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What's in a wait?
Available online at www.sciencedirect.com
Health Policy 85 (2008) 207–217
What’s in a wait? Contrasting management science and economic perspectives on waiting for emergency care Alec Morton ∗ , Gwyn Bevan 1 Operational Research Group, Department of Management, London School of Economics and Political Science, Houghton St, London WC2A 2AE, United Kingdom
Abstract The current paper reviews and contrasts a management science view of waiting for healthcare, which centres on queues as devices for buffering demand, with an economic view, which stresses the role of the incentive structure, in the context of English Accident and Emergency Departments. We demonstrate that the management science view provides insight into waiting time performance within a single facility but is limited in its ability to shed light on variations in performance across facilities. We argue, with reference to supporting data, that such variations may be explainable by a proper understanding of the incentive structure in A&E Departments. © 2007 Elsevier Ireland Ltd. All rights reserved. Keywords: Waiting; Queueing; Accident and emergency
1. Introduction Much healthcare research has been dedicated to the phenomenon of the length of time which patients have to wait in order to receive healthcare services. This reflects the high level of public and policy attention which waiting has historically attracted [1–3]. Historically, waiting lists were viewed (often implicitly) as arising from a “backlog” in the need for care [4]. Despite the survival of the backlog motif in policy ∗
Corresponding author. Tel.: +44 20 7955 6539. E-mail addresses: [email protected] (A. Morton), [email protected] (G. Bevan). 1 Tel.: +44 20 7955 6269.
rhetoric (e.g. Morgan [5]), the repeated failure of policy initiatives predicated on this view of waiting has established beyond doubt the necessity of “realising that waiting lists are . . . a manifestation of a more complicated, dynamic flow through interconnected parts of a whole system of care” [3, p 44] if sustainable reductions in waiting times are to be achieved. Curiously, however, research on waiting-related phenomena has proceeded apace in two quite distinctive research communities, management science and health economics, which have fundamentally different views of the character of this system of care and in the mechanism by which it generates waiting. Management scientists view waiting as arising from the dynamic buffering or smoothing of demand. In this
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view, waiting arises in any system where capacity is fixed in the short run, but where demand fluctuates [6–8]. This insight has been the basis for a powerful analytic technology, queueing theory, which has been widely applied in areas such as the design of call centres [9] but which also has a long-recognised applicability to the healthcare arena [10]. A rich literature exists which discusses this idea in the context of capacity management in healthcare [10–12]. Modelling techniques based on this view of waiting have been applied to the study of both Accident and Emergency Departments (e.g. [13]), and to elective services (e.g. [14,15]). Economic accounts, on the other hand, stress the role of incentives in the generation of waiting. Providers may not have sufficient incentive to exert their maximum level of effort, or may even have a vested interest in the actual generation of waiting. This could arise, for example, because surgeons who work in both state and private sector allow public sector waiting lists to run up in order to generate private sector demand [16,1]); because consultants prioritise patients based on personal criteria (such as how intellectually interesting they find the patient’s condition) which do not relate to societal objectives [17]; or because hospitals can use waiting lists to attract funding [18]. A related stream of research emphasises the role of incentives on the demand-, rather than the supply-side: patients in systems where healthcare is provided free at the point of delivery have little incentive to restrain their consumption of healthcare [19]. Waiting lists fulfil the same role as prices fulfil in conventional markets, depressing demand: it is thus possible to think of waiting as a “time price” as opposed to a “money price” [20]. These perspectives imply quite different views of the motivations of the people who work in healthcare systems, and the appropriate responses to poor performance. The management science view implicitly supposes that healthcare workers are well-intentioned public servants: “knights”, in the terminology of Le Grand [21]. In this case, the appropriate response is essentially a technical one: study work processes and identify and implement improvements. In the English system, this perspective and role has been taken on in recent years by the Institute for Innovation and Improvement (and formerly by its predecessor, the Modernisation Agency), which advises NHS organisations on process redesign (see e.g. [22] for a flavour of this work).
The economic view, on the other hand, supposes that the healthcare sector is staffed by people who, if not quite “knaves” [21], nevertheless have an eye for their own interest. This suggests that the appropriate response to poor performance is to re-align the goals of providers with society’s objectives for the healthcare system. This role has been taken on within the English system by the Department of Health, supported by the Healthcare Commission, which operates a regime of performance measurement and targets by which organisational performance is judged. The main sanction used to give this regime bite is the dismissal of senior management in English trusts judged to be failing [23]. A more pessimistic interpretation of the economic model focusses on the demand-side effects. Enoch Powell, a former UK Minister for Health, championed this view, claiming that reducing waiting lists “is an activity about as hopeful as filling a sieve.” (cited by Yates [1]). Recent econometric work by Martin and Smith [24] and others has somewhat tempered this fatalism, suggesting that the dependency of the demand on waiting times, while real, is nevertheless relatively modest. We see these two views, the queuing view and the incentive view, of the nature of waiting as having complementary roles in understanding how system performance varies within and between facilities. Our aim in this paper is to demonstrate how an analysis informed by both these perspectives can uncover patterns in data which would not be obvious when the data are viewed from either perspective in isolation. A particular focus in this paper is the effect of scale when comparing between facilities: we argue that the absence of an effect which would be predicted on the basis of the queueing model can be explained by the operation of an incentive effect. We develop our analysis in the context of English A&E Departments (A&EDs). An attraction of A&EDs is that they are relatively discrete units for study, as they do not generally share theatre or bed capacity with other parts of hospital. Although our empirical analysis is limited to A&EDs, our broad conceptual arguments are equally valid across all hospital activity. A&EDs have in recent years seen substantial increased investment, in terms of salaries, staffing levels and transitional support for process redesign.
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Accompanying this investment there has been a renewed focus on performance and since 2004, all English hospitals have been required to have at least 98% of patients leave the A&ED in less than 4 hours [25,26]. Progress towards this target has been quite encouraging: Department of Health statistics show that 96.6% of patients spent less than 4 hours in A&E in the first quarter of 2005–2006 as against 87.3% in the same quarter of 2003–2004 [27], itself a substantial improvement on even lower percentages in previous years. Despite reports of gaming and systematic misrepresentation of performance which suggest that these figures should not be taken entirely at face value, it seems likely that there has been some genuine improvement in system performance [28]. For this study, we were supplied by the Healthcare Commission with a dataset from a survey of 252 “Type 1” A&EDs across England, Wales and Northern Ireland (this excludes Walk-in Centres and Minor Injuries Units). These data report aggregate performance at the A&ED level and are the basis for the Healthcare Commission’s recent report on this subject [29]. The A&E audit, conducted in 2004, contains various questions covering diverse aspects of operating and financial performance. We restricted our attention to A&EDs in England only as the regulatory environment in Wales and Northern Ireland differs from that of England. Additionally, we obtained a 1-year extract of patient-level transactional data from an A&E patient administration system provided to us by a hospital with a mid-size A&E department (the “North West General”). An important feature of our analysis is that it relates to individual physically distinct A&EDs, where there is a single shared waiting area, and which fall under the management of a lead A&E consultant. The data sources which we use in this paper allow us to define this physically distinct facility as our unit of analysis, but many data sources on the NHS in England relate to multi-site hospital trusts and do not permit further disaggregation. Often this is a limitation built into the data collection itself, not merely of a feature of the level of aggregation at which data are reported. For the purposes of understanding in detail the drivers of hospital performance, such data are of limited use, as many of drivers of performance relate to features of the individual facility.
