The application of forecasting techniques to modeling emergency medical system calls in Calgary, Alberta

Forecasting to support EMS tactical planning: what is important and what is not

Forecasting emergency medical service (EMS) call volumes is critical for resource allocation and planning. The development of many commercial and free software packages has made a variety of forecasting methods accessible. Practitioners, however, are left with little guidance on selecting the most appropriate method for their needs. Using 5 years of data from 3 cities in Alberta, we compute exponential smoothing and benchmark forecasts for 8-hour periods for each ambulance station catchment area and with a forecast horizon of two weeks-a spatio-temporal resolution appropriate for tactical planning. The methods that we consider differ on three spectra: the number and type of time-series components, whether forecasts are computed individually or jointly, and the way in which forecasts at a specific resolution are converted to forecasts at the resolution of interest. We find that it is important to include a weekly seasonal component when forecasting EMS demand. Multiplicative seasonality, however, shows no benefit over additive seasonality. Adding other time-series components (e.g., trend, ARMA errors, Box-Cox transformation) does not improve performance. Spatial resolutions of station catchment area and lower, and temporal resolution of 4-24 hours perform similarly. We adapt an existing hierarchical forecasting framework to a two-dimensional spatio-temporal hierarchy, but find that hierarchical reconciliation of forecasts does not improve performance at the forecast resolution of interest for tactical planning. Neither does jointly forecasting time series. We show that added complexity does not materially improve forecasting performance. The simple methods that we find perform well are easy to implement and interpret, making implementation in practice more likely. In a simulation study we alter the empirical weekly patterns and demonstrate how extreme differences between the weekly seasonality patterns of different regions cause hierarchically-reconciled bottom-up approaches to outperform top-down approaches.

Forecasting daily emergency ambulance service demand using biometeorological indexes

This study aims to study the effectiveness of using biometeorological indexes in the development of a daily emergency ambulance service demand forecast system for Taipei City, Taiwan, compared to typical weather factors. Around 370,000 emergency ambulance service patient records were aggregated into a daily emergency ambulance service demand time series as the study's dependent variable. To assess the effectiveness of biometeorological indexes in making a 1 to 7-day forecast of daily emergency ambulance service demand, five forecast models were developed to make the comparison. The model with average temperature as the only predictor performed the best consistently from 1 to 7-day forecasts. The models with net effective temperature and apparent temperature as their only predictors ranked second and third, respectively. It is surprising that the model with both average temperature and relative humidity as predictors only ranked fourth. The unexpected outperformance of average temperature over net effective temperature and apparent temperature in forecasting daily emergency ambulance service demand suggested the need to develop updated locational-specific biometeorological indexes so that the benefit of the indexes can be fully utilized. Although adopting popular biometeorological indexes that are already available would be cheap and convenient, the benefit from these general indexes may not be guaranteed.

Predication and Photon Statistics of a Three-Level System in the Photon Added Negative Binomial Distribution

Statistical and artificial neural network models are applied to forecast the quantum scheme of a three-level atomic system (3LAS) and field, initially following a photon added negative binomial distribution (PANBD). The Mandel parameter is used to detect the photon statistics of a radiation field. Explicit forms of the PANBD are given. The prediction of the Mandel parameter, atomic probability of the 3LAS in the upper state, and von Neumann entropy are obtained using time series and artificial neural network methods. The influence of probability success photons and the number of added photons to the NBD are examined. The total density matrix is used to compute and analyze the time evolution of the initial photonic negative binomial probability distribution that governs the 3LAS–field photon entanglement behavior. It is shown that the statistical quantities are strongly affected by probability success photons and the number of added photons to the NBD. Also, the prediction of quantum entropy is achieved by the time series and neural network.

Predicting Covid-19 emergency medical service incidents from daily hospitalisation trends

INTRODUCTION

The aim of our retrospective study was to quantify the impact of Covid-19 on the temporal distribution of emergency medical services (EMS) demand in Travis County, Austin, Texas and propose a robust model to forecast Covid-19 EMS incidents.

METHODS

We analysed the temporal distribution of EMS calls in the Austin-Travis County area between 1 January 2019 and 31 December 2020. Change point detection was performed to identify the critical dates marking changes in EMS call distributions, and time series regression was applied for forecasting Covid-19 EMS incidents.

RESULTS

Two critical dates marked the impact of Covid-19 on the distribution of EMS calls: March 17th, when the daily number of non-pandemic EMS incidents dropped significantly, and 13 May, by which the daily number of EMS calls climbed back to 75% of the number in pre-Covid-19 time. The new daily count of the hospitalisation of Covid-19 patients alone proves a powerful predictor of the number of pandemic EMS calls, with an r² value equal to 0.85. In particular, for every 2.5 cases, where EMS takes a Covid-19 patient to a hospital, one person is admitted.

