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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., (© 2024. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.)

Importance: Delays in transfer for discharge-ready patients from the intensive care unit (ICU) are increasingly described and contribute to strained capacity., Objective: To describe the epidemiological features and health care costs attributable to potentially avoidable delays in ICU discharge in a large integrated health care system., Design, Setting, and Participants: This population-based cohort study was performed in 17 adult ICUs in Alberta, Canada, from June 19, 2012, to December 31, 2016. Participants were patients 15 years or older admitted to a study ICU during the study period. Data were analyzed from October 19, 2018, to May 20, 2020., Exposures: Avoidable time in the ICU, defined as the portion of total ICU patient-days accounted for by avoidable delay in ICU discharge (eg, waiting for a ward bed)., Main Outcomes and Measures: The primary outcome was health care costs attributable to avoidable time in the ICU. Secondary outcomes were factors associated with avoidable time, in-hospital mortality, and measures of use of health care resources, including the number of hours in the ICU and the number of days of hospitalization. Multilevel mixed multivariable regression was used to assess associations between avoidable time and outcomes., Results: In total, 28 904 patients (mean [SD] age, 58.3 [16.8] years; 18 030 male [62.4%]) were included. Of these, 19 964 patients (69.1%) had avoidable time during their ICU admission. The median avoidable time per patient was 7.2 (interquartile range, 2.4-27.7) hours. In multivariable analysis, male sex (odds ratio [OR], 0.92; 95% CI, 0.87-0.98), comorbid hemiplegia or paraplegia (OR 1.47; 95% CI, 1.23-1.75), liver disease (OR 1.20; 95% CI, 1.04-1.37), admission Acute Physiology and Chronic Health Evaluation II score (OR, 1.03; 95% CI, 1.02-1.03), surgical status (OR, 0.90; 95% CI, 0.82-0.98), medium community hospital type (OR, 0.12; 95% CI, 0.04-0.32), and admission year (OR, 1.16; 95% CI, 1.13-1.19) were associated with avoidable time. The cumulative avoidable time was 19 373.9 days, with estimated attributable costs of CAD$34 323 522. Avoidable time accounted for 12.8% of total ICU bed-days and 6.4% of total ICU costs. Patients with avoidable time before ICU discharge showed higher unadjusted in-hospital mortality (1115 [5.6%] vs 392 [4.4%]; P < .001); however, in multivariable analysis, avoidable time was associated with reduced in-hospital mortality (adjusted hazard ratio, 0.74; 95% CI, 0.64-0.85). Results were similar in sensitivity analyses., Conclusions and Relevance: In this study, potentially avoidable discharge delay occurred for most patients admitted to ICUs across a large integrated health system and translated into substantial associated health care costs.

Background: Strained intensive care unit (ICU) capacity represents a fundamental supply-demand mismatch in ICU resources. Strain is likely to be influenced by a range of factors; however, there has been no systematic evaluation of the spectrum of measures that may indicate strain on ICU capacity., Methods: We performed a systematic review to identify indicators of strained capacity. A comprehensive peer-reviewed search of MEDLINE, EMBASE, CINAHL, Cochrane Library, and Web of Science Core Collection was performed along with selected grey literature sources. We included studies published in English after 1990. We included studies that: (1) focused on ICU settings; (2) included description of a quality or performance measure; and (3) described strained capacity. Retrieved studies were screened, selected and extracted in duplicate. Quality was assessed using the Newcastle-Ottawa Quality Assessment Scale (NOS). Analysis was descriptive., Results: Of 5297 studies identified in our search; 51 fulfilled eligibility. Most were cohort studies (n = 39; 76.5%), five (9.8%) were case-control, three (5.8%) were cross-sectional, two (3.9%) were modeling studies, one (2%) was a correlational study, and one (2%) was a quality improvement project. Most observational studies were high quality. Sixteen measures designed to indicate strain were identified 110 times, and classified as structure (n = 4, 25%), process (n = 7, 44%) and outcome (n = 5, 31%) indicators, respectively. The most commonly identified indicators of strain were ICU acuity (n = 21; 19.1% [process]), ICU readmission (n = 18; 16.4% [outcome]), after-hours discharge (n = 15; 13.6% [process]) and ICU census (n = 13; 11.8% [structure]). There was substantial heterogeneity in the operational definitions used to define strain indicators across studies., Conclusions: We identified and characterized 16 indicators of strained ICU capacity across the spectrum of healthcare quality domains. Future work should aim to evaluate their implementation into practice and assess their value for evaluating strategies to mitigate strain., Systematic Review Registration: This systematic review was registered at PROSPERO (March 27, 2015; CRD42015017931 ).