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2. Queueing and scale effects In this section, we briefly review the key ideas of queueing theory and discuss their applicability in the context of an A&ED. The central idea of queueing theory is that variability in the waiting times arises from variability in the arrival process which is either unpredictable, or predictable but unmanageable (as happens in systems which experience “rush-hours”). This variability results in the system becoming congested (a so-called “busy period”), and patients who arrive at this time experience longer waits. Drawing on data from North West General’s patient admission system, we illustrate the variability in the arrival pattern for April 2004 in Fig. 1. It can be seen from this chart that while there is a clear weekly pattern (predictable spikes occur on the 5th, 12th, 19th and 26th, which are all Mondays), there is also a considerable component of random variation in arrivals. Predictable weekly or diurnal variability in demand should not pose serious problems for A&E management as capacity can be flexed in the short run, through appropriate scheduling of staff throughout the day (although some A&EDs may find that physical capacity is a limiting factor at times of peak demand). The random variability component of demand is harder to manage, however. Queueing theory predicts that in response to such variability, the system will become congested, and patients will experience increasingly longer waiting times. Based on transactional data, we reconstructed a process which counts the number of patients in the Department over the month of April 2004. Fig. 2 shows how system congestion varies throughout the month. There is a clear daily pattern: the system fills during the day and then almost completely clears out at night. The spike in congestion on the 25th and 26th of April is clearly associated with the spike in arrivals shown in Fig. 1. We also find, unsurprisingly, that, on average, patients who arrive when the system contains a larger number of patients, experience on average longer waits (see Fig. 3). The relationship becomes harder to discern at the higher levels of congestion because such levels occur infrequently and thus the dataset contains fewer samples of such arrivals. As this analysis demonstrates, queueing theory provides a good account of how waiting is generated in a particular facility is therefore borne out by our analysis of North West General’s patient admission system.
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Fig. 1. Arrival pattern over the month of April at North West General.
In view of the obvious applicability of queueing theory in understanding this sort of system, it is surprising that the lessons of this theory seems to have been ignored by those setting waiting time targets for A&E Departments. The published rationale for the 98% threshold for waiting times less than 4 hours is that while every Department is expected to have the capacity to treat all patients within 4 hours, there may be clinical reasons to keep some small number of patients beyond the 4 hour limit: “the emergency department
offers the only appropriate facilities and expertise that are suited to the treatment of the patient’s current condition” [26]. That variability in demand could lead to variability in performance seems not to have been taken into account. This is surprising as we find considerable appreciation of the role of variability in generating waits amongst staff on the shop floor. The queueing view of waiting has therefore considerable plausibility as an account of how waiting is generated within an individual facility. However, when
Fig. 2. Congestion of the A&E Department over the month of April at North West General.
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Fig. 3. Expected waiting time conditioned on number of patients in Department on arrival.
comparing waiting time performance between facilities, the picture becomes more complex. As it happens, the queueing model makes a strong and testable prediction about performance between different (yet comparable) institutions. Specifically, queueing systems exhibit a predictable scale effect, with larger systems performing better in terms of waiting times than smaller systems with a comparable ratio of capacity to demand. Green [30,31] has stressed the significance of this sort of result in the context of hospital capacity planning. The intuitive explanation of this phenomenon is that larger systems experience demand at an aggregated levels, and as a result, fluctuations in the demand process “even out”, whereas smaller institutions will experience demand as lumpy and irregular. To make this intuition clear, consider two single-handed A&EDs (i.e. one doctor), called A and B, facing a similar volume of demand. In a given stretch of time, the patients which arrive at A are denoted A1 , A2 , A3 and those at who arrive at B are denoted B1 , B2 , B3 , B4 . The charts in Fig. 4 show how patients will be handled at A and B. The vertical axis counts the number of patients in the system either being seen or waiting; the horizontal axis measures time. The blocks describe the phases of the patient journey, with grey blocks representing the time a patient spends with a doctor, and the white blocks representing time waiting. Thus patient A1 arrives and is seen by a doctor, during which time A2 arrives and
asked to wait. After A1 has departed, A2 is called and is seen, and eventually departs. As the doctor is unoccupied, when A3 arrives she can be seen immediately. Events at system B are depicted analogously. In both systems there is some waiting. Suppose A and B were to be aggregated in a new system (“A + B”) with both doctors, and serving both demand streams. In this case, when patient A2 arrives, although the doctor serving A1 is busy, the second doctor has just finished with B1 and is free to see a new patient. Similarly, when B3 arrives, she can be seen by the first doctor immediately. For this reason, there is waiting in both systems A and B, although there is no waiting in the combined system. The technical literature on queueing systems makes this intuition precise via the concept of “fluid limits” (e.g. [32]), the term suggesting that as systems become large, they increasingly experience demand as a smooth continuous flow of fluid rather than as series of irregular discrete events. It is possible to demonstrate this concept with the standard queueing equations [6]. These equations refer to expected steady state system performance, where the demand arrival process and the distribution of service times have a particular form. The simplest model is where there is a single server (i.e. a doctor), and demand arrives and service operates according to a Poisson process (the so-called “M/M/1 queue”). In this case, the mean steady state waiting time (i.e. from the moment when the patient arrives in the A&ED to the moment
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Fig. 4. Aggregation of capacity reduces waiting time.
when she leaves), can be computed as W = 1/(μ − λ), where λ is the rate at which patients arrive and μ is the rate at which the system can treat patients (both expressed in patients per unit time). In the case of a single server, the reciprocal of the service rate (1/μ) has a natural interpretation as the mean “service time” (i.e. the time from when the patient is seen to the time she leaves A&E). Thus, the queueing equation cited above captures the reasonable notion that the longer a doctor spends with a patient on average, the longer will be the waiting times which her patients experience, due to the resulting congestion in the system. Fig. 5 shows how W varies as λ and μ change in such a way as their ratio, conventionally referred to as the traffic intensity, is held constant. One would expect a qualitatively similar relationship to hold in more complex systems. While one would not expect this precise relationship to hold (as the structure of even a small A&ED would be far more complex than that of the M/M/1 queue), one would expect the broad qualitative insight of larger A&EDs enjoying shorter waiting time for comparable levels of demand to obtain.
Fortunately, the A&E audit dataset [29] allows us to explore whether this relationship holds, as it contains, for a large number of A&EDs, the average time spent in the system (called here wait, the analogue of W), the number of patients attending in a year (called here attenders, the analogue of λ, the arrival rate,) and the number of doctors in post (called here doctors, which as a measure of the system’s productive capacity is the analogue of μ). After deleting records for specialist eye and children’s units, and records for which we did not have a complete or consistent list of variables, we had records for 184 A&E Departments (i.e. N = 184). On the strength of the analogy with the above queueing equation, we conducted a linear regression of 1/wait onto attenders and doctors. The results were surprising: while one would have expected a positive sign on doctors and a negative sign on attenders, we obtained a negative sign on both variables, although neither achieved statistical significance at the 5% level. From a queueing theory point of view, our failure to find reduced waiting time associated with larger A&EDs is puzzling. One possible explanation is that larger A&EDs face a heavier traffic intensity, i.e. have
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Fig. 5. Theoretic relationship between size and waiting time performance for the M/M/1 queue.
more patients per doctor. However, a supplementary (quadratic) regression of attenders onto doctors shows a line of best fit with a concave shape suggesting that larger A&EDs tend to have fewer patients per doctor than smaller ones. This leads us to investigate a further line of inquiry, seeking a positive association between the scale of an A&ED and its service rate: it may be that doctors in larger A&EDs each take a longer time on average to deal with a patient than doctors in small A&EDs. This would negate the advantages which larger Departments should be able to obtain by virtue of the scale of their operations. This association could be driven by demand-side factors (such as casemix), or by supply-side factors (such as nursing support or the experience of the medical staff) or it could be a “pure” scale effect. Thus, the key questions are whether such an association exists and, if so, what explanation can be given for it.
