Seasonal and regional fluctuations in the demand for Accident and Emergency care
in English hospitals
Giovanni Forchini
USBE, Umeå Universitet, Umeå Sweden
email: giovanni.forchini@umu.se, Tel. No, +46907867876 Katharina Hauck
Medical School, Imperial College, London, UK Adam Steventon
The Health Foundation, London, UK
Abstract
There is a profusion of evidence on the population and supply side factors explaining demand for emergency care, but surprisingly very little evidence about how seasonal patterns of demand vary across regions. Such information is crucial to help hospitals manage fluctuations in demand and ease capacity constraints. The objective of this study is to analyse the patterns of weekly attendances to Accident and Emergency departments in England, controlling for a wide range of determinants. The study uses both panel and common trend methods on data for 135 English hospitals and their catchment areas merged from a variety of sources over 156 weeks from 2012 to 2015.
Modelling of unobservable factors with common trend models shows systematic patterns in the data related to season and the location of providers. Coastal areas experience more attendances in summer than urban areas, and this trend is reversed in winter, possibly due to temporary population movements. Internal reorganizations between major A&E departments and minor injury units within hospitals lead to structural breaks in attendances. In the panel models, only the share of the working population, weather and socioeconomic deprivation are statistically significant predictors of attendances in the panel models. The forecasting ability of both panel and common trends methods is similar. Fine-tuning funding allocations across trusts and seasons according to temporary population movements could be a promising avenue to help alleviate existing capacity constraints emergency departments.
Keywords: accident and emergency attendances, seasonal and regional fluctuations, internal migration, common trend analysis, demand/utilization of emergency healthcare.
Introduction
Attendances at major Accident and Emergency (A&E) departments in England and other countries have increased markedly over the past 10 years. In 2003/04, 16.5 million people visited an A&E department, and this figure rose to 22.3 million in 2014/15, an increase of more than 35% [1]. This high and increasing demand for urgent care is putting severe pressure on A&E departments, and high waiting times and poor quality of care are a concern.
Many explanations have been put forward for the increasing trend, including population growth and ageing, overstretched social and aged care systems, poor access to primary care, lack of family support, increased awareness among patients of symptoms of acute conditions, patient preferences for a ‘one-stop’ care provider, or the weather [2–5]. Despite, or perhaps because of, this abundance of explanations, there is little agreement regarding which factors are most strongly associated with A&E attendances in practice.
One issue that has been largely ignored in empirical studies for the United Kingdom is the so-called ‘snowbird phenomenon’. There is evidence from the USA that there are strong seasonal fluctuations in the demand for health care by individuals, usually of retirement age, who migrate to States with milder climate during the winter months [6–10]. Demographic research shows that there are also internal migration flows in the United Kingdom [11–14], but there is no direct evidence of the impact of seasonal migration on emergency care.
There are studies investigating age as a determinant of A&E demand. Areas with a high proportion of older people tend to have higher attendance rates, although the main effect may be an increase in average patient complexity, length of stay and inpatient admissions [4,15–17]. There is another strand of literature on seasonal fluctuations in attendances [18–21]; generally, there are fewer visits during autumn and winter than during summer months [22,23]. Particularly hot or cold weather with snowfall may increase attendances [20,24–28], but this has been contested [18,25].
Taken together, this evidence suggests that the seasonal load imposed by internal migrants could make it more challenging to provide high-quality emergency care. It may require increasing funding flexibly for A&E departments in priority regions in certain months to cope
with surges in demand, while at the same time targeting funds better to deal with both unexpected up- and downward fluctuations in demand over the year.
The objective of our study is to analyse seasonal and regional patterns in attendances at accident & emergency departments in England, and identify demand- and supply side determinants of emergency care. We use administrative data on attendances from 135 English A&E hospitals between April 2012 and March 2015, supplemented with data on hospital, population and area characteristics from a wide variety of sources. The unique advantage of our data is that we can disclose the identity and location of hospitals. This allows us to analyse regional patterns and provide targeted policy recommendations, if warranted even on hospital level. Moreover, the dataset allows controlling for important other determinants of attendances.
