Objective To empirically model the determinants of duration of wait of emergency (triage category 2) patients in an emergency department (ED) focusing on two questions: (i) What is the effect of enhancing the degree of choice for non-urgent (triage category 5) patients on duration of wait for emergency (category 2) patients in EDs; and (ii) What is the effect of co-located GP clinics on duration of wait for emergency patients in EDs? The answers to these questions will help in understanding the effectiveness of demand management strategies, which are identified as one of the solutions to ED crowding.
Methods The duration of wait for each patient (difference between arrival time and time first seen by treating doctor) was modelled as a function of input factors (degree of choice, patient characteristics, weekend admission, metro/regional hospital, concentration of emergency (category 2) patients in hospital service area), throughput factors (availability of doctors and nurses) and output factor (hospital bed capacity). The unit of analysis was a patient episode and the model was estimated using a survival regression technique.
Results The degree of choice for non-urgent (category 5) patients has a non-linear effect: more choice for non-urgent patients is associated with longer waits for emergency patients at lower values and shorter waits at higher values of degree of choice. Thus more choice of EDs for non-urgent patients is related to a longer wait for emergency (category 2) patients in EDs. The waiting time for emergency patients in hospital campuses with co-located GP clinics was 19% lower (1.5 min less) on average than for those waiting in campuses without co-located GP clinics.
Conclusion These findings suggest that diverting non-urgent (category 5) patients to an alternative model of care (co-located GP clinics) is a more effective demand management strategy and will reduce ED crowding.
- Survival analysis
- ED Overcrowding
- patient choice
- emergency care systems
- emergency departments
- emergency department management
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- Survival analysis
- ED Overcrowding
- patient choice
- emergency care systems
- emergency departments
- emergency department management
Unprecedented and sustained increases in demand for healthcare services has worsened emergency department (ED) overcrowding, which is common in North America, UK and Australasia,1–3 In 2001, the Victorian government in Australia implemented a hospital demand management strategy to enable more efficient delivery of healthcare. One of the key aspects of this strategy was to establish fast-track services, with a view to diverting non-urgent (category 5) patients presenting themselves in EDs to alternative models of care. The Department of Human Services (DHS) has estimated that about 37% of all attendances at metropolitan EDs in the Australian state of Victoria could be treated by GPs. No reported quantitative evidence on the impact on ED crowding of providing alternative models of care to non-urgent (category 5) patients has been produced. To the best of our knowledge, there is one quantitative study4 which found no significant impact of non-urgent (category 5) patient volume on ED wait and thus concluded that diverting non-urgent patients would not affect ED crowding.
Despite the importance of ED demand management strategies, such as alternative models of care, little is known about their impact on ED overcrowding. Published reports are limited and mainly based on qualitative data.5 We hypothesise that alternative models of care—for example, co-located GP clinics, will reduce duration of wait for emergency category 2 patients. The main reason behind this expectation is that diverting category 5 patients to alternative care will lead to some spare treatment space and staff time in the ED which can be used to treat category 2 patients. The degree to which alternative models of care reduce ED waiting time is unknown. This study helps fill this gap. Further, this study uses patient level survival analysis to compare the effect of increasing patient choice on waiting times for both non-urgent (category 5) and emergency patients. Patients have more choice if they can physically access a larger number of EDs. Our hypothesis is that EDs having greater number of ‘competitive’ EDs in their catchment area will have a relatively higher supply of ED services providing more choice to the patients residing in the catchment and thus reduce ED crowding. Thus our study enables a comparison between two demand management strategies: increasing ED choice for non-urgent patients vis-à-vis diverting them to an alternative model of care.
Goals of this investigation
The goal of this study is to empirically model determinants of duration of wait of emergency (category 2) patients in an ED and test whether diverting non-urgent (category 5) patients away from EDs or increasing their choice of EDs reduces ED waiting times for the emergency patients.
Materials and methods
Our statistical model is drawn from ED crowding literature where the conceptual framework categorises the causes of ED crowding into three broad themes3 6–9: input factors, throughput factors and output factors. The input component of ED crowding includes all the factors that contribute to demand for ED services. The throughput component of ED crowding includes bottlenecks in the ED (eg, inadequate staffing) and the output component includes other bottlenecks of the healthcare system (eg, inpatient boarding and hospital bed capacity) which affect the ED. Based on the above conceptual framework we model duration of wait in the ED as a function of input, throughput and output factors. Input factors include degree of choice of EDs available to non-urgent (category 5) and emergency (category 2) patients, whether co-located GP clinics are present, patient characteristics, location of ED (metro/regional area) and day of patient arrival (weekend/weekday). The throughput factors include the number of full-time equivalent (FTE) doctors and nurses in hospital per 1000 catchment population of ED. The output factor includes hospital bed capacity (average available beds in hospital per 1000 catchment population). Construction of key variables is described next.
