Advanced statistics: developing a formal model of emergency department census and defining operational efficiency

Predicting hospital emergency department visits accurately: A systematic review

OBJECTIVES

The emergency department (ED) is a very important healthcare entrance point, known for its challenging organisation and management due to demand unpredictability. An accurate forecast system of ED visits is crucial to the implementation of better management strategies that optimise resources utilization, reduce costs and improve public confidence. The aim of this review is to investigate the different factors that affect the ED visits forecasting outcomes, in particular the predictive variables and type of models applied.

METHODS

A systematic search was conducted in PubMed, Web of Science and Scopus. The review methodology followed the PRISMA statement guidelines.

RESULTS

Seven studies were selected, all exploring predictive models to forecast ED daily visits for general care. MAPE and RMAE were used to measure models' accuracy. All models displayed good accuracy, with errors below 10%.

CONCLUSIONS

Model selection and accuracy was found to be particularly sensitive to the ED dimension. While ARIMA-based and other linear models have good performance for short-time forecast, some machine learning methods proved to be more stable when forecasting multiple horizons. The inclusion of exogenous variables was found to be advantageous only in bigger EDs.

Diurnal Variation in SARS-CoV-2 PCR Test Results: Test Accuracy May Vary by Time of Day

False negative tests for SARS-CoV-2 are common and have important public health and medical implications. We tested the hypothesis of diurnal variation in viral shedding by assessing the proportion of positive versus negative SARS-CoV-2 reverse transcription polymerase chain reaction (RT-PCR) tests and cycle time (Ct) values among positive samples by the time of day. Among 86,342 clinical tests performed among symptomatic and asymptomatic patients in a regional health care network in the southeastern United States from March to August 2020, we found evidence for diurnal variation in the proportion of positive SARS-CoV-2 tests, with a peak around 1400 h and 1.7-fold variation over the day after adjustment for age, sex, race, testing location, month, and day of week and lower Ct values during the day for positive samples. These findings have important implications for public health testing and vaccination strategies.

Quantifying Dynamic Flow of Emergency Department (ED) Patient Managements: A Multistate Model Approach

Background

Emergency department (ED) crowding and prolonged lengths of stay continue to be important medical issues. It is difficult to apply traditional methods to analyze multiple streams of the ED patient management process simultaneously. The aim of this study was to develop a statistical model to delineate the dynamic patient flow within the ED and to analyze the effects of relevant factors on different patient movement rates.

Methods

This study used a retrospective cohort available with electronic medical data. Important time points and relevant covariates of all patients between January and December 2013 were collected. A new five-state Markov model was constructed by an expert panel, including three intermediate states: triage, physician management, and observation room and two final states: admission and discharge. A day was further divided into four six-hour periods to evaluate dynamics of patient movement over time.

Results

A total of 149,468 patient records were analyzed with a median total length of stay being 2.12 (interquartile range = 6.51) hours. The patient movement rates between states were estimated, and the effects of the age group and triage level on these movements were also measured. Patients with lower acuity go home more quickly (relative rate (RR): 1.891, 95% CI: 1.881–1.900) but have to wait longer for physicians (RR: 0.962, 95% CI: 0.956–0.967) and admission beds (RR: 0.673, 95% CI: 0.666–0.679). While older patients were seen more quickly by physicians (RR: 1.134, 95% CI: 1.131–1.139), they spent more time waiting for the final state (for admission RR: 0.830, 95% CI: 0.821–0.839; for discharge RR: 0.773, 95% CI: 0.769–0.776). Comparing the differences in patient movement rates over a 24-hour day revealed that patients wait longer before seen by physicians during the evening and that they usually move from the ED to admission afternoon. Predictive dynamic illustrations show that six hours after the patients' entry, the probability of still in the ED system ranges from 28% in the evening to 38% in the morning.