CONCLUSION

The mean daily number of non-pandemic EMS demand was significantly less than the period before the Covid-19 pandemic. The number of EMS calls for Covid-19 symptoms can be predicted from the daily new hospitalisation of Covid-19 patients. These findings may be of interest to EMS departments as they plan for future pandemics, including the ability to predict pandemic-related calls in an effort to adjust a targeted response.

Deep ensemble multitask classification of emergency medical call incidents combining multimodal data improves emergency medical dispatch

The objective of this work was to develop a predictive model to aid non-clinical dispatchers to classify emergency medical call incidents by their life-threatening level (yes/no), admissible response delay (undelayable, minutes, hours, days) and emergency system jurisdiction (emergency system/primary care) in real time. We used a total of 1 244 624 independent incidents from the Valencian emergency medical dispatch service in Spain, compiled in retrospective from 2009 to 2012, including clinical features, demographics, circumstantial factors and free text dispatcher observations. Based on them, we designed and developed DeepEMC², a deep ensemble multitask model integrating four subnetworks: three specialized to context, clinical and text data, respectively, and another to ensemble the former. The four subnetworks are composed in turn by multi-layer perceptron modules, bidirectional long short-term memory units and a bidirectional encoding representations from transformers module. DeepEMC² showed a macro F1-score of 0.759 in life-threatening classification, 0.576 in admissible response delay and 0.757 in emergency system jurisdiction. These results show a substantial performance increase of 12.5 %, 17.5 % and 5.1 %, respectively, with respect to the current in-house triage protocol of the Valencian emergency medical dispatch service. Besides, DeepEMC² significantly outperformed a set of baseline machine learning models, including naive bayes, logistic regression, random forest and gradient boosting (α = 0.05). Hence, DeepEMC² is able to: 1) capture information present in emergency medical calls not considered by the existing triage protocol, and 2) model complex data dependencies not feasible by the tested baseline models. Likewise, our results suggest that most of this unconsidered information is present in the free text dispatcher observations. To our knowledge, this study describes the first deep learning model undertaking emergency medical call incidents classification. Its adoption in medical dispatch centers would potentially improve emergency dispatch processes, resulting in a positive impact in patient wellbeing and health services sustainability.

A Comparison of Time-Series Predictions for Healthcare Emergency Department Indicators and the Impact of COVID-19

Across the world, healthcare systems are under stress and this has been hugely exacerbated by the COVID pandemic. Key Performance Indicators (KPIs), usually in the form of time-series data, are used to help manage that stress. Making reliable predictions of these indicators, particularly for emergency departments (ED), can facilitate acute unit planning, enhance quality of care and optimise resources. This motivates models that can forecast relevant KPIs and this paper addresses that need by comparing the Autoregressive Integrated Moving Average (ARIMA) method, a purely statistical model, to Prophet, a decomposable forecasting model based on trend, seasonality and holidays variables, and to the General Regression Neural Network (GRNN), a machine learning model. The dataset analysed is formed of four hourly valued indicators from a UK hospital: Patients in Department; Number of Attendances; Unallocated Patients with a DTA (Decision to Admit); Medically Fit for Discharge. Typically, the data exhibit regular patterns and seasonal trends and can be impacted by external factors such as the weather or major incidents. The COVID pandemic is an extreme instance of the latter and the behaviour of sample data changed dramatically. The capacity to quickly adapt to these changes is crucial and is a factor that shows better results for GRNN in both accuracy and reliability.

The effect of COVID-19 on emergency medical service call volumes and patient acuity: a cross-sectional study in Niagara, Ontario

Background

The COVID-19 pandemic is a major public health problem. Subsequently, emergency medical services (EMS) have anecdotally experienced fluctuations in demand, with reports across Canada of both increased and decreased demand. Our primary objective was to assess the effect of the COVID-19 pandemic on call volumes for several determinants in Niagara Region EMS. Our secondary objective was to assess changes in paramedic-assigned patient acuity scores as determined using the Canadian Triage and Acuity Scale (CTAS).

Methods

We analyzed data from a regional EMS database related to call type, volume, and patient acuity for January to May 2016–2020. We used statistical methods to assess differences in EMS calls between 2016 and 2019 and 2020.

Results

A total of 114,507 EMS calls were made for the period of January 1 to May 26 between 2016 and 2020, inclusive. Overall, the incidence rate of EMS calls significantly decreased in 2020 compared to the total EMS calls in 2016–2019. Motor vehicle collisions decreased in 2020 relative to 2016–2019 (17%), while overdoses relatively increased (70%) in 2020 compared to 2016–2019. Calls for patients assigned a higher acuity score increased (CTAS 1) (4.1% vs. 2.9%).

