Modelling the Dynamic Effects of Elective Hospital Admissions on Emergency Levels in England

In England as elsewhere, policy makers are trying to reduce the pressure on costs due to rising hospital admissions by encouraging GPs to refer fewer patients to hospital specialists. This could have an impact on elective treatment levels, particularly procedures for conditions which are not life-threatening and can be delayed or perhaps withheld entirely. This study attempts to determine whether cost savings in one area of publicly funded health care may lead to cost increases in another and therefore have unintended consequences by offsetting the cost-saving benefits anticipated by policy makers. Using administrative data from Hospital Episode Statistics (HES) in England we estimate dynamic fixed effects panel data models for emergency admissions at Primary Care Trust and Hospital Trust levels for the years 2004–13, controlling for a group of area-specific characteristics and other secondary care variables. We find a negative link between current levels of elective care and future levels of emergency treatment. This observation comes from a time of growing admissions and there is no guarantee that the link between emergency and elective activity will persist if policy is effective in reducing levels of elective treatment, but our results suggest that the cost-saving benefits to the NHS from reducing elective treatment are reduced by between 5.6 per cent and 15.5 per cent in aggregate as a consequence of increased emergency activity.


Introduction
Successive Labour Governments funded exceptional growth in UK health spending at an average of 6.4% per annum between 1996/7 and 2009/10 and while growth has slowed in more recent years (IFS 2015), publicly funded healthcare spending in England has, on the whole, been protected from recent austerity measures that have affected most Government departments. However, the National Health Service (NHS) is expected to improve efficiency and to avoid over-spending, as the NHS planning document "Everyone Counts: Planning for Patients 2013/14" explains. This includes pressure on spending in hospitals, and incentives to encourage GPs to refer fewer patients for specialist hospital care, both of which could impact on elective treatment levels, as procedures can be delayed or perhaps withheld entirely. Our concern is that restricting elective care could lead to an increase in emergency activity as patients seek withheld treatment in other settings. In particular, this study attempts to determine whether cost savings in one area of publicly funded health care may lead to cost increases in another and therefore have unintended consequences by offsetting the cost-saving benefits anticipated by policy makers. A specific policy concern is that if emergency care increases when elective care is reduced, cost-savings achieved by the NHS might not be as significant as the recent efficiency-pursuing policies intend.
Previous studies have looked at the choices doctors face when there are short-term limits on the number of hospital beds available for patient admissions. For example, where "bedblocking" occurs (e.g. Black & Pearson 2002, Jasinarachchi et al 2009, Godden et al 2009, and patients are forced to remain in hospital beds not necessary for their recovery due to a lack of more suitable facilities, or where patients need to be admitted from Accident and Emergency departments (A&E) to meet waiting time targets (e.g. Proudlove 2003). In these situations, it is common for elective admissions to be postponed or cancelled in preference to more urgent emergency admissions. Robb et al (2004) and Nasr et al (2004) study the impact of prioritising emergency operations and admissions over planned procedures. They note that this practice has cost implications and can cause distress and huge inconvenience to the affected patients.
Another section of the literature focuses on conditions for which an elective procedure directly impacts on the requirement for future emergency treatment. For example Simianu et al (2016) look at the impact of elective colon resection on rates of emergency surgery for diverticulitis.
In this particular case, higher rates of elective treatment do not reduce the future requirement for emergency care, but this result may not generalise across all conditions. Morgan et al (2013) perform a systematic review of the literature on interventions used to reduce emergency department utilization. Of the studies they found that considered increased healthcare provision in other settings, four noted statistically significant reductions in emergency care as a result. They also noted that savings ranged from 10% to 20% in three studies that reported cost implications. However, the relationship between emergency and elective treatment levels when there are changes to hospital resources has not been widely studied. As we demonstrate in section 2, it is not clear whether emergency and elective treatment levels will move in the same direction or in opposite directions in response to changes in capacity. In this paper we add to the literature by providing an estimate of the consequences on emergency activity in the NHS in aggregate when elective provision is changed.