3. Scale and service time This section will explore these questions empirically through the further study of the A&E audit data set. There is no precise analogue of service time in the this dataset. However, there is an average time to see a doctor and an average time to leave the Department for each A&ED. While it is not necessarily the case that a doctor will follow the patient through from first encounter to discharge (he may, for example, leave the patient for a time after having commissioned tests to be done), the
difference between these two times, hence dubbed doctortime, will be considered to be a reasonable proxy for the unobservable service time. To study the whether service time depends on the scale of an A&ED’s operation, we set out to conduct a multiple linear regression [33] using OLS of doctortime onto possible explanatory variables including a measure of scale for the data from the A&E audit (a more detailed instrument was used in this round of audit and so it is possible to explore many more variables than with the 2000 data). We take the number of doctors in post in the A&ED, doctors, as our measure of scale. Testing whether a relationship exists between this doctortime and doctors would not be an unambiguous test, however. It could be that larger A&EDs have a more complex casemix than smaller Departments, or alternatively, that there are supply-side explanations: larger A&EDs have more junior and thus less skilled staff than smaller ones, or lower levels of nursing support. Fortunately, the A&E audit dataset is rich enough to help us explore these alternative explanations. On the supply side, we computed the proportion of the doctors in post who were Senior House Officers (sho), and the number of nurses for each doctor (nurseratio). On the demand side, data was available reflecting the percentages of patients: brought in by ambulance (ambulance); suffering from a deliberate overdose (overdose); referred by their GP (gp); under 16 (child); or over 65 (old): these variables were collected by Healthcare Commission researchers as indicators of complexity of casemix.
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The dataset also gives us the percentage of A&E patients admitted to the hospital from A&E (admit). This may be considered a “quasi-demand-side” variable in the sense that it should be reflective of the casemix, but it may also be influenced by institutionspecific factors such as local clinical judgement and management practices. We also computed a variable workload as the number of attenders divided by the number of doctors. The thought here was that in A&EDs which were more heavily loaded, doctors might handle more patients in parallel, and thus the time from seeing a doctor to leaving the A&ED as experienced by a patient might be longer. This would call into question the notion that doctortime is a good proxy for an unobserved service time, as it would suggest that in busier A&EDs doctors work in a more parallel fashion. In this case, a longer time from seeing a doctor to leaving could correspond to the same productive service time. We regressed doctortime onto the scale variable doctors, the supply- and demand-side explanatory variables, admit and workload. After deleting in stepwise fashion the independent variables which were clearly insignificant (nurseratio, sig. level 0.976; admit, 0.815; workload, 0.711; child, 0.621), a model was obtained. The model explained a relatively small proportion of the variance (R2 = 0.160) but was statistically significant (F = 5.631; significance level of 0.000). The statistical significance of the individual regression coefficient t statistics is shown in Table 1. We computed Cook’s distances (none in excess of 0.055) and checked residuals. Visual inspection sug-
gested that the variance of the residuals was more or less constant in the doctors variable: although one would expect system behaviour to based on smaller number of patients and therefore somewhat more variable in smaller institutions, the number of A&E attendances over the course of the year is so large that this does not appear to have a material effect. We did find the distribution of the residuals to be somewhat more bunched (thinner tails) than would be predicted by the normality assumption but not obviously skew or dependent on the variable doctors. As regression is generally robust to violations of the normality assumptions, and as we are more interested in qualitative conclusions rather than in using the model predictively, we were not particularly concerned by this. The results of the model bear comment. No supplyside variables seemed to have a marked effect on the model. overdose and gp both show statistically significant effects, but the effect for overdose points in the wrong direction: the more overdoses, the shorter the service time, constituting an argument against the notion that overdose is a measure of casemix complexity. Despite this ambiguous and confusing message from variables which would seem to be natural explanators of performance, there is a strongly significant effect from doctors. Within the best fitting linear model, adding an additional doctor will, all other things being equal, increase the service time by about 50 seconds. The data thus show that there are pronounced scale effects in the provision of A&E care, favouring smaller, rather than larger A&EDs, which cannot be explained by the available supply- or demand-side variables. Economic, incentive-based accounts provide plausible
Table 1 Regression results when regressing doctortime onto possible explanatory variables
Constant Supply variable sho Demand variables overdose gp ambulance old doctors
Unstandardised coefficients
Standardised coefficients
B
Beta
Std. error
30.75
10.98
−13.69
12.44
−5.20 0.91 0.49 0.66 0.81
2.58 0.41 0.30 0.47 0.23
t
Sig.
2.80
0.006
−0.08
−1.10
0.273
−0.15 0.17 0.13 0.11 0.27
−2.02 2.22 1.63 1.40 3.45
0.045 0.028 0.104 0.163 0.001
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explanations for this observed pattern. Two possible explanations suggest themselves: one relates to a possibly perverse effect of the target system, a second to a problem of group dynamics within the organisational unit. The first explanation relates to “threshold effects” [28] arising from the target system. A danger in any performance management system which involves discrete cut-offs is that what are intended as minimum levels of performance come to be interpreted within the organisation as norms to be aimed for. Smith [34] cites as an example of this sort of phenomenon (which he calls “measure fixation”) a UK target which required a minimum wait for elective surgery of not more than 2 years: while such waits were eliminated, waits of greater than 1 year actually increased. A possible explanation for our finding is that doctors (perhaps subconsciously) choose a service speed which will enable them to hit a particular level of waiting time performance. This would have the effect that doctors in larger A&EDs take longer to see their patients, as they can do so to secure in the knowledge that their waiting time performance targets will be achieved. This need not be a negative feature of system performance. It may be that the longer service time reflects higher quality in the provision of service, but no suitable measures of service quality exist for us to study this hypothesis. A survey of patient satisfaction exists, but unfortunately, these data were gathered at the level of the hospital Trust, rather than at the level of the individual A&ED and so are impossible to interpret for our current purposes. If higher service time were found to be associated with higher quality of care, this would suggest that patients who have the misfortune to attend smaller A&EDs will experience poorer quality of care. This is reminiscent of the equity dilemma similar to that discussed in Bevan [35]: one cannot have simultaneously equality in waiting time performance, equality in service time and thus in quality of care, and equality in funding (e.g. by capitation, irrespective of the characteristics of the facility providing the service). If service time and quality are not associated, however, this suggests that there are significant opportunities for efficiency improvement in the operation of larger A&EDs. The second explanation, which suggested itself to us in discussion with a lead A&E consultant, is a social
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psychological effect known as social loafing. Social loafing is a problem of collective action: when there are many people working in parallel on a task, and performance is measured collectively, each individual has less incentive to contribute the fullest extent of his effort [36]. This is particularly relevant in the English setting as here, where the performance measurement regime seeks to measure the performance of A&EDs as a whole rather than the performance of individual doctors. The earliest demonstration of social loafing related to an unpublished experiment conducted in the early years of the 20th century by Ringelmann, who observed that workers instructed to pull on a rope exerted greater force when pulling individually than when pulling as part of a group. This experiment, however, is flawed in that performance is not necessarily additive over persons, unless the forces which are exerted by all individual rope-pullers are perfectly aligned. However, subsequent experiments [36] in tasks such as making noise by cheering and clapping have demonstrated that even when this “co-ordination loss” is eliminated, there is a residual “motivation loss” or social loafing effect arising from the dilution of incentive. This is a particularly apposite phenomenon to study in the medical context. As in the tasks used to demonstrate social loafing, the production process in A&EDs is fairly parallel, with individual doctors pairing with individual patients and following them through out the course of their care journey. Further, as is well known from studies of the medical profession over the years, groups of doctors do not have strong internal controls, tending to rely on peer group pressure and an internalised professional ethic, rather than on formalised processes of auditing and review [37,38]. In the UK, while medical autonomy has been eroded in recent years [39] with the emergence of a centrally managed target regime at the system level, our impression is that management practice within hospital specialties has remained largely unchanged. However, if social loafing could be demonstrated, it would suggest that there is room for improvement in the professional grouping’s arrangements for regulating themselves. (Or perhaps the problem will take care of itself as the health service becomes more diverse – Karau and Williams [40] present evidence suggesting that women and people from Eastern cultures seem to be less inclined so social loafing.)