Conclusion

We confirmed that overall, EMS calls have decreased since the emergence of COVID-19. However, this effect on call volume was not consistent across all call determinants, as some call types rose while others decreased. These findings indicate that COVID-19 may have led to actual changes in emergency medical service demand and will be of interest to other services planning for future pandemics or further waves of COVID-19.

Binary Programming Model for Rostering Ambulance Crew-Relevance for the Management and Business

The nature of health care services is very complex and specific, thus delays and organizational imperfections can cause serious and irreversible consequences, especially when dealing with emergency medical services. Therefore, constant improvements in various aspects of managing and organizing provision of emergency medical services are vital and unavoidable. The main goal of this paper is the development and application of a binary programming model to support decision making process, especially addressing scheduling workforce in organizations with stochastic demand. The necessary staffing levels and human resources allocation in health care organizations are often defined ad hoc, without empirical analysis and synchronization with the demand for emergency medical services. Thus, irrational allocation of resources can result in various negative impacts on the financial result, quality of medical services and satisfaction of both patients and employees. We start from the desired staffing levels determined in advance and try to find the optimal scheduling plan that satisfies all significant professional and regulatory constraints. In this paper a binary programming model has been developed and implemented in order to minimize costs, presented as the sum of required number of ambulance crews. The results were implemented for staff rostering process in the Ambulance Service Station in Subotica, Serbia. Compared to earlier scheduling done ad hoc at the station, the solution of the formulated model provides a better and equable engagement of crews. The developed model can be easily modified and applied to other organizations with the same, stochastic, nature of the demand.

An empirical investigation of forecasting methods for ambulance calls - a case study

A primary goal of emergency services is to minimise the response times to emergencies whilst managing operational costs. This paper is motivated by real data from the Welsh Ambulance Service which in recent years has been criticised for not meeting its eight-minute response target. In this study, four forecasting approaches (ARIMA, Holt Winters, Multiple Regression and Singular Spectrum Analysis (SSA)) are considered to investigate whether they can provide more accurate predictions to the call volume demand (total and by category) than the current approach on a selection of planning horizons (weekly, monthly and 3-monthly). Each method is applied to a training and test set and root mean square error (RMSE) and mean absolute percentage error (MAPE) error statistics are determined. Results showed that ARIMA is the best forecasting method for weekly and monthly prediction of demand and the long-term demand is best predicted using the SSA method.

Leveraging Machine Learning Techniques and Engineering of Multi-Nature Features for National Daily Regional Ambulance Demand Prediction

The accurate prediction of ambulance demand provides great value to emergency service providers and people living within a city. It supports the rational and dynamic allocation of ambulances and hospital staffing, and ensures patients have timely access to such resources. However, this task has been challenging due to complex multi-nature dependencies and nonlinear dynamics within ambulance demand, such as spatial characteristics involving the region of the city at which the demand is estimated, short and long-term historical demands, as well as the demographics of a region. Machine learning techniques are thus useful to quantify these characteristics of ambulance demand. However, there is generally a lack of studies that use machine learning tools for a comprehensive modeling of the important demand dependencies to predict ambulance demands. In this paper, an original and novel approach that leverages machine learning tools and extraction of features based on the multi-nature insights of ambulance demands is proposed. We experimentally evaluate the performance of next-day demand prediction across several state-of-the-art machine learning techniques and ambulance demand prediction methods, using real-world ambulatory and demographical datasets obtained from Singapore. We also provide an analysis of this ambulatory dataset and demonstrate the accuracy in modeling dependencies of different natures using various machine learning techniques.

Patient classification based on volume and case-mix in the emergency department and their association with performance

Predicting daily patient volume is necessary for emergency department (ED) strategic and operational decisions, such as resource planning and workforce scheduling. For these purposes, forecast accuracy requires understanding the heterogeneity among patients with respect to their characteristics and reasons for visits. To capture the heterogeneity among ED patients (case-mix), we present a patient coding and classification scheme (PCCS) based on patient demographics and diagnostic information. The proposed PCCS allows us to mathematically formalize the arrival patterns of the patient population as well as each class of patients. We can then examine the volume and case-mix of patients presenting to an ED and investigate their relationship to the ED's quality and time-based performance metrics. We use data from five hospitals in February, July and November for the years of 2007, 2012, and 2017 in the city of Calgary, Alberta, Canada. We find meaningful arrival time patterns of the patient population as well as classes of patients in EDs. The regression results suggest that patient volume is the main predictor of time-based ED performance measures. Case-mix is, however, the key predictor of quality of care in EDs. We conclude that considering both patient volume and the mix of patients are necessary for more accurate strategic and operational planning in EDs.