In the decade to 2011/12 hospital admissions in England increased by 35.4% (HSCIC, 2012 (Blatchford & Capewell, 1997;Sharkey & Gillam, 2010, Poteliakhoff & Thompson, 2011; increased ability to detect and treat illness (Hobbs 1995); the effects of changing incentives in the recently introduced framework of paying hospitals via a tariff instead of with block grants (Farrar et al, 2009;Information Centre, 2010); the opening of the market, allowing private providers and in particular Independent Sector Treatment Centres (ISTCs) to perform procedures on NHS-funded patients (Naylor & Gregory, 2009); and "targets" to reduce patients' waiting times for both elective and emergency care. Working practices of GPs have changed, notably with the contract changes that allow them to opt out of providing direct 'out-of-hours' services (Coast et al 1998), and this may also have contributed to increased levels of admissions.
The Nuffield Trust has produced several studies of elective and emergency activity levels separately. Recent work (Blunt et al 2010) shows that the number of emergency admissions has been rising for some time, in part due to a reduction in the clinical threshold used when deciding to admit. Smith et al (2014) show that elective admissions are increasing rapidly, and that pressure on hospital resources is likely to continue into the next decade unless more This important matter has not been well studied in the literature. One explanation for the lack of literature studying the interaction between levels of emergency and elective care over a long time-frame is that it is difficult to identify causal relationships between changes in the two types of care because most shocks that affect demand and supply of healthcare will impact on both emergency and elective simultaneously. We attempt to overcome this issue by estimating dynamic fixed effects panel data models for emergency admissions at PCT (Primary Care Trust) and NHS Hospital Trust level, showing the impact of elective changes on future levels of emergency care, controlling for a group of area-specific characteristics and other secondary care variables. We also estimate a model of elective admission rates using emergency admissions as a dependent variable to identify causality. As a further check we consider also the elective treatment of NHS patients by private providers. Privately owned organisations were encouraged to treat NHS-funded patients by innovations such as the creation of ISTCs in 2003, which provided guaranteed levels of income for operators over a fixed time, and furthermore by letting any private hospital treat NHS patients providing they were willing to do so for the nationally agreed tariff fee (Arora et al 2013).
We find that lower levels of elective admission in a geographical area are associated with higher levels of emergency treatment in later years, with consistently negative coefficients on lagged elective admissions in all specifications of emergency admissions estimated. This effect is observed when local areas are measured at both Hospital Trust and PCT levels.
In all specifications of emergency admissions, the coefficient of lagged emergencies is significant and positive at the one percent level, showing that high rates of emergency admissions are a persistent problem across time for some areas. We also find that elective activity by private providers does not affect emergency admissions.
Our study covers a time during which resources available for hospitals were growing with the increase in admissions and as such staff workloads are likely to have remained fairly constant.
However, as the efficiency drives currently in place take effect, staff workloads are likely to increase, and increasing nurse-workloads have been found to increase the chance of patient mortality in US hospitals (Needleman et al 2011). Evidence from Germany suggests that the increased risk occurs once occupation levels reach a certain threshold, when staff come under greater risk of making mistakes (Kuntz et al 2014). In times of greater workload, lengths of stay for patients can increase (Berry Jaeker & Tucker 2013, Batt & Terwiesch 2012, and these issues are likely to become more important in the NHS as pressure on resources grows.
The rest of the paper is structured as follows. Section 2 shows how the provision of emergency and elective care are likely to respond to changes in policy and the incentives they place on hospital management and patients. Section 3 details the dataset, then section 4 explains the approach used in the econometric analysis. Section 5 provides results. Section 6 discusses the policy implications and concludes.

Supply and Demand processes which could affect hospital admissions
In this section, we briefly consider the processes by which changes in aggregate levels of elective provision could alter the levels of emergency care. Changes in elective activity could affect i) the demand for emergency care from patients and/or ii) the supply of emergency care by hospitals.
i) Demand for emergency care The demand for emergency care when elective supply changes will be affected differently depending on whether elective and emergency care are substitutes or complements.
Withholding an elective procedure may cause the patient's condition to deteriorate to the stage where emergency treatment is required, and in this case the two types of care are substitutes.
For example, not performing an elective hip replacement may increase the likelihood of a patient suffering a fall and thus requiring emergency treatment. If the two types of hospital treatment are substitutes, increasing elective provision would mean less emergency treatment is required by patients. Alternatively, emergency and elective activity could be complements.