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4. Conclusion In this paper, we have reviewed a management science and an economic view of the mechanism underlying waiting for healthcare. We have applied these concepts in the analysis of English A&E Departments, using transactional data from a single A&ED and the Healthcare Commission’s A&E audit database. While the queueing model gives a plausible account of performance variation over time within a particular facility, the systematic scale effects favouring larger units suggested by the queueing model cannot be detected. It seems that doctors take longer to see patients in larger A&EDs: this is a plausible explanation for the failure to observe a scale effect and we suggest that this could arise from differential incentives in small and large A&E Departments. A provocative interpretation of our findings is that “many hands make light work”, not only in the sense that tasks become easier when more people are available to undertake them, but also in the sense that – for one reason or another – doctors in larger A&EDs work less hard. We see the current work as having two main implications for policy research and practice. An immediate implication following on specifically from our analysis and discussion of the A&E dataset is the need put in place monitoring frameworks to track performance at the individual level. For reasons of administrative practicality, if nothing else, we do not expect the regulator to monitor the performance of each individual A&E physician, and will continue to set targets at the A&ED level. However, it may be worth exploring more deeply in setting targets whether organisations have the capacity to communicate and manage these targets internally. We know of one lead A&E consultant who systematically monitors the workload handled by each of his junior colleagues individually (McGlone, personal communication), which would seem an excellent way of guarding against organisational pathologies such as social loafing. The centre could encourage this sort of management practice by developing and promulgating best practice guidelines for using group level targets to set individual performance goals. The analysis also has implications for regulatory target setting suggesting that, in particular, uniform targets across the board may be unfair to smaller units if such units face scale disadvantages.
A broader implication is the that policy analysts should be aware of the mechanisms which underlie particular approaches to modelling waiting. Management science trained researchers naturally respond to waiting by seeking ways to streamline work processes, and introduce greater flexibility in the use of resources. However, they tend to overlook the sort of behavioural responses on the part of the service providers which may be particularly salient in healthcare (compare the degree of freedom of action enjoyed by clinicians with staff in call centres, for example). Economists, on the other hand, tend to focus on the incentives created by the reward system, but may overlook phenomena which arise because of the detailed structure of the production process. This, of course, is because disciplines are ways of seeing, but also ways of not seeing. The challenge for policy makers is to find ways to exploit the different insights which these perspectives provide in designing coherent and effective systems for performance improvement. Acknowledgements The line of inquiry which led to this paper was stimulated by a number of discussions with Dr Ray McGlone, lead A&E consultant at the Royal Lancaster Infirmary. Dr Jonathan Boyce and Mr Bill Alexander of the Healthcare Commission supplied us with key data and gave detailed comments on a previous version of the paper. The work which led to this paper is a spin-off from the DGHSIM project, funded by the UK Engineering and Physical Sciences Research Council, and the authors are pleased to acknowledge helpful discussions with other members of the DGHSIM team, Profs Peter Smith and Mike Pidd, and Mr Murat Gunal. We are also grateful to two anonymous referees whose helpful comments have enabled us to improve the paper. References [1] Yates J. Why are we waiting? An analysis of hospital waiting lists. Oxford: OUP; 1987. [2] National Audit Office. Inpatient and outpatient waiting in the NHS. London: The Stationary Office; 2001. [3] Appleby J, Boyle S, Devlin N, Harley M, Harrison A, Locock L, Thorlby R. Sustaining reductions in waiting times: final report to the Department of Health. London: King’s Fund; 2005.
A. Morton, G. Bevan / Health Policy 85 (2008) 207–217 [4] Harrison A, New B. Access to elective care: what really should be done about waiting lists. London: Kings Fund; 2000. [5] Morgan J. The future of NHS Wales, http://www.conservativeparty.org.uk/tile.do?def=news.story.page&obj id=81356 &speeches=1; 2003. [6] Gross D, Harris CM. Fundamentals of queueing theory. Chichester: Wiley; 1998. [7] Newell GF. Applications of queueing theory. London: Chapman and Hall; 1971. [8] Whitt W. Understanding the efficiency of multi-server service systems. Management Science 1992;38:708–23. [9] Koole G, Mandelbaum A. Queueing models of call centres: an introduction. Annals of Operations Research 2002;113:41–59. [10] Jackson RRP, Welch JD, Fry J. Appointment systems in hospitals and general practice. Operational Research Quarterly 1964;15:219–37. [11] Bagust A, Place M, Posnett JW. Dynamics of bed use on accomodating emergency admissions: stochastic simulation model. British Medical Journal 1999;319:155–8. [12] Gallivan S, Utley M, Treasure T, Valencia O. Booked inpatient admissions and hospital capacity: mathematical modelling study. British Medical Journal 2002;324:280–2. [13] Vassilacopoulos G. Allocating doctors shifts in an Accident and Emergency Department. Journal of the Operational Research Society 1985;36:517–23. [14] Williams J, Griffiths J, Newman J. Modelling hospital waiting lists. in MASHnet Cardiff Workshop. Cardiff; 2006, available online at http://www.pms.ac.uk/mashnet/ index.php?section=main&act=CardiffWorkshopReport3Apr06. [15] Worthington DJ. Queueing models for hospital waiting lists. Journal of the Operational Research Society 1987;38: 413–22. [16] Bloor K, Maynard A, Freemantle N. Variation in the activity rates of consultant surgeons and the influence of reward structures in the English NHS. Journal of Health Services Research and Policy 2004;9:76–84. [17] Frankel S. The natural history of waiting lists: some wider explanations for an unnecessary problem. Health Trends 1989;21:54–8. [18] Iversen T. A theory of hospital waiting lists. Journal of Health Economics 1993;12:55–71. [19] Lindsay CM, Feigenbaum B. Rationing by waiting lists. American Economic Review 1984;74:404–17. [20] Gravelle H, Dusheiko M, Sutton M. The demand for elective surgery in a public system: time and money prices in the UK National Health Service. Journal of Health Economics 2002;21:423–49. [21] Le Grand J. Motivation, agency and public policy: of knights and knaves, Pawns and Queens. Oxford: OUP; 2003.