Since weekly attendances to A&E departments show common patterns across trusts, we first estimate a Common Trend (CT) model. CT models were developed to account for cross-sectional dependence and are now commonly applied in finance and macroeconomics [29–33]. They assume the existence of common factors that affect in principle all A&E providers but allow for heterogeneity in their impact. The changing seasons affect all A&E providers, but they are likely to have diverse effects on different emergency care providers due to the quality of providers’ management, degree of excess capacity, and the characteristics of their local populations, including the age structure. In addition, national policy changes, influenza outbreaks, weather and public holidays affect all providers, but they may differ in the way they can absorb such shocks.
While CT models allow us to uncover common patterns, they do not seek to explain attendances in terms of explanatory variables. We therefore also estimate panel data models using the same data on attendances, supplemented with data on a variety of other determinants. Hospital level analyses tend to suffer from misspecification, and addition of regressors often fails to improve goodness of fit measures [34]. A review by [19] found that standard econometric models could only explain between 30% to 75% of the variability in attendances. Despite our relatively large set of regressors, misspecification of our panel data models is therefore a concern.
To evaluate whether attendances are affected by important unobserved factors, we benchmark the panel data models against the CT model based on forecasting accuracy. If the panel model have smaller forecasting errors than the CT model, we can have trust in the observed determinants of attendances identified as significant by the panel data models. Otherwise, we need to accept that attendances are mostly affected by unobserved variables. In such a situation, policy recommendations based on the CT model are potentially more reliable, despite their inability to analyse the importance of observable determinants of attendances.
Data and methods
Data
This study uses data on 135 English hospitals with a major, type-1 (T1) A&E department, which are 24-hour services with full resuscitation facilities and designated accommodation for A&E patients. Data on attendances to major T1 departments over 156 weeks from 08/04/2012 to 15/02/2015 originates from the National Health Service (NHS) Emergency Care Weekly Situation Reports (SitReps), and data on covariates were collected from various sources (Table 1).
Table 1 here
Table 2 shows summary statistics for 17 covariates that measure the supply of health and social care within the catchment area of the hospital, population characteristics, quality of primary care, and temperature and rainfall. There are 79 T1 hospitals with so-called minor injury units (T3). T3 units treat injuries and illnesses that are not serious even if they require urgent care, and are usually led by nurses. To allow for correlation across T1 and T3 attendances, we control for structural breaks in T1 attendances associated with drastic changes in T3 attendances (Table A2, Figure A3). We also adjust for mergers between
hospital level we create artificial hospital catchment areas by aggregating variables at a higher administrative level and then calculating the proportion of attendances to a hospital from each higher level using patient-level administrative hospital data from 2012/13.
Table 2 here
Figure 1 shows the weekly log attendances for each of the 135 hospitals. Attendances increase or decrease from one week to the next in surprising unison across hospitals, suggesting that weekly attendances in England follow common trends, with shocks affecting multiple hospitals to differing extents. Hospitals with fewer attendances experience more pronounced seasonality than larger hospitals.
Figure 1 here
Statistical Analysis
Objectives of our analyses are to:
1. identify seasonal and regional patterns in attendances to A&E departments in England with time series models,
2. identify the determinants of weekly attendances via panel data models, and
3. assess their validity of panel data models by benchmarking forecasts against those from a time-series model with unobservable determinants of attendances.
First, we undertake a CT analysis of weekly trust attendances to uncover regional and seasonal variations in the demand for emergency care and assess the existence of unobservable determinants of attendances. CT modelling accounts for the fact that data points
taken over time may have an internal structure such as autocorrelation, trend or seasonal variation. It sheds light on the underlying forces and structure that produced the observed data and fits a model to forecast future development of a time series [35]. We regress the log of weekly attendances on a constant and trend that is allowed to vary across trusts and we account for unobservable determinants of attendances by imposing a multifactor structure on the errors:
,
og t f
l (a )it = θi+ βi + δit+ λi t′ + uit (1)
where ait are weekly attendances to major A&E departments in hospital i in week t, θi captures hospital specific, time-invariant, unobserved effects, βi is the trend coefficient specific to the hospital, δit denotes a possible change in intercept for hospital i in week t due to restructures between T1 and T3 departments as explained above, ft denotes a vector of unobservable common factors representing the common trends, λi is a vector of unobservable factor loadings and uit is an idiosyncratic error. We assume that λi and ft are independent and ft has mean zero. This allows us to model common trends in attendances.