This may be true if elective procedures cause complications for patients that later require emergency treatment. It is likely that both of these issues would take some time to become apparent and that we would expect to see a lag between the introduction of the elective supply shock and the impact on emergency activity. Elective and emergency treatments are likely to be substitutes for some conditions and complements for other conditions. As such, it is difficult to predict whether the aggregate demand for emergency care will go up or down as a consequence of increased elective provision.
ii) Supply of emergency care The policies introduced in the early years of the 2000s were designed to extract efficiency gains created by ensuring that hospitals operate in a market with some competitive pressures rather than one in which they had significant market power (Mays et al 2011).
Traditional economic theory proposes that profit maximising agents in a competitive market with two goods would attempt to equalise the marginal profit across the two goods, in this case emergency and elective healthcareif not, profits could be increased by switching resources towards the provision of the more lucrative service. Even after the reforms, hospital managers are unlikely to fully act as profit maximisers, but there are aspects of the new healthcare "market" that influence managers' behaviour and make them increase provision of services that are more lucrative to their hospital. Thus, if additional resources are made available with the intention of increasing elective provision in hospitals, and hospital managers are acting as rational profit maximisers it is likely that the thresholds for both emergency and elective admissions will be relaxed, with some of the additional resources made available for emergency admissions. This would mean that emergency and elective activity levels move in the same direction after a change in resources. However, as with demand side effects, these supply-side changes are likely to take some time to be fully implemented, hence we expect to see a time-lag between the elective supply shock and any impact on emergency activity.
Most of the policies introduced in the NHS are likely to have caused positive supply shocks in elective care, but it is likely that some of the increased aggregate capacity will be used to provide more emergency treatment. It is not clear how patient demand will be affected, and therefore whether emergency or elective activity in aggregate move in the same or a different direction is unclear.

Data
To model emergency activity at PCT and Trust level, we create a panel of variables covering treatment, demographics and supply-side factors for the years 2004 to 2013. at the practice. We focus on four conditions, namely Stroke and Transient Ischaemic Attack, Chronic Obstructive Pulmonary Disease (COPD), Epilepsy and Cancer, and use the raw prevalence rates in our analysis. These rates do not take account of differences between populations in terms of their age or gender profiles, or other factors that can influence the prevalence of conditions. The data on prevalence of the clinical conditions is grouped at PCT level. The data cover almost all GP practices (around 9,000) in England, and are extracted from disease registers submitted to the national Quality Management and Analysis System (QMAS).
We use Office of National Statistics (ONS) mid-year population estimates to calculate elective and emergency hospital admission rates. We also use ONS data on the percentage of the population by age (male population over 65; female population over 60) 4 and gender.
We also include measures that characterise the supply of NHS services, namely the number of specialists per one thousand population and the number of hospitals at PCT level. Furthermore, we also consider the impact of private providers performing elective procedures on NHSfunded patients on emergency admission levels.   Our demographic variables are the proportion of the total population who are men aged 65+ or women aged 60+, and the proportion of women in the total population. We include these two age variables, which are published by the ONS, to give an indication of demand faced by healthcare providers due to older local populations. All three of these series are generally consistent across our timeframe, with the proportion of the population who are men aged 65+ around 6.8%, the proportion of the population who are women aged 60+ between 11.4% and 11.8% and the proportion of women in the population between 50.2% and 50.9%. We

Empirical strategy
Our empirical strategy is to estimate dynamic fixed effects panel data models for emergency admissions, controlling for a group of area-specific characteristics and other secondary care variables, plus a selection of variables intended to show the influence of private providers, at Hospital Trust level and separately at PCT level. The rate of elective admissions could be influenced by the rate of emergency admissions. Moreover, it is not possible to estimate supply and demand separately so our strategy produces reduced form versions of the model of hospital activity. To account for these facts we use the Arellano and Bond (AB, 1991) first differences GMM-IV estimator 5 . As has been shown by Al Sadoon et al (2019), the AB method is consistent even in presence of selection due to sample selection, attrition or merger processes.
We estimate the following model at Hospital Trust and PCT level: where Eit represents the number ( . Finally, we control for time with year effects (µt), PCT with fixed effects (σj) and εjt is a random error term which is assumed to be normally distributed with a variance that is allowed to vary across trusts.
