1 Looking in the wrong place for healthcare improvements: A system dynamics study of an accident and emergency department

Transcription

1 1 Looking in the wrong place for healthcare improvement: A ytem dynamic tudy of an accident and emergency department DC Lane, C Monefeldt and JV Roenhead - The London School of Economic and Political Science Accident and Emergency unit provide a route for patient eeking urgent admiion to acute hopital. Public concern over long waiting time for admiion motivated thi tudy, whoe aim wa to explore the factor which contribute to uch delay. In collaboration with a major London teaching hopital, a ytem dynamic model of the interaction of demand pattern, A&E reource deployment, other hopital procee and bed number wa developed. The paper dicue the formulation of thi model; the calibration of a Bae Cae imulation; and the output of policy analyi run of the model which vary a number of the key parameter. Two ignificant finding appear to have policy implication. One i that while ome delay to patient are unavoidable, reduction can be achieved by elective augmentation of reource within, and relating to, the A&E unit. The econd i that reduction in bed number do not increae waiting time for emergency admiion, their effect intead being to increae harply the number of cancellation of admiion for elective urgery. Thi ugget that baing A&E policy olely on any ingle criterion will ucceed in tranferring the effect of a reource deficit to a different patient group. Introduction Accident and Emergency and the crii in Britih health care The National Health Service (NHS), a treaured Britih intitution, ha been in emi-permanent crii during two decade of government retraint on public ector expenditure. Depite the election of a new government in May 1997, problem endure (Independent, ). Among the indicator of crii have been repeated reorganiation, cloure of facilitie, lengthy waiting lit, cancellation of cheduled admiion to hopital, and depletion of budget before the year end leading to curtailment of activity. In recent year public and political concern ha focued in particular on the performance of Accident and Emergency department at acute hopital. Accident and Emergency (A&E) provide acce to hopital ervice for urgent cae. The normal proce for admiion to hopital i via referral to a hopital conultant in an appropriate pecialty, with the general practitioner (GP) playing a gatekeeper role. However a parallel route i neceary for emergencie. Conequently, the A&E (or caualty) department i ued by individual brought by ambulance and or preenting themelve for treatment. The latter, in particular, include people whoe medical condition vary widely in everity. A&E therefore perform a orting function, deal itelf with a range of le eriouly ill patient and aee more eriou cae for admiion a hopital inpatient. Only ome 15 to 20% of patient arriving at A&E are eventually admitted to bed on hopital ward. 1 Public concern ha focued on what are widely felt to have been exceively long waiting period at A&E. Official guideline pecify that patient requiring treatment a inpatient hould be allocated to a bed within two hour. 2 Although thee tandard apply not to the duration of wait from the individual arrival at A&E but only to the time elaped after a deciion to admit, they are neverthele routinely broken in many hopital. The pectacle of ick people whoe condition merited admiion a inpatient having to wait overnight or longer on trolley, or even being treated in ambulance parked outide the unit (Guardian, ), ha provoked widepread criticim. At time A&E unit have become o congeted that they have been 'cloed to blue light' - even emergency ambulance are barred and are diverted to other hopital (Evening Standard, ). A variety of explanation ha been offered for the crii affecting A&E, a recent report providing a comprehenive account of poible factor. 3 A commonly held view attribute it to the cloure of hopital bed and the conequent reduction in hopital bed capacity. The Britih Medical Aociation etimated that 9000 acute bed were cloed in England ; and the Labour Party (when in oppoition) produced figure of 13,000 acute bed cloure between 1989/90 and 1995/6 - ome 11% of the total (Guardian , ). Shortage of bed, in thi view, have multiple effect on A&E. Directly, patient arriving via A&E find that there i no bed available. Indirectly, bed hortage caue cancellation of cheduled non-emergency admiion; a a reult of delay, ome of thee become emergency cae, neceitating entry through A&E. Perhap, it ha been uggeted, the urge of attendance at A&E (up from 3,260,000 in London financial year to over 3,825,000 in ) ha been a behavioural repone by patient and their GP to the difficulty of gaining admiion through the referral procedure. Thi rie in the number of emergency admiion ha occurred at the ame time a bed number have been falling, and a difficultie of A&E taff in admitting emergency patient to hopital bed ha been growing. 1 Other factor poibly implicated in the A&E crii are bed blocked by patient fit for dicharge becaue local government lack community care reource to receive them; and government waiting lit reduction initiative. The