We further control for restructures between T1 and T3 departments as explained above. Note that the CT model does not use the characteristics of the hospitals or their catchment areas to model attendances. We estimate the common factors using principal components analysis on the detrended attendances, and we look for patterns in our data that can then be modelled using standard time-series methods.
Second, we estimate classical panel data models of the log of weekly attendances regressed on a comprehensive list of covariates using both fixed (FE) and random effects (RE) estimators:
,
og z x
l (a )it = θi+ γ′ i+ δit+ β′ it+ uit (2)
where θi is an unobserved hospital specific effect, δit is a possible change in intercept for hospital i at week t due to presence of a T3 unit or restructures between T1 and T3 departments, zi is the vector of time-invariant hospital characteristics, xit is the vector of time-varying hospital characteristics, and uit is an error having zero mean. A total of 16
hospitals restructures between T1 and T3 departments. Alternative specifications without controls for T3 units are estimated.
To assess the panel data and CT models, we forecast the last five weeks of the data, and compare their forecasting precision using two commonly used methods [35]: the square-root of the average squared prediction error (RMSPE), and the median absolute prediction error (MAPE). The weeks between 08/04/2012 and 15/02/2015 were used for model estimation and the remaining five weeks (22/02/2015 to 29/03/2015) for validation. All estimations were undertaken in R version 3.3.1 (2016-06-21).
Results
The results from the panel data model (2) show that very few variables are significant determinants of attendances (Table 3, Table A5 for additional specifications). Of the 17 regressors included in the model, only the proportion of the aged population, the proportion of welfare recipients, temperature extremes, rainfall, quality of primary care, and hospital restructures are significantly associated with attendances.
Table 3 about here
Hospitals that serve a population with a higher proportion of people aged above 65 have significantly fewer attendances; a 1% higher proportion of 65+ is associated with around 10 fewer attendances of the 1,934 average weekly attendances per week. This implies that hospitals that serve an area with a larger working age population have higher attendances.
Further, hospitals in areas with higher proportion of welfare benefit recipients have higher attendances. A 1% higher proportion is associated with 0.7% more attendances, which equates to around 13 attendances per week. Attendances are positively associated with temperatures and fluctuations in temperatures, but the relationships are nonlinear.
Attendances increase until about 15C° (0.009/0.0003*2) in average temperature, above which they decrease. In weeks with greater differences between minimum and maximum
temperatures attendances are higher. Weeks with high rainfall have lower attendances.
Magnitudes are very small, however.
The results on the patient-reported quality of primary care are counterintuitive. In areas where a 1% higher proportion of patients report that the GP surgery opening times are not convenient, there are about 22 fewer weekly attendances on average. The restructure dummies indicating changes in capacity of T1 and T3 units within the same hospital are all highly statistically significant (Table A6). The dummy for the presence of a T3 unit within the same hospital is also significant, but the effect on attendances to the major department is small at less than 2 attendances per week. This suggests that the presence of a minor injury unit within the same provider does not substantially curb emergency care demand, although this is a commonly cited reason for their introduction [36].
The number of non-acute hospitals, other A&E hospitals, and private hospitals in the catchment area of the hospital were not significantly associated with attendances. Similarly, the number of care home sites had no association with attendances according to our findings, although the availability and quality of aged and social care is considered an important determinant of emergency attendances [37]. The proportion of ethnic minorities and immigrants is not associated with attendances, and neither is the illness profile of the population in the catchment area of hospitals.
The results of the CT model (1) are estimates of the detrended attendances plotted in Figure A7. Although de-trending removes the hospital specific trends in the series, there is still a lot of common variation around the hospitals’ attendances. This implies that there are common factors affecting all hospitals that result in systematically more or less attendances in certain weeks. There is seasonality, with generally more attendances in summer than in winter, a finding confirmed by previous studies [22,23].