An Examination of the Determination of Medical Capacity under a National Health Insurance Program

This paper examines the capacity determination factors of medical services at a national level through the analysis of a mathematical model that maximizes social welfare, which consists of the consumption of private goods and the medical capacity provided by the society. A sensitivity analysis is conducted to investigate the impact of these factors on the medical capacity provided. Furthermore, a case example based on the data provided by the government is presented to discuss the results derived from the theoretical analysis. The results of the sensitivity analysis indicate that individual disposable income, the medical expenditure for each treatment, the level of premium payments, and substitution parameters have a positive impact on medical capacity, while the medical costs and preference parameter negatively affect medical capacity. The results of the correlation analysis based on the data of the case example are consistent with the findings of the theoretical analysis.

Identifying rural-urban differences in the predictors of emergency ambulance service demand and misuse

OBJECTIVE

This study aims to assess rural-urban differences in the predictors of emergency ambulance service (EAS) demand and misuse in New Taipei City. Identifying the predictors of EAS demand will help the EAS service managing authority in formulating focused policies to maintain service quality.

METHODS

Over 160,000 electronic EAS usage records were used with a negative binomial regression model to assess rural-urban differences in the predictors of EAS demand and misuse.

RESULTS

The factors of 1) ln-transformed population density, 2) percentage of residents who completed up to junior high school education, 3) accessibility of hospitals without an emergency room, and 4) accessibility of EAS were found to be predictors of EAS demand in rural areas, whereas only the factor of percentage of people aged above 65 was found to predict EAS demand in urban areas. For EAS misuse, only the factor of percentage of low-income households was found to be a predictor in rural areas, whereas no predictor was found in the urban areas.

CONCLUSION

Results showed that the factors predicting EAS demand and misuse in rural areas were more complicated compared to urban areas and, therefore, formulating EAS policies for rural areas based on the results of urban studies may not be appropriate.

Demand Forecast and Multi-Objective Ambulance Allocation

This study considers the two-fold dynamic ambulance allocation problem, which includes forecasting the distribution of Emergency Medical Service (EMS) requesters and allocating ambulances dynamically according to the predicted distribution of requesters. EMSs demand distribution forecasting is based on on-record historical demands. Subsequently, a multi-objective ambulance allocation model (MOAAM) is solved by a mechanism called Jumping Particle Swarm Optimization (JPSO) according to the forecasted distribution of demands. Experiments were conducted using recorded historical data for EMS requesters in New Taipei City, Taiwan, for the years 2014 and 2015. EMS demand distribution for 2015 is forecasted according to the on-record historical demand of 2014. Ambulance allocation for 2015 is determined according to the anticipated demand distribution. The predicted demand distribution and ambulance allocation solved by JPSO are compared with historic data of 2015. The comparisons verify that the proposed methods yield lower forecasting error rates and better ambulance allocation than the actual one.

Sizing capacity levels in emergency medical services dispatch centers: Using the newsvendor approach

BACKGROUND

The increased volume in demand worldwide in the present day has led to the need for the establishment of effective ambulance services. As call centers have become the primary contact point between patients and emergency service providers, the planning of the call center has become a key task for administrators.

OBJECTIVES

The aim of this study is to apply a widely used operations management method, the newsvendor model, for optimizing the capacity level in EMS call centers with a minimum cost in order to efficiently meet the calls arriving.

METHODS

Real-life data from a call center for ambulance services in a major city in Turkey was used. We propose using the newsvendor model for optimizing this call center's capacity level based on the forecasts of periodic call volumes via basic methods.

RESULTS

Ambulance service call volumes vary during the day and weekday call profiles are different from weekends. By separating the analysis into weekdays and weekends and illustrating shorter time intervals within the days, call volume can be forecast. Taking not only the point forecast but also the variation of the forecast into account, the capacity level of each period can be planned in a cost-effective way.

CONCLUSIONS

This paper provides a basis for operation planning strategies of ambulance services by reconsidering the uncertainties of demand. The newsvendor model, which works well under parameter uncertainty, can be used in planning the capacities of health care services, especially when high service levels are required.

Daily volume of cases in emergency call centers: construction and validation of a predictive model

Background

Variations in the activity of emergency dispatch centers are an obstacle to the rationalization of resource allocation. Many explanatory factors are well known, available in advance and could predict the volume of emergency cases. Our objective was to develop and evaluate the performance of a predictive model of daily call center activity.

Methods

A retrospective survey was conducted on all cases from 2005 to 2011 in a large medical emergency call center (1,296,153 cases). A generalized additive model of daily cases was calibrated on data from 2005 to 2008 (1461 days, development sample) and applied to the prediction of days from 2009 to 2011 (1095 days, validation sample). Seventeen calendar and epidemiological variables and a periodic function for seasonality were included in the model.