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[22] Modernisation Agency. 10 High impact changes for service improvement and delivery: a guide for NHS leaders. Leicester: Modernisation Agency; 2004. [23] Bevan G. Setting Targets for Health Care Performance: Lessons from a Case Study of the English NHS. National Institute Economic Review 2006;197:67–79. [24] Martin S, Smith PC. Rationing by waiting lists: an empirical investigation. Journal of Public Economics 1999;71:141–69. [25] Department of Health. The NHS Plan: a plan for investment, a plan for reform. London: Department of Health; 2000. [26] Department of Health. Clinical exceptions to the 4 h emergency care target. London: Department of Health; 2003. [27] Department of Health. Hospital activity statistics: Total Time in A&E Data files, available for download. http://www. performance.doh.gov.uk/hospitalactivity/data requests/total time ae.htm; 2006. [28] Bevan G, Hood C. What’s measured is what matters: targets and gaming in the English public health system. Public Administration 2006;84:517–38. [29] Healthcare Commission. Acute Hospital portfolio review: accident and emergency. London: Healthcare Commission; 2005. [30] Green LV. How many hospital beds? Inquiry 2002–2003;36: 68–77. [31] Green LV. Capacity planning and management in hospitals. In: Saintfort F, Brandeau ML, Pierskalla W, editors. Handbook of operations research and health care. Boston: Kluwer; 2004. [32] Altman E, Jimenez T, Koole G. On the comparison of queueing systems with their fluid limits. Probability in the Engineering and Informational Sciences 2001;15:165–78. [33] Weisberg S. Applied linear regression. Chichester: Wiley; 2005. [34] Smith P. On the unintended consequences of publishing performance data in the public sector. International Journal of Public Administration 1995;18:277–310. [35] Bevan G. Taking equity seriously: a dilemma for government from allocating resources to primary care groups. British Medical Journal 1998;319:39–42. [36] Latan´e B, Williams K, Harkins S. Many hands make light the work: the causes and consequences of social loafing. Journal of Personality and Social Psychology 1979;37:822–32. [37] Freidson E. Profession of medicine: a study of the sociology of applied knowledge. Chicago: University of Chicago Press; 1970. [38] Freidson E. Doctoring together: a study of professional social control. Chicago: University of Chicago Press; 1975. [39] Harrison S, Ahmad WIU. Medical Autonomy and the UK state. Sociology 2000;34:129–46. [40] Karau SJ, Williams KD. Social loafing —a meta-analytic review and theoretical integration. Journal of Personality and Social Psychology 1993;65(4):681–706.
Health Policy 85 (2008) 207–217
What’s in a wait? Contrasting management science and economic perspectives on waiting for emergency care Alec Morton ∗ , Gwyn Bevan 1 Operational Research Group, Department of Management, London School of Economics and Political Science, Houghton St, London WC2A 2AE, United Kingdom
Abstract The current paper reviews and contrasts a management science view of waiting for healthcare, which centres on queues as devices for buffering demand, with an economic view, which stresses the role of the incentive structure, in the context of English Accident and Emergency Departments. We demonstrate that the management science view provides insight into waiting time performance within a single facility but is limited in its ability to shed light on variations in performance across facilities. We argue, with reference to supporting data, that such variations may be explainable by a proper understanding of the incentive structure in A&E Departments. © 2007 Elsevier Ireland Ltd. All rights reserved. Keywords: Waiting; Queueing; Accident and emergency
1. Introduction Much healthcare research has been dedicated to the phenomenon of the length of time which patients have to wait in order to receive healthcare services. This reflects the high level of public and policy attention which waiting has historically attracted [1–3]. Historically, waiting lists were viewed (often implicitly) as arising from a “backlog” in the need for care [4]. Despite the survival of the backlog motif in policy ∗
Corresponding author. Tel.: +44 20 7955 6539. E-mail addresses: [email protected] (A. Morton), [email protected] (G. Bevan). 1 Tel.: +44 20 7955 6269.
rhetoric (e.g. Morgan [5]), the repeated failure of policy initiatives predicated on this view of waiting has established beyond doubt the necessity of “realising that waiting lists are . . . a manifestation of a more complicated, dynamic flow through interconnected parts of a whole system of care” [3, p 44] if sustainable reductions in waiting times are to be achieved. Curiously, however, research on waiting-related phenomena has proceeded apace in two quite distinctive research communities, management science and health economics, which have fundamentally different views of the character of this system of care and in the mechanism by which it generates waiting. Management scientists view waiting as arising from the dynamic buffering or smoothing of demand. In this
0168-8510/$ – see front matter © 2007 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.healthpol.2007.07.014
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view, waiting arises in any system where capacity is fixed in the short run, but where demand fluctuates [6–8]. This insight has been the basis for a powerful analytic technology, queueing theory, which has been widely applied in areas such as the design of call centres [9] but which also has a long-recognised applicability to the healthcare arena [10]. A rich literature exists which discusses this idea in the context of capacity management in healthcare [10–12]. Modelling techniques based on this view of waiting have been applied to the study of both Accident and Emergency Departments (e.g. [13]), and to elective services (e.g. [14,15]). Economic accounts, on the other hand, stress the role of incentives in the generation of waiting. Providers may not have sufficient incentive to exert their maximum level of effort, or may even have a vested interest in the actual generation of waiting. This could arise, for example, because surgeons who work in both state and private sector allow public sector waiting lists to run up in order to generate private sector demand [16,1]); because consultants prioritise patients based on personal criteria (such as how intellectually interesting they find the patient’s condition) which do not relate to societal objectives [17]; or because hospitals can use waiting lists to attract funding [18]. A related stream of research emphasises the role of incentives on the demand-, rather than the supply-side: patients in systems where healthcare is provided free at the point of delivery have little incentive to restrain their consumption of healthcare [19]. Waiting lists fulfil the same role as prices fulfil in conventional markets, depressing demand: it is thus possible to think of waiting as a “time price” as opposed to a “money price” [20]. These perspectives imply quite different views of the motivations of the people who work in healthcare systems, and the appropriate responses to poor performance. The management science view implicitly supposes that healthcare workers are well-intentioned public servants: “knights”, in the terminology of Le Grand [21]. In this case, the appropriate response is essentially a technical one: study work processes and identify and implement improvements. In the English system, this perspective and role has been taken on in recent years by the Institute for Innovation and Improvement (and formerly by its predecessor, the Modernisation Agency), which advises NHS organisations on process redesign (see e.g. [22] for a flavour of this work).
The economic view, on the other hand, supposes that the healthcare sector is staffed by people who, if not quite “knaves” [21], nevertheless have an eye for their own interest. This suggests that the appropriate response to poor performance is to re-align the goals of providers with society’s objectives for the healthcare system. This role has been taken on within the English system by the Department of Health, supported by the Healthcare Commission, which operates a regime of performance measurement and targets by which organisational performance is judged. The main sanction used to give this regime bite is the dismissal of senior management in English trusts judged to be failing [23]. A more pessimistic interpretation of the economic model focusses on the demand-side effects. Enoch Powell, a former UK Minister for Health, championed this view, claiming that reducing waiting lists “is an activity about as hopeful as filling a sieve.” (cited by Yates [1]). Recent econometric work by Martin and Smith [24] and others has somewhat tempered this fatalism, suggesting that the dependency of the demand on waiting times, while real, is nevertheless relatively modest. We see these two views, the queuing view and the incentive view, of the nature of waiting as having complementary roles in understanding how system performance varies within and between facilities. Our aim in this paper is to demonstrate how an analysis informed by both these perspectives can uncover patterns in data which would not be obvious when the data are viewed from either perspective in isolation. A particular focus in this paper is the effect of scale when comparing between facilities: we argue that the absence of an effect which would be predicted on the basis of the queueing model can be explained by the operation of an incentive effect. We develop our analysis in the context of English A&E Departments (A&EDs). An attraction of A&EDs is that they are relatively discrete units for study, as they do not generally share theatre or bed capacity with other parts of hospital. Although our empirical analysis is limited to A&EDs, our broad conceptual arguments are equally valid across all hospital activity. A&EDs have in recent years seen substantial increased investment, in terms of salaries, staffing levels and transitional support for process redesign.