The analysis of common variation using principal components analysis shows that the first two principal components explain about 65% of the variance of the detrended log attendances (Figures A8 and A9). Further analysis shows that the first factor represents the detrended average log-attendances for England times -1 in each week (see A10 for detailed explanations). This means that there is a time-varying factor that captures the correlation of
attendances across all hospitals, irrespective of where they were located. It could be driven by macro or national influences which affected the whole of England rather than being specific to a certain hospital, for example, seasonal influenza, changes in weather or national policy changes.
The second principal component exhibits seasonal fluctuations. Moreover, it is negative in summer months and positive in winter months and it varies across hospitals. When we plot on a Map of England the location of hospitals with attendances that are very high or low in comparison to what we would have predicted, a common pattern emerges (Figure 2).
Figure 2 here
For hospitals displayed in blue, attendances are higher in the summer months and lower in the winter months than what the model predicts. The opposite occurs for the hospitals in red:
attendances are lower in the summer months and higher in the winter months. Almost all of the blue hospitals are located in coastal areas, while the red hospitals are located in urban areas (Table A11). It seems that the second principal component captures the seasonal movement of individuals from cities to holiday areas. The proportion of working age population is positively associated with attendances according to the panel data models, and these population groups are the most mobile ones [38]. Data from VisitBritain shows that most tourism nights are spent in the areas where the blue hospitals are located (see p. 29 [38]), and over 16% of trips are made with a member of the party having one or more of a chronic clinical condition.
We then model the two factors with standard time-series methods to generate forecasts (Table A12) and compare them with forecasts from the panel data models for the same period. Table A13 reports the RMSPE and MAPE for all models, for attendances in both log and natural units. It is remarkable that the CT and FE models have very similar prediction errors according to both measures, despite their major differences in terms of specification and estimation. This suggests that the regressors in the FE models and the unobserved factor of the CT model do a very similarly good job in explaining the variation in log attendances. CT and FE models predict better than the RE model, with prediction errors about six times higher for the RE model. This implies that the time invariant variables –which are included in the
RE but not the FE model by design- could adequately capture the heterogeneity of the hospitals.
Conclusions
This study uses both panel and CT models to analyse the geographical and seasonal variations and other determinants of weekly attendances to major A&E departments in England between April 2012 and March 2015. CT methods are used to benchmark the performance of panel data models that aim to identify unobserved determinants associated with attendances from a pool of 17 potential candidates. They are also used to identify unobserved factors that are common to all hospitals.
This study has limitations. First, our study period ends in March 2015, because NHS England stopped collecting data on weekly attendances. Ideally, we would have data covering a longer time period. However, we choose this data for analysis because it allows us to disclose the identity and location of providers and give hospital specific recommendation. It also allows us to collate a unique merged dataset on hospital level with a comprehensive number of potential determinants of attendances. Still, some potentially important covariates may have remained unobserved or captured by poor proxies. We also have some variables with limited variation over time, for example population age proportions and socio-demographic characteristics. However, for most of these variables we would not expect much change over 3 years anyway. Attendances were reported on hospital and not hospital-site level. Some hospitals, in particular in regional areas, are relatively large and defining all covariates with respect to the administrative centre of the hospital may not correctly reflect the characteristics of their catchment areas.
Although the predictive power of the panel data model is good when assessed against the CT model, only few factors are significant: Extreme temperature fluctuations, socio-economic deprivation, a high proportion of working age population, and primary care quality. In addition, the opening and closing of minor injury units -or a substantial change in capacity- have drastic effects on attendances to the major A&E department within the same hospital.
Previous studies have confirmed the impact of weather and climate [20,24–27], and the
association between deprivation and attendances[39–44]. However, the previous literature is conflicting on whether the elderly have higher attendances, or whether their main implication for providers relates to their greater medical complexity [4,15,16]. Previous evidence is also conflicting on the association between primary care provision and A&E attendances, with some studies finding an association [45–47] but others not [48]. As far as we are aware, there is no previous evidence on the relation between major and minor emergency provision within the same hospitals. Our findings on the association between T1 and T3 departments requires further research.
