Daily Patient Outflow From a Ward Having No Real-Time Clinical Data

Background: Modeling patient flow is crucial in understanding resource demand and prioritization. We study patient outflow from an open ward in an Australian hospital, where currently bed allocation is carried out by a manager relying on past experiences and looking at demand. Automatic methods that provide a reasonable estimate of total next-day discharges can aid in efficient bed management. The challenges in building such methods lie in dealing with large amounts of discharge noise introduced by the nonlinear nature of hospital procedures, and the nonavailability of real-time clinical information in wards.

A Conceptual Framework for Improving Critical Care Patient Flow and Bed Use

RATIONALE

High demand for intensive care unit (ICU) services and limited bed availability have prompted hospitals to address capacity planning challenges. Simulation modeling can examine ICU bed assignment policies, accounting for patient acuity, to reduce ICU admission delays.

OBJECTIVES

To provide a framework for data-driven modeling of ICU patient flow, identify key measurable outcomes, and present illustrative analysis demonstrating the impact of various bed allocation scenarios on outcomes.

METHODS

A description of key inputs for constructing a queuing model was outlined, and an illustrative simulation model was developed to reflect current triage protocol within the medical ICU and step-down unit (SDU) at a single tertiary-care hospital. Patient acuity, arrival rate, and unit length of stay, consisting of a "service time" and "time to transfer," were estimated from 12 months of retrospective data (n = 2,710 adult patients) for 36 ICU and 15 SDU staffed beds. Patient priority was based on acuity and whether the patient originated in the emergency department. The model simulated the following hypothetical scenarios: (1) varied ICU/SDU sizes, (2) reserved ICU beds as a triage strategy, (3) lower targets for time to transfer out of the ICU, and (4) ICU expansion by up to four beds. Outcomes included ICU admission wait times and unit occupancy.

MEASUREMENTS AND MAIN RESULTS

With current bed allocation, simulated wait time averaged 1.13 (SD, 1.39) hours. Reallocating all SDU beds as ICU decreased overall wait times by 7.2% to 1.06 (SD, 1.39) hours and increased bed occupancy from 80 to 84%. Reserving the last available bed for acute patients reduced wait times for acute patients from 0.84 (SD, 1.12) to 0.31 (SD, 0.30) hours, but tripled subacute patients' wait times from 1.39 (SD, 1.81) to 4.27 (SD, 5.44) hours. Setting transfer times to wards for all ICU/SDU patients to 1 hour decreased wait times for incoming ICU patients, comparable to building one to two additional ICU beds.

CONCLUSIONS

Hospital queuing and simulation modeling with empiric data inputs can evaluate how changes in ICU bed assignment could impact unit occupancy levels and patient wait times. Trade-offs associated with dedicating resources for acute patients versus expanding capacity for all patients can be examined.

Optimizing nurse capacity in a teaching hospital neonatal intensive care unit

Patients in intensive care units need special attention. Therefore, nurses are one of the most important resources in a neonatal intensive care unit. These nurses are required to have highly specialized training. The random number of patient arrivals, rejections, or transfers due to lack of capacity (such as nurse, equipment, bed etc.) and the random length of stays, make advanced knowledge of the optimal nurse a requirement, for levels of the unit behave as a stochastic process. This stochastic nature creates difficulties in finding optimal nurse staffing levels. In this paper, a stochastic approximation which is based on the required nurse: patient ratio and the number of patients in a neonatal intensive care unit of a teaching hospital, has been developed. First, a meta-model was built to generate simulation results under various numbers of nurses. Then, those experimented data were used to obtain the mathematical relationship between inputs (number of nurses at each level) and performance measures (admission number, occupation rate, and satisfaction rate) using statistical regression analysis. Finally, several integer nonlinear mathematical models were proposed to find optimal nurse capacity subject to the targeted levels on multiple performance measures. The proposed approximation was applied to a Neonatal Intensive Care Unit of a large hospital and the obtained results were investigated.

Planning intensive care unit design using computer simulation modeling: optimizing integration of clinical, operational, and architectural requirements

Nurses have increasingly been regarded as critical members of the planning team as architects recognize their knowledge and value. But the nurses' role as knowledge experts can be expanded to leading efforts to integrate the clinical, operational, and architectural expertise through simulation modeling. Simulation modeling allows for the optimal merge of multifactorial data to understand the current state of the intensive care unit and predict future states. Nurses can champion the simulation modeling process and reap the benefits of a cost-effective way to test new designs, processes, staffing models, and future programming trends prior to implementation. Simulation modeling is an evidence-based planning approach, a standard, for integrating the sciences with real client data, to offer solutions for improving patient care.