Conclusions

The five-state model well described the dynamic ED patient flow and analyzed the effects of relevant influential factors at different states. The model can be used in similar medical settings or incorporate different important covariates to develop individually tailored approaches for the improvement of efficiency within the health professions.

Machine Learning-Based Patient Load Prediction and IoT Integrated Intelligent Patient Transfer Systems

A mismatch between staffing ratios and service demand leads to overcrowding of patients in waiting rooms of health centers. Overcrowding consequently leads to excessive patient waiting times, incomplete preventive service delivery and disgruntled medical staff. Worse, due to the limited patient load that a health center can handle, patients may leave the clinic before the medical examination is complete. It is true that as one health center may be struggling with an excessive patient load, another facility in the vicinity may have a low patient turn out. A centralized hospital management system, where hospitals are able to timely exchange patient load information would allow excess patient load from an overcrowded health center to be re-assigned in a timely way to the nearest health centers. In this paper, a machine learning-based patient load prediction model for forecasting future patient loads is proposed. Given current and historical patient load data as inputs, the model outputs future predicted patient loads. Furthermore, we propose re-assigning excess patient loads to nearby facilities that have minimal load as a way to control overcrowding and reduce the number of patients that leave health facilities without receiving medical care as a result of overcrowding. The re-assigning of patients will imply a need for transportation for the patient to move from one facility to another. To avoid putting a further strain on the already fragmented ambulatory services, we assume the existence of a scheduled bus system and propose an Internet of Things (IoT) integrated smart bus system. The developed IoT system can be tagged on buses and can be queried by patients through representation state transfer application program interfaces (APIs) to provide them with the position of the buses through web app or SMS relative to their origin and destination stop. The back end of the proposed system is based on message queue telemetry transport, which is lightweight, data efficient and scalable, unlike the traditionally used hypertext transfer protocol.

A generic method for evaluating crowding in the emergency department

Background

Crowding in the emergency department (ED) has been studied intensively using complicated non-generic methods that may prove difficult to implement in a clinical setting. This study sought to develop a generic method to describe and analyse crowding from measurements readily available in the ED and to test the developed method empirically in a clinical setting.

Methods

We conceptualised a model with ED patient flow divided into separate queues identified by timestamps for predetermined events. With temporal resolution of 30 min, queue lengths were computed as Q(t + 1) = Q(t) + A(t) – D(t), with A(t) = number of arrivals, D(t) = number of departures and t = time interval. Maximum queue lengths for each shift of each day were found and risks of crowding computed. All tests were performed using non-parametric methods. The method was applied in the ED of Aarhus University Hospital, Denmark utilising an open cohort design with prospectively collected data from a one-year observation period.

Results

By employing the timestamps already assigned to the patients while in the ED, a generic queuing model can be computed from which crowding can be described and analysed in detail. Depending on availability of data, the model can be extended to include several queues increasing the level of information. When applying the method empirically, 41,693 patients were included. The studied ED had a high risk of bed occupancy rising above 100 % during day and evening shift, especially on weekdays. Further, a ‘carry over’ effect was shown between shifts and days.

Conclusions

The presented method offers an easy and generic way to get detailed insight into the dynamics of crowding in an ED.

Ensemble-based methods for forecasting census in hospital units

BACKGROUND

The ability to accurately forecast census counts in hospital departments has considerable implications for hospital resource allocation. In recent years several different methods have been proposed forecasting census counts, however many of these approaches do not use available patient-specific information.

METHODS

In this paper we present an ensemble-based methodology for forecasting the census under a framework that simultaneously incorporates both (i) arrival trends over time and (ii) patient-specific baseline and time-varying information. The proposed model for predicting census has three components, namely: current census count, number of daily arrivals and number of daily departures. To model the number of daily arrivals, we use a seasonality adjusted Poisson Autoregressive (PAR) model where the parameter estimates are obtained via conditional maximum likelihood. The number of daily departures is predicted by modeling the probability of departure from the census using logistic regression models that are adjusted for the amount of time spent in the census and incorporate both patient-specific baseline and time varying patient-specific covariate information. We illustrate our approach using neonatal intensive care unit (NICU) data collected at Women & Infants Hospital, Providence RI, which consists of 1001 consecutive NICU admissions between April 1st 2008 and March 31st 2009.