Results

The average number of cases per day was 507 (95% confidence interval: 500 to 514) (range, 286 to 1251). Factors significantly associated with increased case volume were the annual increase, weekend days, public holidays, regional incidence of influenza in the previous week and regional incidence of gastroenteritis in the previous week. The adjusted R for the model was 0.89 in the calibration sample. The model predicted the actual number of cases within ± 100 for 90.5% of the days, with an average error of −13 cases (95% CI: -17 to 8).

Conclusions

A large proportion of the variability of the medical emergency call center’s case volume can be predicted using readily available covariates.

Electronic supplementary material

The online version of this article (10.1186/s13049-017-0430-9) contains supplementary material, which is available to authorized users.

A window-based time series feature extraction method

This study proposes a robust similarity score-based time series feature extraction method that is termed as Window-based Time series Feature ExtraCtion (WTC). Specifically, WTC generates domain-interpretable results and involves significantly low computational complexity thereby rendering itself useful for densely sampled and populated time series datasets. In this study, WTC is applied to a proprietary action potential (AP) time series dataset on human cardiomyocytes and three precordial leads from a publicly available electrocardiogram (ECG) dataset. This is followed by comparing WTC in terms of predictive accuracy and computational complexity with shapelet transform and fast shapelet transform (which constitutes an accelerated variant of the shapelet transform). The results indicate that WTC achieves a slightly higher classification performance with significantly lower execution time when compared to its shapelet-based alternatives. With respect to its interpretable features, WTC has a potential to enable medical experts to explore definitive common trends in novel datasets.

Time series modelling to forecast prehospital EMS demand for diabetic emergencies

BACKGROUND

Acute diabetic emergencies are often managed by prehospital Emergency Medical Services (EMS). The projected growth in prevalence of diabetes is likely to result in rising demand for prehospital EMS that are already under pressure. The aims of this study were to model the temporal trends and provide forecasts of prehospital attendances for diabetic emergencies.

METHODS

A time series analysis on monthly cases of hypoglycemia and hyperglycemia was conducted using data from the Ambulance Victoria (AV) electronic database between 2009 and 2015. Using the seasonal autoregressive integrated moving average (SARIMA) modelling process, different models were evaluated. The most parsimonious model with the highest accuracy was selected.

RESULTS

Forty-one thousand four hundred fifty-four prehospital diabetic emergencies were attended over a seven-year period with an increase in the annual median monthly caseload between 2009 (484.5) and 2015 (549.5). Hypoglycemia (70%) and people with type 1 diabetes (48%) accounted for most attendances. The SARIMA (0,1,0,12) model provided the best fit, with a MAPE of 4.2% and predicts a monthly caseload of approximately 740 by the end of 2017.

CONCLUSIONS

Prehospital EMS demand for diabetic emergencies is increasing. SARIMA time series models are a valuable tool to allow forecasting of future caseload with high accuracy and predict increasing cases of prehospital diabetic emergencies into the future. The model generated by this study may be used by service providers to allow appropriate planning and resource allocation of EMS for diabetic emergencies.

An analysis of Emergency Medical Services demand: Time of day, day of the week, and location in the city

OBJECTIVE

Effective planning of Emergency Medical Services (EMS), which is highly dependent on the analysis of past data trends, is important in reducing response time. Thus, we aimed to analyze demand for these services based on time and location trends to inform planning for an effective EMS.

MATERIALS AND METHODS

Data for this retrospective study were obtained from the Izmir EMS 112 system. All calls reaching these services during first six months of 2013 were descriptively analyzed, based on time and location trends as a heat-map form.

RESULTS

The analyses showed that demand for EMS varied within different time periods of day, and according to day of the week. For the night period, demand was higher at the weekend compared to weekdays, whereas for daytime hours, demand was higher during the week. For weekdays, a statistically significant relation was observed between the call distribution of morning and evening periods. It was also observed that the percentage of demand changed according to location. Among 30 locations, the five most frequent destinations for ambulances, which are also correlated with high population densities, accounted for 55.66% of the total.

CONCLUSION

The results of this study shed valuable light on the areas of call center planning and optimal ambulance locations of Izmir, which can also be served as an archetype for other cities.

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.

Real-time prediction of inpatient length of stay for discharge prioritization

OBJECTIVE

Hospitals are challenged to provide timely patient care while maintaining high resource utilization. This has prompted hospital initiatives to increase patient flow and minimize nonvalue added care time. Real-time demand capacity management (RTDC) is one such initiative whereby clinicians convene each morning to predict patients able to leave the same day and prioritize their remaining tasks for early discharge. Our objective is to automate and improve these discharge predictions by applying supervised machine learning methods to readily available health information.