Mathematical modelling of patient flows to predict critical care capacity required following the merger of two district general hospitals into one

There is both medical and political drive to centralise secondary services in larger hospitals throughout the National Health Service. High-volume services in some areas of care have been shown to achieve better outcomes and efficiencies arising from economies of scale. We sought to produce a mathematical model using the historical critical care demand in two District General Hospitals to determine objectively the requisite critical care capacity in a newly built hospital. We also sought to determine how well the new single unit would be able to meet changes in demand. The intention is that the model should be generic and transferable for those looking to merge and rationalise services on to one site. One of the advantages of mathematical modelling is the ability to interrogate the model to investigate any number of different scenarios; some of these are presented.

Surge capacity: analysis of census fluctuations to estimate the number of intensive care unit beds needed

OBJECTIVE

To compare methods of characterizing intensive care unit (ICU) bed use and estimate the number of beds needed.

STUDY SETTING

Three geographic regions in the Canadian province of Manitoba.

STUDY DESIGN

Retrospective analysis of population-based data from April 1, 2000, to March 31, 2007.

METHODS

We compared three methods to estimate ICU bed requirements. Method 1 analyzed yearly patient-days. Methods 2 and 3 analyzed day-to-day fluctuations in patient census; these differed by whether each hospital needed to independently fulfill its own demand or this resource was shared across hospitals.

PRINCIPAL FINDINGS

Three main findings were as follows: (1) estimates based on yearly average usage generally underestimated the number of beds needed compared to analysis of fluctuations in census, especially in the smaller regions where underestimation ranged 25-58 percent; (2) 4-29 percent fewer beds were needed if it was acceptable for demand to exceed supply 18 days/year, versus 4 days/year; and (3) 13-36 percent fewer beds were needed if hospitals within a region could effectively share ICU beds.

CONCLUSIONS

Compared to using yearly averages, analyzing day-to-day fluctuations in patient census gives a more accurate picture of ICU bed use. Failing to provide adequate "surge capacity" can lead to demand that frequently and severely exceeds supply.

Optimal occupancy in the ICU: a literature review

INTRODUCTION

In intensive care, occupancy is a commonly used measure. There is inconsistency however in its measurement and optimal occupancy targets need to be defined. The objectives of this literature review were to explore how occupancy is measured, reported, and interpreted and investigate optimal occupancy levels for ICUs.

METHOD

A literature search was performed using the Medline, Embase and CINAHL databases and citation tracking identified additional relevant articles. Articles published since 1997, written in English and focused on the adult ICU setting were included. As a result, 16 articles were selected for this review.

RESULTS

Although it was apparent there was no commonly accepted or used method for calculating ICU occupancy, methods described as more accurate enumerate actual patient hours in the ICU, use operational (and preferably fully staffed) beds as the denominator, and are calculated daily. Issues pertaining to the utility, interpretation, and reporting of ICU occupancy measures were identified and there were indications that optimal ICU occupancy rates were around 70-75%. It was evident however that setting a uniform target figure for all ICUs would be problematic as there are a range of factors both at the unit and the hospital level that impact occupancy figures and optimal occupancy levels.

IMPLICATIONS

This literature review informed the recommendation of a proposed method for calculating ICU occupancy which provides a realistic measure of occupied bed hours as a percentage of available beds. Despite the importance of gaining an understanding of ICU occupancy at the local and broader health system levels, there are a number of unknown factors that require further research. Appropriate occupancy targets, impact of unavailable beds, and the intrinsic and extrinsic factors on occupancy measurement are a few examples of where more information is required to adequately inform ICU monitoring, planning and evaluation activities.

A generic simulation model for planning critical care resource requirements

Intensive care capacity planning based on factual or forecasted mean admission numbers and mean length of stay without taking non-linearity and variability into account is fraught with error. Simulation modelling may allow for a more accurate assessment of capacity needs. We developed a generic intensive care simulation model using data generated from anonymised patient records of all admissions to four different hospital intensive care units. The model was modified and calibrated stepwise to identify important parameters and their values to obtain a match between model predictions and actual data. The most important characteristic of the final model was the dependency of admission rate on actual occupancy. Occupancy, coverage and transfers of the final model were found to be within 2% of the actual data for all four simulated intensive care units. We have shown that this model could provide accurate decision support for planning critical care resource requirements.