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Accompanying this investment there has been a renewed focus on performance and since 2004, all English hospitals have been required to have at least 98% of patients leave the A&ED in less than 4 hours [25,26]. Progress towards this target has been quite encouraging: Department of Health statistics show that 96.6% of patients spent less than 4 hours in A&E in the first quarter of 2005–2006 as against 87.3% in the same quarter of 2003–2004 [27], itself a substantial improvement on even lower percentages in previous years. Despite reports of gaming and systematic misrepresentation of performance which suggest that these figures should not be taken entirely at face value, it seems likely that there has been some genuine improvement in system performance [28]. For this study, we were supplied by the Healthcare Commission with a dataset from a survey of 252 “Type 1” A&EDs across England, Wales and Northern Ireland (this excludes Walk-in Centres and Minor Injuries Units). These data report aggregate performance at the A&ED level and are the basis for the Healthcare Commission’s recent report on this subject [29]. The A&E audit, conducted in 2004, contains various questions covering diverse aspects of operating and financial performance. We restricted our attention to A&EDs in England only as the regulatory environment in Wales and Northern Ireland differs from that of England. Additionally, we obtained a 1-year extract of patient-level transactional data from an A&E patient administration system provided to us by a hospital with a mid-size A&E department (the “North West General”). An important feature of our analysis is that it relates to individual physically distinct A&EDs, where there is a single shared waiting area, and which fall under the management of a lead A&E consultant. The data sources which we use in this paper allow us to define this physically distinct facility as our unit of analysis, but many data sources on the NHS in England relate to multi-site hospital trusts and do not permit further disaggregation. Often this is a limitation built into the data collection itself, not merely of a feature of the level of aggregation at which data are reported. For the purposes of understanding in detail the drivers of hospital performance, such data are of limited use, as many of drivers of performance relate to features of the individual facility.
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2. Queueing and scale effects In this section, we briefly review the key ideas of queueing theory and discuss their applicability in the context of an A&ED. The central idea of queueing theory is that variability in the waiting times arises from variability in the arrival process which is either unpredictable, or predictable but unmanageable (as happens in systems which experience “rush-hours”). This variability results in the system becoming congested (a so-called “busy period”), and patients who arrive at this time experience longer waits. Drawing on data from North West General’s patient admission system, we illustrate the variability in the arrival pattern for April 2004 in Fig. 1. It can be seen from this chart that while there is a clear weekly pattern (predictable spikes occur on the 5th, 12th, 19th and 26th, which are all Mondays), there is also a considerable component of random variation in arrivals. Predictable weekly or diurnal variability in demand should not pose serious problems for A&E management as capacity can be flexed in the short run, through appropriate scheduling of staff throughout the day (although some A&EDs may find that physical capacity is a limiting factor at times of peak demand). The random variability component of demand is harder to manage, however. Queueing theory predicts that in response to such variability, the system will become congested, and patients will experience increasingly longer waiting times. Based on transactional data, we reconstructed a process which counts the number of patients in the Department over the month of April 2004. Fig. 2 shows how system congestion varies throughout the month. There is a clear daily pattern: the system fills during the day and then almost completely clears out at night. The spike in congestion on the 25th and 26th of April is clearly associated with the spike in arrivals shown in Fig. 1. We also find, unsurprisingly, that, on average, patients who arrive when the system contains a larger number of patients, experience on average longer waits (see Fig. 3). The relationship becomes harder to discern at the higher levels of congestion because such levels occur infrequently and thus the dataset contains fewer samples of such arrivals. As this analysis demonstrates, queueing theory provides a good account of how waiting is generated in a particular facility is therefore borne out by our analysis of North West General’s patient admission system.
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Fig. 1. Arrival pattern over the month of April at North West General.
In view of the obvious applicability of queueing theory in understanding this sort of system, it is surprising that the lessons of this theory seems to have been ignored by those setting waiting time targets for A&E Departments. The published rationale for the 98% threshold for waiting times less than 4 hours is that while every Department is expected to have the capacity to treat all patients within 4 hours, there may be clinical reasons to keep some small number of patients beyond the 4 hour limit: “the emergency department
offers the only appropriate facilities and expertise that are suited to the treatment of the patient’s current condition” [26]. That variability in demand could lead to variability in performance seems not to have been taken into account. This is surprising as we find considerable appreciation of the role of variability in generating waits amongst staff on the shop floor. The queueing view of waiting has therefore considerable plausibility as an account of how waiting is generated within an individual facility. However, when
Fig. 2. Congestion of the A&E Department over the month of April at North West General.
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Fig. 3. Expected waiting time conditioned on number of patients in Department on arrival.
comparing waiting time performance between facilities, the picture becomes more complex. As it happens, the queueing model makes a strong and testable prediction about performance between different (yet comparable) institutions. Specifically, queueing systems exhibit a predictable scale effect, with larger systems performing better in terms of waiting times than smaller systems with a comparable ratio of capacity to demand. Green [30,31] has stressed the significance of this sort of result in the context of hospital capacity planning. The intuitive explanation of this phenomenon is that larger systems experience demand at an aggregated levels, and as a result, fluctuations in the demand process “even out”, whereas smaller institutions will experience demand as lumpy and irregular. To make this intuition clear, consider two single-handed A&EDs (i.e. one doctor), called A and B, facing a similar volume of demand. In a given stretch of time, the patients which arrive at A are denoted A1 , A2 , A3 and those at who arrive at B are denoted B1 , B2 , B3 , B4 . The charts in Fig. 4 show how patients will be handled at A and B. The vertical axis counts the number of patients in the system either being seen or waiting; the horizontal axis measures time. The blocks describe the phases of the patient journey, with grey blocks representing the time a patient spends with a doctor, and the white blocks representing time waiting. Thus patient A1 arrives and is seen by a doctor, during which time A2 arrives and
asked to wait. After A1 has departed, A2 is called and is seen, and eventually departs. As the doctor is unoccupied, when A3 arrives she can be seen immediately. Events at system B are depicted analogously. In both systems there is some waiting. Suppose A and B were to be aggregated in a new system (“A + B”) with both doctors, and serving both demand streams. In this case, when patient A2 arrives, although the doctor serving A1 is busy, the second doctor has just finished with B1 and is free to see a new patient. Similarly, when B3 arrives, she can be seen by the first doctor immediately. For this reason, there is waiting in both systems A and B, although there is no waiting in the combined system. The technical literature on queueing systems makes this intuition precise via the concept of “fluid limits” (e.g. [32]), the term suggesting that as systems become large, they increasingly experience demand as a smooth continuous flow of fluid rather than as series of irregular discrete events. It is possible to demonstrate this concept with the standard queueing equations [6]. These equations refer to expected steady state system performance, where the demand arrival process and the distribution of service times have a particular form. The simplest model is where there is a single server (i.e. a doctor), and demand arrives and service operates according to a Poisson process (the so-called “M/M/1 queue”). In this case, the mean steady state waiting time (i.e. from the moment when the patient arrives in the A&ED to the moment
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Fig. 4. Aggregation of capacity reduces waiting time.