The logarithm of the emergency (triage category 2) patient's duration of wait in the ED (difference between arrival time and time first seen by treating doctor) is used as a dependent variable.
Degree of choice
Degree of choice is measured by the inverse of the Hirschman–Herfindahl index (HHI).10 The HHI for a hospital system can be perceived as a measure of size of the hospitals in relation to the whole hospital system. In our setting this indicates a measure of supply. For example, a hospital system which includes a single hospital or supplier will have an HHI of 1, which means that all patients will get treated in this hospital and thus will have no choice for hospital treatment. If another hospital opens up (with equal patient share), this will reduce the value of HHI to 0.5 and increase choice for patients. Thus the inverse of HHI (with value 2) indicates the number of ‘effective suppliers’ of hospital services, which in turn can be perceived as a measure of the degree of choice for patients. More effective suppliers in a hospital system imply a greater degree of choice for patients. Thus a negative relationship between the inverse of HHI for non-urgent (category 5) patients and waiting time will imply that duration of wait of emergency (category 2) patients will decrease with more choice for non-urgent patients. The HHI index is estimated using actual statistical local area (SLA) level patient-flow data to define hospital catchment areas, based on Zwangiger and Melnick's methodology11 subsequently used by Bamezai et al.12 As a first step, the above method calculates the catchment population for each hospital based on patient-flow data for different categories of patients. We calculate hospital-level HHI separately for emergency (category 2) and non-urgent patients.
Patient characteristics include patient age, gender, country of origin (southeast Europe, Eastern Europe, Western Europe, SE Asia and UK with Australia as the reference category), indigenous status and socioeconomic indices for education and social disadvantage in the patient's SLA of residence.
The staffing of EDs is captured by FTE nurses and doctors employed in a hospital. The hospital bed capacity is measured as the average number of available beds in the hospital. Four hospital campuses, accounting for 21% of total emergency patient presentations in Victoria, have a co-located GP clinic. These GP clinics are part of the government's strategy to improve the hospital ability to manage emergency demand, improve patient services and reduce ED waiting times. We include a variable to capture the effect of co-located in-hospital GP clinics on waiting times which is given the value 1 if a hospital has a co-located after hours GP clinic and 0 otherwise.
Setting and selection of participants
The analysis presented here is based on the Victorian Emergency Minimum Dataset (VEMD) collected by the DHS in the Victorian state of Australia. The VEMD contains anonymised demographic, administrative and clinical data detailing all presentations at Victorian public hospitals with 24 h EDs. Ethics approval was obtained for the analysis of patient-level data. Data analysis was carried out for July 2005 to June 2006 (financial year) for all 38 hospital campuses with EDs. The triage scale for EDs is consistent across all hospitals and has five levels (resuscitation=1; emergency=2; urgent=3; semi-urgent=4 and non-urgent=5). There were 1 158 474 presentations in Victorian EDs in 2005–6, of which 84 291 were emergency (category 2) patients and 199 973 were non-urgent (category 5) patients. In our sample, 31% of emergency patients waited more than the target waiting time before being first seen by the doctor.
Primary data analysis
The outcome variable in our analysis is duration of wait for the patient in the ED and the event is to be seen by a treating doctor. Our primary source of data is the VEMD, which includes information on patient arrival time, time seen by the treating doctor, patient's age, gender, place of birth, indigenous status, SLA of residence and triage category. The inverse of HHI and hospital catchment population are derived using VEMD data. These data are supplemented with other variables, number of FTE doctors and nurses (provided by the DHS), SLA level socioeconomic indices (sourced from the Australian Bureau of Statistics13), metro/regional location and co-located GP clinic.
We used survival analysis to analyse the duration of wait for patients because using ordinary least squares to analyse these duration data would have imposed an unrealistic restriction on its distribution—namely, that waiting time, conditional on its covariates will be assumed to follow a normal distribution. This assumed normality would not be appropriate for ED waiting time. Survival analysis framework allows substituting a more reasonable distributional assumption for waiting time depending on the nature of the event. The other advantages of using survival analysis is that it allows analysis of censored events arising from scenarios where, for example, the patient leaves the ED without being seen by the doctor.
The statistical model uses a specification where dependent and independent variables are logarithmically transformed. The model includes quadratic terms for continuous variables to allow for non-linearities. Models are estimated using the streg command of the Stata statistical analysis package (version 10.0).
In a preliminary examination of the data we plotted Nelson–Aalen estimates of the cumulative hazard functions for emergency (category 2) patients. The hazard function shows that the probability of being seen by a treating doctor increases with duration of wait. Choice of correct distribution is crucial to obtaining sensible parameter estimates and a good model fit. We used several diagnostic tests to test for mis-specification and found that the generalised γ model fits best to the data; we used this distribution for estimation purposes.