Balancing operating theatre and bed capacity in a cardiothoracic centre

Cardiothoracic surgery requires many expensive resources. This paper examines the balance between operating theatres and beds in a specialist facility providing elective heart and lung surgery. Without both operating theatre time and an Intensive Care bed a patient's surgery has to be postponed. While admissions can be managed, there are significant stochastic features, notably the cancellation of theatre procedures and patients' length of stay on the Intensive Care Unit. A simulation was developed, with clinical and management staff, to explore the interdependencies of resource availabilities and the daily demand. The model was used to examine options for expanding the capacity of the whole facility. Ideally the bed and theatre capacity should be well balanced but unmatched increases in either resource can still be beneficial. The study provides an example of a capacity planning problem in which there is uncertainty in the demand for two symbiotic resources.

MATHEMATICAL MODELING: THE CASE OF EMERGENCY DEPARTMENT WAITING TIMES

A decision analytic model often comprises a significant part of a health technology assessment. As health technology assessment in the hospital setting evolves, there is an increased need for modeling methods that account for patient care pathways and interactions between patients and their environment. For example, an evaluation of a computed tomography (CT) scanner for a new indication would need to consider the current and increased demand of the machine and how that may affect service in other areas of the hospital. This problem solving approach views “problems” through a systems perspective.

Statistical analysis of patients' characteristics in neonatal intensive care units

The staff in the neonatal intensive care units is required to have highly specialized training and the using equipment in this unit is so expensive. The random number of arrivals, the rejections or transfers due to lack of capacity and the random length of stays, make the advance knowledge of the optimal staff; equipment and materials requirement for levels of the unit behaves as a stochastic process. In this paper, the number of arrivals, the rejections or transfers due to lack of capacity and the random length of stays in a neonatal intensive care unit of a university hospital has been statistically analyzed. The arrival patients are classified according to the levels based on the required nurse: patient ratio and gestation age. Important knowledge such as arrivals, transfers, gender and length of stays are analyzed. Finally, distribution functions for patients' arrivals, rejections and length of stays are obtained for each level in the unit.

Modelling patient flows as an aid to decision making for critical care capacities and organisation

Using real data from a number of hospitals, we predicted the patient flows following a capacity or organisational change. Clinically recognisable patient groups obtained through classification and regression tree analysis were used to tune a simulation model for the flow of patients in critical care units. A tuned model which accurately reflected the base case of the flow of patients was used to predict alterations in service provision in a number of scenarios which included increases in bed numbers, alterations in patients' lengths of stay, fewer delayed discharges, caring for long stay patients outside the formal intensive care unit and amalgamating small units. Where available the predictions' accuracy was checked by comparison with real hospital data collected after an actual capacity change. The model takes variability and uncertainty properly into account and it provides the necessary information for making better decisions about critical care capacity and organisation.

Integration of modeling and simulation into hospital-based decision support systems guiding pediatric pharmacotherapy

Background

Decision analysis in hospital-based settings is becoming more common place. The application of modeling and simulation approaches has likewise become more prevalent in order to support decision analytics. With respect to clinical decision making at the level of the patient, modeling and simulation approaches have been used to study and forecast treatment options, examine and rate caregiver performance and assign resources (staffing, beds, patient throughput). There us a great need to facilitate pharmacotherapeutic decision making in pediatrics given the often limited data available to guide dosing and manage patient response. We have employed nonlinear mixed effect models and Bayesian forecasting algorithms coupled with data summary and visualization tools to create drug-specific decision support systems that utilize individualized patient data from our electronic medical records systems.

Methods

Pharmacokinetic and pharmacodynamic nonlinear mixed-effect models of specific drugs are generated based on historical data in relevant pediatric populations or from adults when no pediatric data is available. These models are re-executed with individual patient data allowing for patient-specific guidance via a Bayesian forecasting approach. The models are called and executed in an interactive manner through our web-based dashboard environment which interfaces to the hospital's electronic medical records system.

Results

The methotrexate dashboard utilizes a two-compartment, population-based, PK mixed-effect model to project patient response to specific dosing events. Projected plasma concentrations are viewable against protocol-specific nomograms to provide dosing guidance for potential rescue therapy with leucovorin. These data are also viewable against common biomarkers used to assess patient safety (e.g., vital signs and plasma creatinine levels). As additional data become available via therapeutic drug monitoring, the model is re-executed and projections are revised.