None of the other factors have an impact on attendances according to our findings. In particular, a higher number of other NHS providers in the catchment area of a hospital does not help to relieve pressure on demand, and neither does the number of primary health care providers, private sector providers, and aged and social care homes. Our results therefore do not support the notion that there are unwarranted A&E attendances that can be reduced by improving primary and secondary healthcare, or aged and social care provision in the area.
This is a finding confirmed by a number of previous studies in England and other countries [42,43,48,49]. Our findings support the position that overcrowding in A&E departments is mainly due to a growth in demand that is not matched by equivalent growth in funding [50].
The CT model shows that weekly attendances change from one week to the next in surprising unison across hospitals because of factors that are common to all hospitals but for which we do not have data. They cause distinct patterns related to season and the location of providers that affect attendances. Some hospitals in coastal areas experience unusually high attendances in summer, and this trend is reversed in winter when some hospitals in urban areas experience unusually high demand for their services. This may be related to temporary population movements between urban and coastal regions in the summer and winter months, similar to the impact of the ‘snowbird’ effect on healthcare demand in the USA [6–10]. We identify and map these providers. Our lack of findings on specific factors associated with demand for emergency care poses a challenge to those who attempt to identify effective country-wide supply-side interventions that could help manage demand for emergency providers across the board. Our findings call for impact evaluations of specific interventions using
quasi-experimental research designs that allow controlling for a wide range of other determinants, and underlying time trends.
Results from our CT model can give policy makers guidance on how to structure funding allocations to help specific hospitals cope with high fluctuations in demand and improve their performance in critical time periods when they need additional support. In particular, our findings could be used to fine tune the current winter funding allocations across providers in England. In the winter of 2018/19, hospital and social care providers received a total of £420 million funding for improvements to be better equipped for winter, including £145 million funding for winter improvements in hospitals [51]. It is worth considering if these funds should be more closely tailored to times of increased and decreased demand for certain hospitals. Our findings can help to make funding decisions more granular. Predicted patterns in attendances allow us to single out specific providers that should receive more funding in winter months, and they also identified those providers that experienced lower demand in winter.
Using a CT model, we could not identify exogenous factors that explain variations in attendances, but we could nevertheless uncover patterns which, when combined with other forms of insight, help identify strategies for improving health care and resource allocation decisions in very practical ways. This is particularly helpful if causal models provide little guidance to policy makers, as in our study. Such methods are agnostic approaches to our attempt to understand the past to make decisions about the future. There is a long tradition in using the results of CT modelling for making strategic decisions, most notably in macro-economic policy and in finance. We see no reason why they could not help inform funding allocations for major A&E provision on national level.
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Compliance with Ethical Standards
The authors acknowledge funding from The Health Foundation for conducting this study.
KH acknowledges funding from National Institute for Health Research Health Protection Research Unit (NIHR HPRU), Grant/Award Number: HPRU-2012-10080, and Centre funding from the UK Medical Research Council and Department for International Development, MRC Centre for Global Infectious Disease Analysis, reference MR/R015600/1.
KH also acknowledges funding for work unrelated to this study from the National Institute of Allergy and Infectious Diseases (NIAID) under Cooperative Agreements UM1-AI068619, UM1-AI068617, and UM1-AI068613, with funding from PEPFAR. Additional funding is provided by 3ie with support from the Bill & Melinda Gates Foundation, as well as by NIAID, the National Institute on Drug Abuse (NIDA), and the National Institute of Mental Health (NIMH), all part of NIH. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIAID, NIMH, NIDA, PEPFAR, 3ie, or the Bill & Melinda Gates Foundation.
KH acknowledges personal fees from The Global Fund and the international Decision Support Initiative for work unrelated to this study.