2 latter are targeted at the tail of thoe who have been waiting longet - the effect can be to give precedence to le eriou cae, dilodging more urgent one which may then require emergency admiion (Daily Telegraph ). Another plauible mechanim i that competition on price promoted ince 1990 by the internal market in health ervice ha increaed bed occupancy rate to a level where there i inadequate lack left to cope with demand variation. All of thee explanation implicate one or more apect of the then government policie on the NHS, or on public expenditure more generally, in the deterioration of A&E performance. The governmental repone wa, typically, to urge hopital to manage their bed more effectively, and to permit hopital to employ doctor in A&E department beyond agreed quota (ibid.). Origin of the preent tudy 'Caualty Watch' i a project etablihed in 1992 a a repone to public concern that cut in the NHS, epecially bed cloure, were producing an inadequate caualty ervice and harming patient. It wa et up and i till run by Southwark Community Health Council (in South London). Initially ponored by the Greater London Aociation of Community Health Council, it wa ubequently funded by Lambeth, Southwark and Lewiham Health Authority and now by the South Thame Aociation of CHC. (Community Health Council, or CHC, are tatutory bodie et up to repreent the community view on local health ervice proviion.) Caualty Watch monitor the performance of hopital caualty department throughout London, a well a ome further afield. It work by volunteer making imultaneou co-ordinated monthly viit to A&E unit and collecting data, both by obervation and from the hopital information ytem, on the number and waiting time to date of patient currently in A&E. Thee urvey enable the trend in performance to be tracked, and publicied if appropriate. The Caualty Watch urvey, however, did not attempt to analye the caue of the delay and congetion in the ytem which it recorded. Thi wa perceived a a limitation, and collaboration between the project and the Department of Operational Reearch at the London School of Economic in 1995 reulted in a joint effort to build a computer model to explore how factor internal and external to A&E contribute to delay in caualty. The modelling expertie wa provided by LSE, while orientation to the problem area, judgement on deign choice, and introduction to takeholder were upplied by Caualty Watch. Sytem dynamic wa elected a the appropriate modelling medium, and the model wa developed through two MSc tudent project in 1995 and In the firt of thee a prototype model wa produced, which in the econd project wa piloted in an outer London A&E department. From October 1996 a nine month project wa etablihed, funded partly by Caualty Watch and partly by LSE, to turn the prototype into a fully operational model. During thi period a cloe working relationhip wa etablihed with the A&E department of an inner London teaching hopital - which for reaon of confidentiality we will refer to a 'St. Dane '. With acce to information held by taff and the hopital databae, the model ha been calibrated to fit St. Dane, the relationhip within it have been confirmed and model parameter have been etimated. Thi model ha been ued to invetigate the enitivity of wait at A&E to change in parameter value, reource level and allocation policie. Content of thi paper Thi paper report on the tructure of the A&E ytem dynamic model and on it ue to explore the dynamic of the ytem of which A&E i a part. The econd ection outline the principal feature of an A&E department, jutifie the choice of ytem dynamic, propoe a focu for the model and then decribe it tructure. The following ection preent an analyi of the output of a 'Bae Cae' imulation - including elaboration of ome noteworthy apect of the model formulation - and addree the quetion of model validity. In the penultimate ection thi Bae Cae i compared with a number of intereting cenario, notably involving change in bed capacity but alo incorporating change in the pattern of demand. A final ection derive leon from thee imulation experiment, draw ome general policy concluion, and identifie further work to be performed. Model Conceptualiation and Formulation In thi ection we firt decribe the activitie in and around an A&E department in a way uitable for modelling. We then jutify the ue of ytem dynamic a an appropriate approach, preent the focu of our modelling tudy and give an overview of the model formulation. Initial Conceptualiation of the A&E Sytem It i eminently poible to decribe the activitie of an A&E department, together with it interaction with the environment, in coniderable detail. However, we have the pecific aim of exploring the iue raied in the introduction: the repone of A&E waiting time to reduction in bed capacity. For the purpoe of modelling that iue we can focu our decription. We can therefore conceptualie the A&E ytem in term of two area: the