In order to specify the G function we consider two specification options: i) eLindsjt which represents the log number of elective admissions at NHS-funded for patients from PCT j in time t; and ii) a dummy variable ELDjt, which equals 1 if PCT j had any NHS-funded patients treated by a private provider in year t, and 0 if the PCT had no NHS-funded patients treated by a private provider that year. In addition to this, we allow for structural changes after the introduction of a private provider in a given PCT by interacting the (log) lagged emergencies, Eijt-1, and the (log) lagged elective admissions, ELijt-1, at the trust with the ELDj dummy.
To account for the possibility that behaviour of trusts at the PCT level are not (fully) independent we also analyse the model aggregating data at the PCT level. Thus, we alternatively consider the following model: 5 In the literature there are two standard estimators, namely the Arellano and Bond, and the System estimator. The nature of our problem led us to prefer the first of these estimators.
= 1 −1 + 2 −1 + 3 ( ) + 3 + 4 + + + In our model all lags dated t-2 and backwards are potential instruments for the predetermined variables. The rest of the variables are considered strictly exogenous and are introduced in the regressions as standard IV instruments. We report robust standard errors throughout. 6 Table 2 presents results for the estimated specifications of equation (1) using data at Trust level.

Results using Trust level data
The first three columns present results in which the effect of private providers is proxied with a dummy variable (ELD), while the other columns present results using the per capita number of elective interventions (eLinds). Columns (1) and (4) present the basic specification with socio-economic and supply side controls, while columns (2) and (3)  Alternatively, the (elasticity) coefficient of the lagged elective admissions is always found to be negative, between -0.17 and -0.26, but is only significant at the 10 percent level. These values suggest that an additional hundred elective admissions in the previous year can be expected to reduce emergencies by between 17 and 26.
In order to check possible complementarity between emergency and elective admissions we estimate a similar model with the current level of elective admissions as the dependent variable instead of the current level of emergency admissions. We find that the only significant driver is the lagged (log) number of elective admissions at the Trust level (with a coefficient always between 0.6 and 0.7). In particular the lagged number of emergencies is never found to be significant (neither alone or interacted with the ELD dummy). Thus, we do not find strong evidence of complementarities. 9 In general we do not find important (significant) direct effects of the variables related to the treatment of NHS-funded patients treated by private providers (the ELD dummy has the correct sign but is significant at the 10 percent level in just one specification; the eLinds variable is not significant). However, we find interesting effects of their interaction with the site level variables, although they are only significant in the specification in which they are not instrumented. In this specification the estimated effects are found to partially (in the case of emergencies) or fully (in the case of elective care) balance the effects found in the specifications without interactions. That is, the interaction with the lagged emergencies is negative, partially compensating the dynamic coefficients, and the interaction with lagged electives is positive, practically compensating the dynamic component.
In general we find that the demographic variables have non-significant effects across all specifications. The coefficients of the supply factors have the expected signs. In particular, the hospital per capita variable is found significant in the non-instrumented interaction specifications (columns (2) and (5)).
As a placebo test we have also estimated a model of elective admissions using emergency as an explanatory variable (see Appendix 2). This test is performed to reject the hypothesis that increasing emergency admissions has no effect on elective admissions. We observe that the coefficient of emergency admissions is always negative in all of the specifications estimated but is never statistically significant.

Results using PCT level data
9 Results from these experiments are not reported but are available upon request.
In this section we evaluate the model at the PCT level. The results obtained regarding the key coefficients of the model at this level of aggregation will allow us to assess whether decisions are taken at the trust (hospital) or the PCT level. Table 3 shows the results for the estimated specifications of equation (2) using data aggregated at the PCT level. As in Table 2, the first three columns present results in which the effect of private provision is proxied with a dummy (ELD) while the rest present results using the per capita number of elective interventions (eLinds). Columns (1) and (4) present the basic specification with demographic and supply side controls, while columns (2) and (3)  Both of the variables relating to the treatment of NHS-funded patients by private providers show the expected sign, but in neither case are they significant. The same happens with the interaction terms, which are not found to be significant in any specification.
As in the previous specifications, the demographics coefficients are always non-significant.
Finally, the supply factors are found to have the expected signs. As in the case with PCTs, the hospital per capita variable is the stronger factor, but is never found to be significant at the five per cent level.