Figures and tables
Table 1: Variable descriptions, 135 English hospitals with major T1 A&E departments
Variable Definition Level Time
period
Time scale
Source
Attend_T1 A&E attendances Type 1 Departments - Major A&E
Hospital
08/04/2012 to
29/03/2015
Weekly
NHS Weekly Situation Report
https://www.england.n hs.uk/statistics/statistic al-work-areas/ae-waiti ng-times-and-activity/
Attend_T3 A&E attendances Type 3 Departments - Other type of A&E/minor injury T3 (minor injury) care provision
T3 1 AttenT3Depts>0, 0
otherwise Supply of health and social care
AEproviders Number of A&E providers
Postcode 2015 Weekly NHS Digital, Other NHS organizations http://systems.digital.n hs.uk/data/ods/datado wnloads/othernhs NHSprovider
s
Number of NHS provider that are not A&E
Care_homes Number of care home sites
GPs Number of GPs Postcode 2015 Weekly NHS Digital, GPs, GP
practices, Nurses, Pharmacies
http://systems.digital.n hs.uk/data/ods/datado wnloads/gppractice INDproviders Number of independent
service providers
Postcode 2015 Weekly NHS Digital, Non
NHS Organisations http://systems.digital.n hs.uk/data/ods/datado wnloads/nonnhs Characteristics of local populations
Pop>15 Percentage of population
<=15 by CCG, mid-year population estimate
CCG
mid 2012, 2013, 2014 and 2015
Annual
Office for National Statistics, People,
Population and
Community
http://www.ons.gov.uk /peoplepopulationandc ommunity
Pop>65 Percentage of population
>=65 by CCG, mid-year population estimate Males Proportion of males by
CCG, mid-year
population estimate
Ethnic_min BME 2011: Black and
minority ethnic
population (%)
MSOAs 2011 One-time Public Health England – Local Health http://www.localhealth .org.uk/#l=en;v=map4 Benefits IMD 2010: Population
reliant on means tested benefits (%)
MSOAs 2010 One-time
Migrants National insurance number registrations 2013-14 (%, total)
OSLAU A
2012-14 One-time Department for Work and Pensions, National Insurance number allocations to adult overseas nationals entering the UK to September 2014 https://www.gov.uk/go vernment/statistics/nat ional-insurance-numbe r-allocations-to-adult- overseas-nationals-ent ering-the-uk-to-septem ber-2014
Ill_1 to Ill_5 5 principal components for morbidity profile
GP practice
2012 - 2013 One-time Quality and Outcomes Framework (QOF) for April 2012 - March 2013, England http://content.digital.n hs.uk/QOF
Meteorological data
Temp_max Mean daily maximum temperature at nearest historical weather station
Postcode 2012-2015 Monthly
Met Office, Historic station data
http://www.metoffice.
gov.uk/public/weather /climate-historic/#?tab
=climateHistoric Temp_min Mean daily minimum
temperature at nearest historical weather station Rain Total rainfall at nearest historical weather station Quality of Primary Care
GP_wait
Percentage of patients who reply ‘On the same or next day’ on the questions how long after initially contacting the surgery did they actually see or speak to the GP.
CCG 2012/13-20
13/14 Annual
NHS England, GP patient survey, patient experience
https://gp-patient.co.u k/surveys-and-reports GP_open Percentage of patients
who reply ‘No’ to the question whether their GP surgery is currently open
at times that are convenient for them.
Notes: The website addresses were accurate at the time the data were collected but may become outdated.
Variables that were only observed once over the study period were included as time-invariant variables, and variables that were observed yearly, quarterly or monthly were attributed to the week closest to their collection time, and held constant until the date of the next collection. Hospitals that underwent complex restructures and dissolutions were removed from the analysis (These are hospitals with codes RYQ, RJZ, RJ2, RJE, RL4, RJD, and RC9), but we retained records for hospitals that were merged or taken over. In those instances, we applied the structure that existed at the end of the observation period, retrospectively creating values over the whole period by adding up the attendances for the constituent hospitals prior to the merge or take-over. Specifically, RCB and RCC merged on 1 July 2012 (RCB is the resulting hospitals), RC3 and RV1 merged on 1 October 2012 to form R1K, RD7 was acquired by RDU on 1 October 2014, and RVL was taken over by RAL on 1 July 2014.