Conclusion

The management of pediatric pharmacotherapy can be greatly enhanced via the immediate feedback provided by decision analytics which incorporate the current, best-available knowledge pertaining to dose-exposure and exposure-response relationships, especially for narrow therapeutic agents that are difficult to manage.

Computer simulation and discrete-event models in the analysis of a mammography clinic patient flow

OBJECTIVE

This work develops a discrete-event computer simulation model for the analysis of a mammography clinic performance.

MATERIAL AND METHODS

Two mammography clinic computer simulation models were developed, based on an existing public sector clinic of the Brazilian Cancer Institute, located in Rio de Janeiro city, Brazil. Two clinics in a total of seven configurations (number of equipment units and working personnel) were studied. Models tried to simulate changes in patient arrival rates, number of equipment units, available personnel (technicians and physicians), equipment maintenance scheduling schemes and exam repeat rates. Model parameters were obtained by direct measurements and literature reviews. A commercially-available simulation software was used for model building.

RESULTS

The best patient scheduling (patient arrival rate) for the studied configurations had an average of 29 min for Clinic 1 (consisting of one mammography equipment, one to three technicians and one physician) and 21 min for Clinic 2 (two mammography equipment units, one to four technicians and one physician). The exam repeat rates and equipment maintenance scheduling simulations indicated that a large impact over patient waiting time would appear in the smaller capacity configurations.

CONCLUSIONS

Discrete-event simulation was a useful tool for defining optimal operating conditions for the studied clinics, indicating the most adequate capacity configurations and equipment maintenance schedules.

Applying the variety reduction principle to management of ancillary services

BACKGROUND

As central diagnostic facilities, computer tomography (CT) scans appear to be bottlenecks in many patient-care processes. This study describes a case study concerning redesign of a CT scan department in the Academic Medical Center in Amsterdam, the Netherlands.

PURPOSES

The aim was to decrease access time for the CT-scan and simultaneously increase utilization level.

METHODOLOGY/APPROACH

An important cause of relatively low-capacity utilization is variability in the time needed for the scanning process. We performed a qualitative and quantitative analysis of current processes; identified bottlenecks and selected interventions with the greatest expected reduction of variability in flow time.

FINDINGS

The most promising and most feasible opportunity appeared to be to reallocate the insertion of intravenous access lines to a preparation room. The time needed for this activity was very hard to predict and needed a lot of slack in the lead time for appointments. By removing it from the CT room, lead time could be reduced by 5 minutes. The intervention resulted in a decrease of access time from 21 days to less than 5 days, and an increase of the utilization rate from 44% to 51%. This contributed directly to patient service and indirectly to cost reduction.

PRACTICE IMPLICATIONS

Our strategy is applicable in every appointment-based hospital facility with variation in the length of time of the process. It allows to simultaneously reduce costs and improve service for the patient.

Choice of Models for the Analysis and Forecasting of Hospital Beds

There is growing concern that current health care services are not sustainable. The compartmental flow model provides the opportunity for improved decision-making about bed occupancy decisions, particularly those of a strategic nature. This modelling can be applied to complement infrastructure and workforce-planning methods. Discussion about appropriateness of the level of model complexity, the degree of fit and the ability to use compartmental flow models for generalization and forecasting has been lacking. The authors investigated model selection and assessment in relation to hospital bed compartment flow models. A compartment model for a range of scenarios was created. The training and test data related to the 1998 and 1999 calendar years, respectively. The majority of scenarios tested were based upon commonly used periods that describe periods of time. The goodness-of-fit achieved by optimisation was measured against the training and test data. Model fit improved with increasing complexity as expected. The analysis of model fit against the test data showed that increasing model complexity did result in over-fitting, and better prediction was achieved with a relatively simple model. In terms of generalisation, the seasonal models performed best. Single day census type models, which have been used by Millard and his colleagues, were also generated. The performance of these models was similar, but inferior to that of the models generated from a full year of training data. The additional data make the models better able to capture the variation across the year in activity.

Evaluating and planning ICUs: methods and approaches to differentiate between need and demand

OBJECTIVE

In all western countries the demand for ICU-services is increasing and complaints about a lack of ICU-beds arise--independent of the actual density of ICU-services. The demand for more ICU-beds triggered a debate on whether it is possible to define an "objective" need. It was the aim of the assessment to analyze conventional as well as innovative approaches to plan and to evaluate ICU-services.

METHOD

Systematic review, multistep searches in Medline, EmBase, Cochrane, HTA-Database, websearches, informal searches through planning and HTA-networks.