MATERIALS AND METHODS

The authors use supervised machine learning methods to predict patients' likelihood of discharge by 2 p.m. and by midnight each day for an inpatient medical unit. Using data collected over 8000 patient stays and 20 000 patient days, the predictive performance of the model is compared to clinicians using sensitivity, specificity, Youden's Index (i.e., sensitivity + specificity - 1), and aggregate accuracy measures.

RESULTS

The model compared to clinician predictions demonstrated significantly higher sensitivity (P < .01), lower specificity (P < .01), and a comparable Youden Index (P > .10). Early discharges were less predictable than midnight discharges. The model was more accurate than clinicians in predicting the total number of daily discharges and capable of ranking patients closest to future discharge.

CONCLUSIONS

There is potential to use readily available health information to predict daily patient discharges with accuracies comparable to clinician predictions. This approach may be used to automate and support daily RTDC predictions aimed at improving patient flow.

Time-Series Approaches for Forecasting the Number of Hospital Daily Discharged Inpatients

For hospitals where decisions regarding acceptable rates of elective admissions are made in advance based on expected available bed capacity and emergency requests, accurate predictions of inpatient bed capacity are especially useful for capacity reservation purposes. As given, the remaining unoccupied beds at the end of each day, bed capacity of the next day can be obtained by examining the forecasts of the number of discharged patients during the next day. The features of fluctuations in daily discharges like trend, seasonal cycles, special-day effects, and autocorrelation complicate decision optimizing, while time-series models can capture these features well. This research compares three models: a model combining seasonal regression and ARIMA, a multiplicative seasonal ARIMA (MSARIMA) model, and a combinatorial model based on MSARIMA and weighted Markov Chain models in generating forecasts of daily discharges. The models are applied to three years of discharge data of an entire hospital. Several performance measures like the direction of the symmetry value, normalized mean squared error, and mean absolute percentage error are utilized to capture the under- and overprediction in model selection. The findings indicate that daily discharges can be forecast by using the proposed models. A number of important practical implications are discussed, such as the use of accurate forecasts in discharge planning, admission scheduling, and capacity reservation.

The Impact of Ambulance and Patient Diversion on Crowdedness of Multiple Emergency Departments in a Region

Emergency department (ED) overcrowding threatens healthcare quality. Ambulance diversion (AD) may relieve ED overcrowding; however, diverting patients from an overcrowded ED will load neighboring EDs with more patients and may result in regional overcrowding. The purpose of this study was to evaluate the impact of different diversion strategies on the crowdedness of multiple EDs in a region. The importance of regional coordination was also explored. A queuing model for patient flow was utilized to develop a computer program for simulating AD among EDs in a region. Key parameters, including patient arrival rates, percentages of patients of different acuity levels, percentage of patients transported by ambulance, and total resources of EDs, were assigned based on real data. The crowdedness indices of each ED and the regional crowdedness index were assessed to evaluate the effectiveness of various AD strategies. Diverting patients equally to all other EDs in a region is better than diverting patients only to EDs with more resources. The effect of diverting all ambulance-transported patients is similar to that of diverting only low-acuity patients. To minimize regional crowdedness, ambulatory patients should be sent to proper EDs when AD is initiated. Based on a queuing model with parameters calibrated by real data, patient flows of EDs in a region were simulated by a computer program. From a regional point of view, randomly diverting ambulatory patients provides almost no benefit. With regards to minimizing the crowdedness of the whole region, the most promising strategy is to divert all patients equally to all other EDs that are not already crowded. This result implies that communication and coordination among regional hospitals are crucial to relieve overall crowdedness. A regional coordination center may prioritize AD strategies to optimize ED utility.

The association between weekly work hours, crew familiarity, and occupational injury and illness in emergency medical services workers

OBJECTIVE

Emergency Medical Services (EMS) workers are shift workers in a high-risk, uncontrolled occupational environment. EMS-worker fatigue has been associated with self-reported injury, but the influence of extended weekly work hours is unknown.

METHODS

A retrospective cohort study was designed using historical shift schedules and occupational injury and illness reports. Using multilevel models, we examined the association between weekly work hours, crew familiarity, and injury or illness.

RESULTS

In total, 966,082 shifts and 950 reports across 14 EMS agencies were obtained over a 1-3 year period. Weekly work hours were not associated with occupational injury or illness. Schedule characteristics that yield decreased exposure to occupational hazards, such as part-time work and night work, conferred reduced risk of injury or illness.

CONCLUSIONS

Extended weekly work hours were not associated with occupational injury or illness. Future work should focus on transient exposures and agency-level characteristics that may contribute to adverse work events.

An observational study of shift length, crew familiarity, and occupational injury and illness in emergency medical services workers

OBJECTIVES

Emergency medical services (EMS) clinicians are shift workers deployed in two-person teams. Extended shift duration, workplace fatigue, poor sleep and lack of familiarity with teammates are common in the EMS workforce and may contribute to workplace injury. We sought to examine the relationship between shift length and occupational injury while controlling for relevant shift work and teamwork factors.