Background: The matching of critical care service supply with demand is fundamental for the efficient delivery of advanced life support to patients in urgent need. Mismatch in this supply/demand relationship contributes to "intensive care unit (ICU) capacity strain," defined as a time-varying disruption in the ability of an ICU to provide well-timed and high-quality intensive care support to any and all patients who are or may become critically ill. ICU capacity strain leads to suboptimal quality of care and may directly contribute to heightened risk of adverse events, premature discharges, unplanned readmissions, and avoidable death. Unrelenting strain on ICU capacity contributes to inefficient health resource utilization and may negatively impact the satisfaction of patients, their families, and frontline providers. It is unknown how to optimally quantify the instantaneous and temporal "stress" an ICU experiences due to capacity strain., Methods: We will perform a systematic review to identify, appraise, and evaluate quality and performance measures of strain on ICU capacity and their association with relevant patient-centered, ICU-level, and health system-level outcomes. Electronic databases (i.e., MEDLINE, EMBASE, CINAHL, Cochrane Database of Systematic Reviews, Cochrane Central Register of Controlled Trials, Web of Science, and the Agency of Healthcare Research and Quality (AHRQ) - National Quality Measures Clearinghouse (NQMC)) will be searched for original studies of measures of ICU capacity strain. Selected gray literature sources will be searched. Search themes will focus on intensive care, quality, operations management, and capacity. Analysis will be primarily narrative. Each identified measure will be defined, characterized, and evaluated using the criteria proposed by the US Strategic Framework Board for a National Quality Measurement and Reporting System (i.e., importance, scientific acceptability, usability, feasibility)., Discussion: Our systematic review will comprehensively identify, define, and evaluate quality and performance measures of ICU capacity strain. This is a necessary step towards understanding the impact of capacity strain on quality and performance in intensive care and to develop innovative interventions aimed to improve efficiency, avoid waste, and better anticipate impending capacity shortfalls., Systematic Review Registration: PROSPERO, CRD42015017931.

Like many others, the St. Louis Veterans Administration Medical Center (VAMC) Pharmacy help desk receives far more calls than can be processed by current staffing levels. The objective of the study is to improve pharmaceutical services provided by the call center, by using queueing theory and discrete event dynamic simulation to analyze incoming telephone traffic to the help desk. Queueing and simulation models using both archival and hand-gathered data over a 1-year period were created, compared, and presented in order to determine the minimum quantities of staff needed to reach the desired service threshold. The simulation model was validated in comparison with real-world data. Results suggest that telephone traffic congestion in this setting may be alleviated by increasing the number of staff responsible for telephone services from 2 to 6 throughout the week, with an additional one serving on Monday. Both queueing and simulative models can be used to improve overwhelm pharmacy call centers, by determining the theoretical minimal staff needed to reach a service threshold.

We describe an ambulance location optimization model that minimizes the number of ambulances needed to provide a specified service level. The model measures service level as the fraction of calls reached within a given time standard and considers response time to be composed of a random delay (prior to travel to the scene) plus a random travel time. In addition to modeling the uncertainty in the delay and in the travel time, we incorporate uncertainty in the ambulance availability in determining the response time. Models that do not account for the uncertainty in all three of these components may overestimate the possible service level for a given number of ambulances and underestimate the number of ambulances needed to provide a specified service level. By explicitly modeling the randomness in the ambulance availability and in the delays and the travel times, we arrive at a more realistic ambulance location model. Our model is tractable enough to be solved with general-purpose optimization solvers for cities with populations around one Million. We illustrate the use of the model using actual data from Edmonton.

We develop and evaluate time-series models of call volume to the emergency medical service of a major Canadian city. Our objective is to offer simple and effective models that could be used for realistic simulation of the system and for forecasting daily and hourly call volumes. Notable features of the analyzed time series are: a positive trend, daily, weekly, and yearly seasonal cycles, special-day effects, and positive autocorrelation. We estimate models of daily volumes via two approaches: (1) autoregressive models of data obtained after eliminating trend, seasonality, and special-day effects; and (2) doubly-seasonal ARIMA models with special-day effects. We compare the estimated models in terms of goodness-of-fit and forecasting accuracy. We also consider two possibilities for the hourly model: (3) a multinomial distribution for the vector of number of calls in each hour conditional on the total volume of calls during the day and (4) fitting a time series to the data at the hourly level. For our data, (1) and (3) are superior.