when she leaves), can be computed as W = 1/(μ − λ), where λ is the rate at which patients arrive and μ is the rate at which the system can treat patients (both expressed in patients per unit time). In the case of a single server, the reciprocal of the service rate (1/μ) has a natural interpretation as the mean “service time” (i.e. the time from when the patient is seen to the time she leaves A&E). Thus, the queueing equation cited above captures the reasonable notion that the longer a doctor spends with a patient on average, the longer will be the waiting times which her patients experience, due to the resulting congestion in the system. Fig. 5 shows how W varies as λ and μ change in such a way as their ratio, conventionally referred to as the traffic intensity, is held constant. One would expect a qualitatively similar relationship to hold in more complex systems. While one would not expect this precise relationship to hold (as the structure of even a small A&ED would be far more complex than that of the M/M/1 queue), one would expect the broad qualitative insight of larger A&EDs enjoying shorter waiting time for comparable levels of demand to obtain.
Fortunately, the A&E audit dataset [29] allows us to explore whether this relationship holds, as it contains, for a large number of A&EDs, the average time spent in the system (called here wait, the analogue of W), the number of patients attending in a year (called here attenders, the analogue of λ, the arrival rate,) and the number of doctors in post (called here doctors, which as a measure of the system’s productive capacity is the analogue of μ). After deleting records for specialist eye and children’s units, and records for which we did not have a complete or consistent list of variables, we had records for 184 A&E Departments (i.e. N = 184). On the strength of the analogy with the above queueing equation, we conducted a linear regression of 1/wait onto attenders and doctors. The results were surprising: while one would have expected a positive sign on doctors and a negative sign on attenders, we obtained a negative sign on both variables, although neither achieved statistical significance at the 5% level. From a queueing theory point of view, our failure to find reduced waiting time associated with larger A&EDs is puzzling. One possible explanation is that larger A&EDs face a heavier traffic intensity, i.e. have
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Fig. 5. Theoretic relationship between size and waiting time performance for the M/M/1 queue.
more patients per doctor. However, a supplementary (quadratic) regression of attenders onto doctors shows a line of best fit with a concave shape suggesting that larger A&EDs tend to have fewer patients per doctor than smaller ones. This leads us to investigate a further line of inquiry, seeking a positive association between the scale of an A&ED and its service rate: it may be that doctors in larger A&EDs each take a longer time on average to deal with a patient than doctors in small A&EDs. This would negate the advantages which larger Departments should be able to obtain by virtue of the scale of their operations. This association could be driven by demand-side factors (such as casemix), or by supply-side factors (such as nursing support or the experience of the medical staff) or it could be a “pure” scale effect. Thus, the key questions are whether such an association exists and, if so, what explanation can be given for it.
3. Scale and service time This section will explore these questions empirically through the further study of the A&E audit data set. There is no precise analogue of service time in the this dataset. However, there is an average time to see a doctor and an average time to leave the Department for each A&ED. While it is not necessarily the case that a doctor will follow the patient through from first encounter to discharge (he may, for example, leave the patient for a time after having commissioned tests to be done), the
difference between these two times, hence dubbed doctortime, will be considered to be a reasonable proxy for the unobservable service time. To study the whether service time depends on the scale of an A&ED’s operation, we set out to conduct a multiple linear regression [33] using OLS of doctortime onto possible explanatory variables including a measure of scale for the data from the A&E audit (a more detailed instrument was used in this round of audit and so it is possible to explore many more variables than with the 2000 data). We take the number of doctors in post in the A&ED, doctors, as our measure of scale. Testing whether a relationship exists between this doctortime and doctors would not be an unambiguous test, however. It could be that larger A&EDs have a more complex casemix than smaller Departments, or alternatively, that there are supply-side explanations: larger A&EDs have more junior and thus less skilled staff than smaller ones, or lower levels of nursing support. Fortunately, the A&E audit dataset is rich enough to help us explore these alternative explanations. On the supply side, we computed the proportion of the doctors in post who were Senior House Officers (sho), and the number of nurses for each doctor (nurseratio). On the demand side, data was available reflecting the percentages of patients: brought in by ambulance (ambulance); suffering from a deliberate overdose (overdose); referred by their GP (gp); under 16 (child); or over 65 (old): these variables were collected by Healthcare Commission researchers as indicators of complexity of casemix.
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The dataset also gives us the percentage of A&E patients admitted to the hospital from A&E (admit). This may be considered a “quasi-demand-side” variable in the sense that it should be reflective of the casemix, but it may also be influenced by institutionspecific factors such as local clinical judgement and management practices. We also computed a variable workload as the number of attenders divided by the number of doctors. The thought here was that in A&EDs which were more heavily loaded, doctors might handle more patients in parallel, and thus the time from seeing a doctor to leaving the A&ED as experienced by a patient might be longer. This would call into question the notion that doctortime is a good proxy for an unobserved service time, as it would suggest that in busier A&EDs doctors work in a more parallel fashion. In this case, a longer time from seeing a doctor to leaving could correspond to the same productive service time. We regressed doctortime onto the scale variable doctors, the supply- and demand-side explanatory variables, admit and workload. After deleting in stepwise fashion the independent variables which were clearly insignificant (nurseratio, sig. level 0.976; admit, 0.815; workload, 0.711; child, 0.621), a model was obtained. The model explained a relatively small proportion of the variance (R2 = 0.160) but was statistically significant (F = 5.631; significance level of 0.000). The statistical significance of the individual regression coefficient t statistics is shown in Table 1. We computed Cook’s distances (none in excess of 0.055) and checked residuals. Visual inspection sug-
gested that the variance of the residuals was more or less constant in the doctors variable: although one would expect system behaviour to based on smaller number of patients and therefore somewhat more variable in smaller institutions, the number of A&E attendances over the course of the year is so large that this does not appear to have a material effect. We did find the distribution of the residuals to be somewhat more bunched (thinner tails) than would be predicted by the normality assumption but not obviously skew or dependent on the variable doctors. As regression is generally robust to violations of the normality assumptions, and as we are more interested in qualitative conclusions rather than in using the model predictively, we were not particularly concerned by this. The results of the model bear comment. No supplyside variables seemed to have a marked effect on the model. overdose and gp both show statistically significant effects, but the effect for overdose points in the wrong direction: the more overdoses, the shorter the service time, constituting an argument against the notion that overdose is a measure of casemix complexity. Despite this ambiguous and confusing message from variables which would seem to be natural explanators of performance, there is a strongly significant effect from doctors. Within the best fitting linear model, adding an additional doctor will, all other things being equal, increase the service time by about 50 seconds. The data thus show that there are pronounced scale effects in the provision of A&E care, favouring smaller, rather than larger A&EDs, which cannot be explained by the available supply- or demand-side variables. Economic, incentive-based accounts provide plausible
Table 1 Regression results when regressing doctortime onto possible explanatory variables
Constant Supply variable sho Demand variables overdose gp ambulance old doctors
Unstandardised coefficients
Standardised coefficients
B
Beta
Std. error
30.75
10.98
−13.69
12.44
−5.20 0.91 0.49 0.66 0.81
2.58 0.41 0.30 0.47 0.23
t
Sig.