Table 2: Descriptive Statistics for all variables, 135 English hospitals for the weeks from April 2012 and March 2015
Variable Mean St. Dev. Min Median Max
Dependent Variable
Attend_T1 1,932.88 882.81 616 1,765.00 7,122.00 T3 (minor injury) care provision
Attend_T3 375.82 630.72 0 0 4,216
Supply of health and social care
AEproviders 2.04 1.03 0.16 1.99 7.24
NHSproviders 202.45 126.24 42.65 172.47 687.73 Care_homes 157.83 95.97 36.37 134.13 513.64
GPs 88.35 35.2 30.43 80.64 211.54
INDproviders 48.27 41 2.53 34.72 279.46
Characteristics of local populations
Pop>15 19.03 1.22 16.26 19.04 22.72
Pop>65 17.01 2.91 9.08 16.89 25.41
Males 49.32 0.52 48.16 49.28 51.44
Ethnic_min 13 12.36 1.58 8.29 54.07
Benefits 14.88 4.86 7.21 14.31 28.7
Migrants 1.04 1.01 0.17 0.71 5.27
Ill_1 -0.002 0.06 -0.14 -0.01 0.26
Ill_2 0.003 0.01 -0.03 0.004 0.08
Ill_3 -0.004 0.01 -0.05 -0.003 0.03
Ill_4 0.001 0.01 -0.02 0.001 0.03
Ill_5 -0.002 0.01 -0.03 -0.002 0.02
Quality of primary care
GP_wait 0.49 0.04 0.39 0.49 0.61
GP_open 0.76 0.03 0.67 0.76 0.86
Meteorological data
Temp_max 14.42 5.5 4.4 14.7 27
Temp_min 6.97 4.25 -1.8 6.9 15.2
Rain 72.59 40.82 3.2 65.8 247.4
Table 3: Panel data models results for determinants of weekly attendances to 135 English Type 1 A&E departments, 08/04/2012 to 15/02/2015
Fixed effect model Random effect model
Constant 3.150* (1.682)
Supply of health and social care
AEproviders 0.002 (0.005) 0.001 (0.005)
NHSproviders 0.00001 (0.0002) 0.00002 (0.0001)
Care_homes 0.001 (0.001) 0.0004 (0.001)
GPs -0.0004 (0.0003) -0.0005 (0.0003)
INDproviders 0.00003 (0.0001) 0.00003 (0.0001)
Characteristics of local populations
log(Pop>15 * pop) -0.584*** (0.199) -0.511*** (0.178)
log(Pop>65 * pop) 1.017 (0.732) 0.892 (0.676)
log(Males * pop) 0.311 (0.942) -0.796 (0.827)
log(Ethnic_min * pop) 0.066 (0.056)
log(Benefits * pop) 0.701*** (0.150)
log(Migrants * pop) 0.036 (0.065)
Ill_1 -0.326 (0.711)
Ill_2 0.607 (3.098)
Ill_3 -0.139 (3.331)
Ill_4 -0.204 (5.992)
Ill_5 -6.876 (5.206)
Meteorological data
(Temp_min + Temp_max)/2 0.009*** (0.001) 0.009*** (0.001) ((Temp_min + Temp_max)/2)^2 -0.0003*** (0.0001) -0.0003*** (0.0001)
(-Temp_min + Temp_max) -0.009 (0.007) -0.009 (0.007)
(-Temp_min + Temp_max)^2 0.001** (0.0004) 0.001** (0.0004)
log(Rain) -0.013*** (0.001) -0.013*** (0.001)
Quality of primary care
GP_wait 0.228 (0.157) 0.212 (0.155)
GP_open -1.059*** (0.130) -1.118*** (0.132)
T3 (minor injury) care provision
T3 .014* (0.008) -0.015* (0.008)
Hospitals with T1/T3 restructures
x*** x***
Hausman test (p) 0.0066
Note: Standard errors in parenthesis; *p<0.1; **p<0.05; ***p<0.01; 16 dummies for hospitals with structural breaks in attendances due to reorganizations between T1 and T3 departments are included in models and coefficient estimates reported in the A.
Figure 1: Weekly log attendances to major A&E (T1) departments of 135 hospitals in England between April 2012 and March 2015.
Figure 2: Hospitals with high unexplained seasonal variations in attendances
Note: Red hospitals have higher attendances in winter and lower attendances in summer than would be predicted; blue hospitals have high attendances in summer and low attendances in winter.
Red hospitals have high positive loadings for the second principal factor at above 0.7; Blue hospitals have very low negative loadings for the second principal factor at below -0.7.