RESULTS

Our results demonstrate statistically significant improved prediction accuracy for 3, 5, and 7 day census forecasts and increased precision of our forecasting model compared to a forecasting approach that ignores patient-specific information.

CONCLUSIONS

Forecasting models that utilize patient-specific baseline and time-varying information make the most of data typically available and have the capacity to substantially improve census forecasts.

CrowdED: crowding metrics and data visualization in the emergency department

OBJECTIVES

Emergency department (ED) crowding metrics were validated in our facility and a new technique of data visualization is proposed.

DESIGN

A sequential cross-sectional study was conducted in our ED during October 2007. Data were collected every 2 hours by a research assistant and included patient arrivals and acuity levels, available inpatient and ED beds, ambulance diversion status, staff present, and patient reneging. The charge nurse and an attending physician also completed a single-question crowding instrument. Pearson correlation coefficients were calculated and logistic regression were performed to test the usefulness of the crowding score and test significance of the data visualization trends.

SETTING/PARTICIPANTS

Our ED is an adult, level-III, veterans administration ED in urban southern California. It is open 24 hours per day, has 15 treatment beds with 4 cardiac monitors, and typically sees about 30 000 patients per year.

MAIN OUTCOME MEASURE(S)

The key outcome variables were patient reneging (number of patients who left before being seen by a physician) and ambulance diversion status.

RESULTS

Average response rate was 72% (n = 227) of sampling times. Emergency Department Work Index, demand value, lack of inpatient beds, census, patients seen in alternate locations, and patient reneging correlated significantly (P < .01) with the crowding instrument. Staff workload ranks predicted patient reneging (odds ratio 6.0, 95% confidence interval 2.3-15.4). The data visualization focused on common ED overcrowding metrics and was supported by logistic regression modeling.

CONCLUSIONS

The demand value, ED Work Index, and patient reneging are valid measures of crowding in the studied ED, with staff workload rank being an easy, 1-question response. Data visualization may provide the site-specific crowding component analysis needed to guide quality improvement projects to reduce ED crowding and its impact on patient outcome measures.

Forecasting emergency department crowding: a discrete event simulation

STUDY OBJECTIVE

To develop a discrete event simulation of emergency department (ED) patient flow for the purpose of forecasting near-future operating conditions and to validate the forecasts with several measures of ED crowding.

METHODS

We developed a discrete event simulation of patient flow with evidence from the literature. Development was purely theoretical, whereas validation involved patient data from an academic ED. The model inputs and outputs, respectively, are 6-variable descriptions of every present and future patient in the ED. We validated the model by using a sliding-window design, ensuring separation of fitting and validation data in time series. We sampled consecutive 10-minute observations during 2006 (n=52,560). The outcome measures--all forecast 2, 4, 6, and 8 hours into the future from each observation--were the waiting count, waiting time, occupancy level, length of stay, boarding count, boarding time, and ambulance diversion. Forecasting performance was assessed with Pearson's correlation, residual summary statistics, and area under the receiver operating characteristic curve.

RESULTS

The correlations between crowding forecasts and actual outcomes started high and decreased gradually up to 8 hours into the future (lowest Pearson's r for waiting count=0.56; waiting time=0.49; occupancy level=0.78; length of stay=0.86; boarding count=0.79; boarding time=0.80). The residual means were unbiased for all outcomes except the boarding time. The discriminatory power for ambulance diversion remained consistently high up to 8 hours into the future (lowest area under the receiver operating characteristic curve=0.86).

CONCLUSION

By modeling patient flow, rather than operational summary variables, our simulation forecasts several measures of near-future ED crowding, with various degrees of good performance.