2.80
0.006
−0.08
−1.10
0.273
−0.15 0.17 0.13 0.11 0.27
−2.02 2.22 1.63 1.40 3.45
0.045 0.028 0.104 0.163 0.001
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explanations for this observed pattern. Two possible explanations suggest themselves: one relates to a possibly perverse effect of the target system, a second to a problem of group dynamics within the organisational unit. The first explanation relates to “threshold effects” [28] arising from the target system. A danger in any performance management system which involves discrete cut-offs is that what are intended as minimum levels of performance come to be interpreted within the organisation as norms to be aimed for. Smith [34] cites as an example of this sort of phenomenon (which he calls “measure fixation”) a UK target which required a minimum wait for elective surgery of not more than 2 years: while such waits were eliminated, waits of greater than 1 year actually increased. A possible explanation for our finding is that doctors (perhaps subconsciously) choose a service speed which will enable them to hit a particular level of waiting time performance. This would have the effect that doctors in larger A&EDs take longer to see their patients, as they can do so to secure in the knowledge that their waiting time performance targets will be achieved. This need not be a negative feature of system performance. It may be that the longer service time reflects higher quality in the provision of service, but no suitable measures of service quality exist for us to study this hypothesis. A survey of patient satisfaction exists, but unfortunately, these data were gathered at the level of the hospital Trust, rather than at the level of the individual A&ED and so are impossible to interpret for our current purposes. If higher service time were found to be associated with higher quality of care, this would suggest that patients who have the misfortune to attend smaller A&EDs will experience poorer quality of care. This is reminiscent of the equity dilemma similar to that discussed in Bevan [35]: one cannot have simultaneously equality in waiting time performance, equality in service time and thus in quality of care, and equality in funding (e.g. by capitation, irrespective of the characteristics of the facility providing the service). If service time and quality are not associated, however, this suggests that there are significant opportunities for efficiency improvement in the operation of larger A&EDs. The second explanation, which suggested itself to us in discussion with a lead A&E consultant, is a social
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psychological effect known as social loafing. Social loafing is a problem of collective action: when there are many people working in parallel on a task, and performance is measured collectively, each individual has less incentive to contribute the fullest extent of his effort [36]. This is particularly relevant in the English setting as here, where the performance measurement regime seeks to measure the performance of A&EDs as a whole rather than the performance of individual doctors. The earliest demonstration of social loafing related to an unpublished experiment conducted in the early years of the 20th century by Ringelmann, who observed that workers instructed to pull on a rope exerted greater force when pulling individually than when pulling as part of a group. This experiment, however, is flawed in that performance is not necessarily additive over persons, unless the forces which are exerted by all individual rope-pullers are perfectly aligned. However, subsequent experiments [36] in tasks such as making noise by cheering and clapping have demonstrated that even when this “co-ordination loss” is eliminated, there is a residual “motivation loss” or social loafing effect arising from the dilution of incentive. This is a particularly apposite phenomenon to study in the medical context. As in the tasks used to demonstrate social loafing, the production process in A&EDs is fairly parallel, with individual doctors pairing with individual patients and following them through out the course of their care journey. Further, as is well known from studies of the medical profession over the years, groups of doctors do not have strong internal controls, tending to rely on peer group pressure and an internalised professional ethic, rather than on formalised processes of auditing and review [37,38]. In the UK, while medical autonomy has been eroded in recent years [39] with the emergence of a centrally managed target regime at the system level, our impression is that management practice within hospital specialties has remained largely unchanged. However, if social loafing could be demonstrated, it would suggest that there is room for improvement in the professional grouping’s arrangements for regulating themselves. (Or perhaps the problem will take care of itself as the health service becomes more diverse – Karau and Williams [40] present evidence suggesting that women and people from Eastern cultures seem to be less inclined so social loafing.)
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4. Conclusion In this paper, we have reviewed a management science and an economic view of the mechanism underlying waiting for healthcare. We have applied these concepts in the analysis of English A&E Departments, using transactional data from a single A&ED and the Healthcare Commission’s A&E audit database. While the queueing model gives a plausible account of performance variation over time within a particular facility, the systematic scale effects favouring larger units suggested by the queueing model cannot be detected. It seems that doctors take longer to see patients in larger A&EDs: this is a plausible explanation for the failure to observe a scale effect and we suggest that this could arise from differential incentives in small and large A&E Departments. A provocative interpretation of our findings is that “many hands make light work”, not only in the sense that tasks become easier when more people are available to undertake them, but also in the sense that – for one reason or another – doctors in larger A&EDs work less hard. We see the current work as having two main implications for policy research and practice. An immediate implication following on specifically from our analysis and discussion of the A&E dataset is the need put in place monitoring frameworks to track performance at the individual level. For reasons of administrative practicality, if nothing else, we do not expect the regulator to monitor the performance of each individual A&E physician, and will continue to set targets at the A&ED level. However, it may be worth exploring more deeply in setting targets whether organisations have the capacity to communicate and manage these targets internally. We know of one lead A&E consultant who systematically monitors the workload handled by each of his junior colleagues individually (McGlone, personal communication), which would seem an excellent way of guarding against organisational pathologies such as social loafing. The centre could encourage this sort of management practice by developing and promulgating best practice guidelines for using group level targets to set individual performance goals. The analysis also has implications for regulatory target setting suggesting that, in particular, uniform targets across the board may be unfair to smaller units if such units face scale disadvantages.
A broader implication is the that policy analysts should be aware of the mechanisms which underlie particular approaches to modelling waiting. Management science trained researchers naturally respond to waiting by seeking ways to streamline work processes, and introduce greater flexibility in the use of resources. However, they tend to overlook the sort of behavioural responses on the part of the service providers which may be particularly salient in healthcare (compare the degree of freedom of action enjoyed by clinicians with staff in call centres, for example). Economists, on the other hand, tend to focus on the incentives created by the reward system, but may overlook phenomena which arise because of the detailed structure of the production process. This, of course, is because disciplines are ways of seeing, but also ways of not seeing. The challenge for policy makers is to find ways to exploit the different insights which these perspectives provide in designing coherent and effective systems for performance improvement. Acknowledgements The line of inquiry which led to this paper was stimulated by a number of discussions with Dr Ray McGlone, lead A&E consultant at the Royal Lancaster Infirmary. Dr Jonathan Boyce and Mr Bill Alexander of the Healthcare Commission supplied us with key data and gave detailed comments on a previous version of the paper. The work which led to this paper is a spin-off from the DGHSIM project, funded by the UK Engineering and Physical Sciences Research Council, and the authors are pleased to acknowledge helpful discussions with other members of the DGHSIM team, Profs Peter Smith and Mike Pidd, and Mr Murat Gunal. We are also grateful to two anonymous referees whose helpful comments have enabled us to improve the paper. References [1] Yates J. Why are we waiting? An analysis of hospital waiting lists. Oxford: OUP; 1987. [2] National Audit Office. Inpatient and outpatient waiting in the NHS. London: The Stationary Office; 2001. [3] Appleby J, Boyle S, Devlin N, Harley M, Harrison A, Locock L, Thorlby R. Sustaining reductions in waiting times: final report to the Department of Health. London: King’s Fund; 2005.
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