METHODS

We obtained 3 years of shift schedules and occupational injury and illness reports were from 14 large EMS agencies. We abstracted shift length and additional scheduling and team characteristics from shift schedules. We matched occupational injury and illness reports to shift records and used hierarchical logistic regression models to test the relationship between shift length and occupational injury and illness while controlling for teammate familiarity.

RESULTS

The cohort contained 966,082 shifts, 4382 employees and 950 outcome reports. Risk of occupational injury and illness was lower for shifts ≤8 h in duration (RR 0.70; 95% CI 0.51 to 0.96) compared with shifts >8 and ≤12 h. Relative to shifts >8 and ≤12 h, risk of injury was 60% greater (RR 1.60; 95% CI 1.22 to 2.10) for employees that worked shifts >16 and ≤24 h.

CONCLUSIONS

Shift length is associated with increased risk of occupational injury and illness in this sample of EMS shift workers.

Weather factors in the short-term forecasting of daily ambulance calls

The daily ambulance demand for Hong Kong is rising, and it has been shown that weather factors (temperature and humidity) play a role in the demand for ambulance services. This study aimed at developing short-term forecasting models of daily ambulance calls using the 7-day weather forecast data as predictors. We employed the autoregressive integrated moving average (ARIMA) method to analyze over 1.3 million cases of emergency attendance in May 2006 through April 2009 and the 7-day weather forecast data for the same period. Our results showed that the ARIMA model could offer reasonably accurate forecasts of daily ambulance calls at 1-7 days ahead of time and with improved accuracy by including weather factors. Specifically, the inclusion of average temperature alone in our ARIMA model improved the predictability of the 1-day forecast when compared to that of a simple ARIMA model (8.8% decrease in the root mean square error, RMSE=53 vs 58). The improvement in the 7-day forecast with average temperature as a predictor was more pronounced, with a 10% drop in prediction error (RMSE=62 vs 69). These findings suggested that weather forecast data can improve the 1- to 7-day forecasts of daily ambulance demand. As weather forecast data are readily accessible from Hong Kong Observatory's official website, there is virtually no cost to including them in the ARIMA models, which yield better prediction for forward planning and deployment of ambulance manpower.

Modeling Throughput of Emergency Departments via Time Series

In this article, the expectation maximization (EM) algorithm is applied for modeling the throughput of emergency departments via available time-series data. The dynamics of emergency department throughput is developed and evaluated, for the first time, as a stochastic dynamic model that consists of the noisy measurement and first-order autoregressive (AR) stochastic dynamic process. By using the EM algorithm, the model parameters, the actual throughput, as well as the noise intensity, can be identified simultaneously. Four real-world time series collected from an emergency department in West London are employed to demonstrate the effectiveness of the introduced algorithm. Several quantitative indices are proposed to evaluate the inferred models. The simulation shows that the identified model fits the data very well.

Managing emergency department overcrowding via ambulance diversion: a discrete event simulation model

BACKGROUND/PURPOSE

Ambulance diversion (AD) is considered one of the possible solutions to relieve emergency department (ED) overcrowding. Study of the effectiveness of various AD strategies is prerequisite for policy-making. Our aim is to develop a tool that quantitatively evaluates the effectiveness of various AD strategies.

METHODS

A simulation model and a computer simulation program were developed. Three sets of simulations were executed to evaluate AD initiating criteria, patient-blocking rules, and AD intervals, respectively. The crowdedness index, the patient waiting time for service, and the percentage of adverse patients were assessed to determine the effect of various AD policies.

RESULTS

Simulation results suggest that, in a certain setting, the best timing for implementing AD is when the crowdedness index reaches the critical value, 1.0 - an indicator that ED is operating at its maximal capacity. The strategy to divert all patients transported by ambulance is more effective than to divert either high-acuity patients only or low-acuity patients only. Given a total allowable AD duration, implementing AD multiple times with short intervals generally has better effect than having a single AD with maximal allowable duration.

CONCLUSION

An input-throughput-output simulation model is proposed for simulating ED operation. Effectiveness of several AD strategies on relieving ED overcrowding was assessed via computer simulations based on this model. By appropriate parameter settings, the model can represent medical resource providers of different scales. It is also feasible to expand the simulations to evaluate the effect of AD strategies on a community basis. The results may offer insights for making effective AD policies.