INTRODUCTION

The differences between the density of intensive care in Europe and other parts of the western world is enormous. At a first superficial glance, Austria and Germany--in absolute figures--have many more ICU-beds than any other European country. In relative figures, taken into consideration that Austria and Germany have also many more acute care beds, the number of ICU-beds is among European average. It is therefore, impossible to analyze the need for ICU-beds without taking into account the national context of delivered acute hospital services. Although ICU-services take about 15-20% of the hospital budgets, there are still more questions than answers.

RESULTS

Recent planning-documents: a review of trends in recent planning shows that all planners calculate on the basis of existing style of practice within their countries; the figures change only marginally. But while planners in countries with a relatively low ICU-bed density (Great Britan, Australia, Canada) certify a certain need for an increase, planners in countries with high density (USA, Germany, Austria) state a "satisfied need" and an over-provision of ICU-services. Innovative planners apply an "appropriateness of ICU-use" approach with analysing the actual utilisation by interpreting scores (especially TISS) and by identifying "low-risk" groups and propose a more flexible organisation of ICUs and a higher proportion of (intermediate care unit) IMCU-beds. Clinical and ICU-management tools, such as admission and discharge guidelines, strategies to reduce treatment-variations, certain organisational changes (leadership, horizontal hierarchy) and costing methods gain importance for better, more efficient and co-ordinated use of ICU-resources.

CONCLUSION

In countries with a high density of ICU-services--such as Austria and Germany--not an expanding of the capacities, but a better use of the existing resources is recommended. For a fair comparison, participation in national databases, in registers as well as benchmarking and quality-assurance programs should be enforced.

The enhanced postoperative care system

The perioperative care system is a continuum that includes preoperative patient evaluation, operating room scheduling, the operation itself, and postoperative care. This costly fast-paced system requires its various components to function efficiently and interact effectively. This review explores the interrelation between the operational elements of the enhanced care postoperative care system (intensive care units, intermediate care units, postanesthesia care units, and monitored floor beds) and other perioperative care activities. This care system provides patients with enhanced (from routine floor) nursing and medical care, continuous physiological monitoring, and sophisticated treatments (eg, continuous infusion of vasoactive substances). A management, rather than clinical, approach is used to provide insight into the operations of the perioperative care system so that bottlenecks to patient flow may be identified and eliminated. Emphasis is placed on the need to switch from a "fiefdom" mentality, where each component of the system acts independently and defensively, to systems thinking, in which complex interrelated patterns are identified, analyzed, and optimized.

Simulation and critical care modeling

PURPOSE OF REVIEW

Decisions made in critical care are often complicated, requiring an in-depth understanding of the relations between complex diseases, available interventions, and patients with a wide range of characteristics. Standard modeling techniques such as decision trees and statistical modeling have difficulty in capturing these interactions as the complexity of the problem increases.

RECENT FINDINGS

Recent models in the literature suggest that simulation modeling techniques such as Markov modeling, Monte Carlo simulation, and discrete-event simulation are useful tools for analyzing complex systems in critical care. These simulation techniques are reviewed briefly, and examples from the literature are presented to demonstrate their usefulness in understanding real problems in critical care.

SUMMARY

Simulation models provide useful tools for organizing and analyzing the interactions between therapies, tradeoffs, and outcomes.

A simple method to optimize hospital beds capacity

OBJECTIVE

The number of acute hospital beds is determined by health authorities using methods based on ratios and/or target bed occupancy rates. These methods fail to consider the variability in hospitalization demands over time. On the other hand, the implementation of sophisticated models requires the decision concerning the number of beds to be made by an expert. Our aim is to develop a new method that is as simple to use as the ratio method while minimizing the roundabout approaches of these methods.

METHOD

A score was constructed with three parameters: number of transfers due to lack of space, number of days with no possibility for S unscheduled admissions and number of days with at least a threshold of U unoccupied beds. The optimal number of beds is the number for which both the mean and the standard deviation of the score reach their minimum. We applied this method to two internal medicine departments and one urological surgery department and we compared the solutions proposed by this method with those put forward by the ratio method.

RESULTS

The solutions proposed by this method were intermediate to those calculated by the local and national length of Stays ratio methods. Simulating an unusual increase in admission requests had no consequence on the bed number selected, indicating that the method was robust.

CONCLUSION

Our tool represents a real alternative to the ratio methods. A software has been developed and is now available for use.