In 2016/17, the average unit cost for an elective inpatient admission was £3,684; the average unit cost of a non-elective inpatient admission was £1,590. If policy was successful in reducing elective admissions by 1% (from 7,555,200 to 7,479,648), this would lead to savings on elective care of approximately £278m (£3,684 x 75,552) but our estimates suggest that in this situation, emergency admissions would increase by between 13 per cent and 36 per cent of the decrease in elective admissionsbetween 9,821 and 27,198. If admissions went up by 9,821 then this would cost £16m and if the increase was 21,198 then this would cost £43m, thus reducing the savings to the NHS by between 5.6 per cent and 15.5 per cent of those accrued by reducing elective admissions.

Discussion and Conclusions
There is significant pressure on the NHS in England to control expenditure at a time when the public purse is being restricted. This is likely to impact on all aspects of healthcare, but particularly those elective treatments which are for conditions that are not life-threatening and can be delayed or withheld entirely if resources are severely limited. We find, using a panel data model for emergency admissions at PCT and Trust level, that there appears to be a negative relationship between elective activity within hospitals and future emergency activityi.e. that changing levels of elective activity will likely lead to an opposite effort to the number of patients that require emergency treatment in the future. This presents a problem for policy makers, as it means cost-saving measures that target elective hospital care are unlikely to reap the benefits in aggregate that they had hoped forour estimates suggest that any reduction to elective care could lead to increases in emergency spending of between 5.6 per cent and 15.5 per cent of the savings achieved by reducing elective care. It becomes increasingly important for practitioners and policy makers to be as efficient as possible, making sure that where possible patients are treated in primary care settings and focusing specialist referrals on to patients who stand to gain the most to limit the number who require emergency care.
There are other factors to consider. The negative relationship between current levels of elective care and future levels of emergency activity that we observe in this research comes using data from a time when elective provision was generally increasing year-on-year. It does not necessarily follow that the same negative relationship will persist in the different circumstances associated with reducing elective activity. The concept of supply-induced demand (Evans, 1974) where demand expands to fill the available capacity, is a particular issue in healthcare and is one reason to be cautious about the generalisability of our conclusion.
14 A second issue is that we only consider aggregate emergency and elective treatment. A more disaggregated study may be able to identify conditions or pathways in which reducing elective care will not create additional workload for emergency departments.
Even without further work, the results presented here suggest that the NHS faces a complex problem and that efforts to reduce elective care are likely to have unanticipated consequences for other areas of the NHS that could require costly solutions.   Robust z-statistics in parentheses; *** p<0.01, ** p<0.05, * p<0.10. Time dummies are present in the specification but omitted from the table. GMM Instruments: lags (2, 5) of Eijt-1 and ELijt-1 in all columns; lags (2, 2) of Eijt-1*ELD and ELijt-1*ELD in columns (2) and (5). The rest of the variables are not instrumented. All the specifications pass the standard specification test. Additional notes: The Hansen statistics evaluates the validity of the over-identifying instruments used. The m1 (first order serial correlation of the errors) and m2 (second order serial correlation), evaluate whether the level errors are white noise (as required by the AB estimator). Robust z-statistics in parentheses; *** p<0.01, ** p<0.05, * p<0.10. Time dummies are present in the specification but omitted from the table. GMM Instruments: lags (2, 5) of Eijt-1 and ELijt-1 in all columns; lags (2, 2) of Eijt-1*ELD and ELijt-1*ELD in columns (2) and (5). The rest of the variables are not instrumented. All the specifications pass the standard specification test. Additional notes: The Hansen statistics evaluates the validity of the over-identifying instruments used. The m1 (first order serial correlation of the errors) and m2 (second order serial correlation), evaluate whether the level errors are white noise (as required by the AB estimator).
""Compliance with Ethical Standard"" Disclosure of potential conflicts of interest. Sergi Jiménez-Martín declares that he has no conflict of interest. Stuart Redding declares that he has no conflict of interest. Catia Nicodemo declares that she has no conflict of interest.
Ethical approval: This article does not contain any studies with animals performed by any of the authors. This article does not contain any studies with human participants or animals performed by any of the authors.
Appendix 2: Log elective Hospital Site Level specifications. Arellano-Bond estimator.