Results for the generalised γ model are summarised in table 1. Detailed results are available on request. The results are presented in accelerated failure time format and can be interpreted as regression equations for ln(waiting time). The natural logarithms of continuous variables are used as covariates and each coefficient can be interpreted directly as an elasticity,14 calculated as the percentage change in waiting time for a 1% change in continuous variables and a unit change in categorical variables.
The inverse of HHI capturing choice for non-urgent patients has a statistically significant positive effect on duration of wait for emergency (category 2) patients. The square of this variable is also significant but with a negative coefficient. This implies that the impact of a non-urgent (category 5) patient's choice on emergency (category 2) patient waiting time is at first positive but its magnitude decreases as the number of hospitals increases and that at a certain number of hospitals (threshold level) the impact of choice becomes negative.
As reported in table 1, at the sample mean, the effect of choice is negative as only 15% of hospitals have a catchment area which includes more than the threshold number of hospitals.
The choice for emergency (category 2) patients has a statistically significant negative impact on their duration of wait with the squared term being positive. This implies that the impact of an emergency (category 2) patient's choice on waiting time is at first negative but becomes positive as number of hospital increases beyond a threshold level. As reported in table 1, at the sample mean, the effect of choice is negative as only 18% of hospitals have a catchment area which includes more than the threshold level of hospitals.
The duration of wait for emergency (category 2) patients in hospitals with co-located GP clinics is 19% less (1.5 min less at the sample mean) than those waiting in hospitals without co-located GP clinics.
An increase in five FTE nurses per 1000 catchment population will reduce the duration of wait by 2 min at the sample mean, whereas an increase in five FTE doctors per 1000 catchment population will increase the duration of wait by 3 s (a very small effect of no clinical significance). An increase in one available bed per thousand catchment population reduces the duration of wait by 1.13 min.
Although not the main focus of this study, the other significant determinants of waiting time are age (older patients wait for a shorter time), location (patients wait for a shorter time in metro area hospitals relative to regional areas) and day of the week (patients wait longer at the weekend).
In the absence of data on FTE nurses and FTE doctors employed in the ED, this study uses the number of nurses and doctors employed in the hospital. It should be noted that the effect of hospital staffing levels on duration of wait might also capture hospital bottlenecks outside the ED and thus can be perceived as output factors rather than throughput factors in our setting. Thus the result of a positive effect of doctors on duration of wait seems intuitive as higher doctor levels may reflect bed differentiation and less ability to move patients from the ED. On the other hand, nursing staff levels relate to total hospital capacity and our results show that an increase in nursing staff levels will lead to a reduction in waiting times.
Some of the patient characteristics (eg, socioeconomic indices) were not available at patient level and thus proxies at SLA level are used. However, it should be noted that these variables are not the main focus of our study and more accurate data will at best refine their coefficients, keeping the results qualitatively the same.
The main contribution of this study is that it quantifies the likely gains from improved ED demand management of non-urgent (category 5) patients. Our results suggest that the presence of a co-located GP clinic reduces the mean wait of emergency (category 2) patient in an ED by 19% or 1.5 min on average. Existing publications on the use of EDs by non-urgent patients have focused on safety concerns associated with diverting non-urgent patients elsewhere,15 16 or the impact of non-urgent patient volume on ED length of stay.4 However, none of these studies have explicitly quantified and compared the impact on ED waiting times of enhancing ED choice for non-urgent patients or diverting them to dedicated fast-track centres like co-located GP clinics. Further, the study by Schull et al,4 while analysing the impact of non-target patient volume on ED length of stay (over an 8 h interval), could not control for critical throughput factors such as availability of doctors and nurses, and used a less accurate length of stay variable in the absence of data on the time of patient arrival in the ED. Our study uses robust survival analysis (which allows for distribution of waiting times being determined by the data) controlling for a full set of covariates (input, throughput and output factors) to predict the impact of ED demand management strategies on patient-level waiting times.
The results for non-urgent (category 5) patients suggest that more choice of EDs is related to longer wait for emergency (category 2) patients. This might indicate a supply-induced demand effect, where ED catchments with higher number of EDs generate demand by non-urgent patients.
The effective ED demand management strategy will be to divert non-urgent (category 5) patients to an alternative model of care (co-located GP clinics) rather than enhancing their ED choice.
Funding This paper is part of a project supported by National Health and Medical Research Council (NHMRC), grant ID: 334114.
Competing interests None.
Ethics approval This study was conducted with the approval of Monash University Ethics Committee
Provenance and peer review Not commissioned; externally peer reviewed.
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