Characteristics of service requests and service processes of fire and rescue service dispatch centers: analysis of real world data and the underlying probability distributions

A sufficient staffing level in fire and rescue dispatch centers is crucial for saving lives. Therefore, it is important to estimate the expected workload properly. For this purpose, we analyzed whether a dispatch center can be considered as a call center. Current call center publications very often model call arrivals as a non-homogeneous Poisson process. This bases on the underlying assumption of the caller's independent decision to call or not to call. In case of an emergency, however, there are often calls from more than one person reporting the same incident and thus, these calls are not independent. Therefore, this paper focuses on the dependency of calls in a fire and rescue dispatch center. We analyzed and evaluated several distributions in this setting. Results are illustrated using real-world data collected from a typical German dispatch center in Cottbus ("Leitstelle Lausitz"). We identified the Pólya distribution as being superior to the Poisson distribution in describing the call arrival rate and the Weibull distribution to be more suitable than the exponential distribution for interarrival times and service times. However, the commonly used distributions offer acceptable approximations. This is important for estimating a sufficient staffing level in practice using, e.g., the Erlang-C model.

Determining minimum staffing levels during snowstorms using an integrated simulation, regression, and reliability model

Emergency medical services (EMS) provide life-saving care and hospital transport to patients with severe trauma or medical conditions. Severe weather events, such as snow events, may lead to adverse patient outcomes by increasing call volumes and service times. Adequate staffing levels during such weather events are critical for ensuring that patients receive timely care. To determine staffing levels that depend on weather, we propose a model that uses a discrete event simulation of a reliability model to identify minimum staffing levels that provide timely patient care, with regression used to provide the input parameters. The system is said to be reliable if there is a high degree of confidence that ambulances can immediately respond to a given proportion of patients (e.g., 99 %). Four weather scenarios capture varying levels of snow falling and snow on the ground. An innovative feature of our approach is that we evaluate the mitigating effects of different extrinsic response policies and intrinsic system adaptation. The models use data from Hanover County, Virginia to quantify how snow reduces EMS system reliability and necessitates increasing staffing levels. The model and its analysis can assist in EMS preparedness by providing a methodology to adjust staffing levels during weather events. A key observation is that when it is snowing, intrinsic system adaptation has similar effects on system reliability as one additional ambulance.

Resource planning for ambulance services in mass casualty incidents: a DES-based policy model

Due to an increasing number of mass casualty incidents, which are generally complex and unique in nature, we suggest that decision makers consider operations research-based policy models to help prepare emergency staff for improved planning and scheduling at the emergency site. We thus develop a discrete-event simulation policy model, which is currently being applied by disaster-responsive ambulance services in Austria. By evaluating realistic scenarios, our policy model is shown to enhance the scheduling and outcomes at operative and online levels. The proposed scenarios range from small, simple, and urban to rather large, complex, remote mass casualty emergencies. Furthermore, the organization of an advanced medical post can be improved on a strategic level to increase rescue quality, including enhanced survival of injured victims. In particular, we consider a realistic mass casualty incident at a brewery relative to other exemplary disasters. Based on a variety of such situations, we derive general policy implications at both the macro (e.g., strategic rescue policy) and micro (e.g., operative and online scheduling strategies at the emergency site) levels.

Using a discrete-event simulation to balance ambulance availability and demand in static deployment systems

OBJECTIVES

To improve ambulance response time, matching ambulance availability with the emergency demand is crucial. To maintain the standard of 90% of response times within 9 minutes, the authors introduce a discrete-event simulation method to estimate the threshold for expanding the ambulance fleet when demand increases and to find the optimal dispatching strategies when provisional events create temporary decreases in ambulance availability.

METHODS

The simulation model was developed with information from the literature. Although the development was theoretical, the model was validated on the emergency medical services (EMS) system of Tainan City. The data are divided: one part is for model development, and the other for validation. For increasing demand, the effect was modeled on response time when call arrival rates increased. For temporary availability decreases, the authors simulated all possible alternatives of ambulance deployment in accordance with the number of out-of-routine-duty ambulances and the durations of three types of mass gatherings: marathon races (06:00-10:00 hr), rock concerts (18:00-22:00 hr), and New Year's Eve parties (20:00-01:00 hr).

RESULTS

Statistical analysis confirmed that the model reasonably represented the actual Tainan EMS system. The response-time standard could not be reached when the incremental ratio of call arrivals exceeded 56%, which is the threshold for the Tainan EMS system to expand its ambulance fleet. When provisional events created temporary availability decreases, the Tainan EMS system could spare at most two ambulances from the standard configuration, except between 20:00 and 01:00, when it could spare three. The model also demonstrated that the current Tainan EMS has two excess ambulances that could be dropped. The authors suggest dispatching strategies to minimize the response times in routine daily emergencies.

CONCLUSIONS

Strategies of capacity management based on this model improved response times. The more ambulances that are out of routine duty, the better the performance of the optimal strategies that are based on this model.