3 community and the hopital, with the relevant function of the hopital ub-divided into three; the A&E department, the management of elective patient, and the ward. Thee can be briefly characteried a follow: The Community. Patient flow into the hopital from the urrounding community and are ubequently dicharged back into the community. There are two main patient group: emergency patient and elective patient. Emergency patient are individual who have been brought by ambulance, a well a walk in patient who have preented themelve at the A&E department. The latter group include elf-referral ; individual whoe GP ha not ecured a direct referral to a conultant and who have therefore choen to enter A&E without prior arrangement. The rate at which emergency patient arrive in the A&E department depend on many characteritic of the community: denity and average age of the population, acceibility to other hopital etc. Elective patient are individual requiring non-urgent medical treatment who tay on a waiting lit until cheduled for treatment. The rate of cheduled elective admiion depend on the capability of the hopital (cale of facilitie, range of ervice offered etc.) and the characteritic of the catchment area. The reaon for variation in thee two arrival pattern i outide the cope of thi tudy; arrival rate of patient to caualty are bet conidered a exogenou to any model. For both of thee rate we therefore aimed to ue hitorical data when modelling. The rate at which patient are dicharged back into the community influence hopital occupancy and i itelf related to length of tay. Length of tay i influenced by a variety of factor: individual characteritic of the patient, the range and quality of hopital ervice, the availability of care in the community 5-8 etc. The variou factor affecting the length of time patient tay in hopital are not ditinguihed in the model but rather aggregated into a ingle value for thi parameter. The Hopital - A&E Department. Many element make up the time which elape between a patient arriving in A&E and, if in-patient care i decided upon, ubequently leaving the department to go to a bed on one of the ward (Figure 1). Patient follow different pathway through A&E before they are eventually admitted (if indeed they are). When patient arrive in A&E they are triaged and regitered and then wait for an initial conultation with an A&E doctor (we ue thi term to deignate collectively Senior Houe Officer - the lowet pot-regitration medical training grade - and Regitrar in A&E). The number of A&E doctor on duty varie during a day. Patient may be treated and dicharged, or might be the ubject of further clinical appraial and teting prior to treatment and dicharge. More evere cae are referred to a Specialty Doctor, a member of a pecialty upport team called to A&E from elewhere in the hopital. Such patient may undergo further tet procedure and then be treated and dicharged. Alternatively, they may be admitted to a ward and ubequently leave the hopital after completing treatment a inpatient. The main procedure neceary to determine whether hopital admiion i required for emergency patient, and the reource required to perform thee procedure, are hown in Figure 1. The Hopital - Management of Elective Patient. Treatment for which elective patient are waiting can be urgical, e.g. hip replacement, or medical, e.g. chemotherapy. To enure that operating theatre, urgical team or appropriate equipment are available, uch treatment are cheduled well in advance. Patient are cheduled for admiion to ward the day before their treatment and prepped (e.g. blood tet, ECG reading, tarving in preparating for the reception of drug, etc.) by nure. On their cheduled day of admiion patient are aked to contact the hopital by telephone to confirm their appointment. If confirmation i received then they are aked to travel to the hopital. Alternatively, they may be told that no bed i available. In thi cae their admiion may be cancelled or they may be aked to wait at home in the hope that ward round later in the day may unexpectedly free-up a bed. A mall proportion of patient are unable to keep their appointment, or cancel it themelve, and they loe their cheduled lot. Elective patient who are allocated a bed are admitted onto a ward, perhap after delay in the day room. Thi i true for thoe whoe admiion i confirmed early and for thoe found a bed only later in the day. Conequently, thee elective patient arrive on the ward throughout the day, though rarely reaching them later than 18:00. They are prepped and made ready for treatment the next day. Elective patient who fail to have a bed allocated to them may have to be cancelled (and recheduled for another date). However, St Dane ha a hotel unit in which ome may be aked to tay overnight. On the following day thee patient mut rapidly be found a bed and then prepped in good time for treatment that day. Thi option i labour intenive and only a mall proportion of patient can be handled in thi. The Hopital - Ward. The rate at which a hopital can admit new patient - whether emergencie or elective - i influenced by the management and taffing of bed. Becaue lack of available bed on ward may contribute to delay in an A&E department, a model mut incorporate information about bed occupancy - the tatu of bed on the ward. Occupancy i determined by the ratio of the accumulated number of emergency or elective patient on the ward to the total number of hopital bed. A occupancy rie, increaing priority i given to admitting onto the ward patient from A&E whilt cheduled elective treatment increaingly need to be cancelled. Patient are dicharged from ward during normal opening hour. In principal, thi free a bed. However, both patient and bed mut firt be identified, cleaned and got ready. Thi all take nuring time and nure have other dutie; during daylight hour current patient are more active and need attending to, meal and drug mut be

4 ditributed and viitor aited. In conequence, emptied bed do not immediately become available. Thi turnover interval introduce a delay between patient dicharge and new patient admiion. Emergency Patient Patient waiting in the reception area to be een by an A&E doctor in the Major Treatment Area (They have been triaged by a nure and regitered) Sytem Boundary Patient een by an A&E doctor Treated and dicharged without invetigation Tet Treated and dicharged after interpretation of tet reult Patient referred to a peciality Doctor after interpretation of tet reult Patient waiting to be een by a Specialty Doctor Patient referred to a Specialty Doctor by a GP Patient een by a Specialty doctor. Treated and dicharged without further invetigation Treated and dicharged after interpretation of further tet reult Tet Referred to ward for hopital admiion after interpretation of further tet reult Referred to ward for hopital admiion without further invetigation in A&E Patient waiting in A&E for a bed to become ready Patient leaving A&E to go to a bed on hopital ward Figure 1 Schematic repreentation of A&E element, procee and pathway included in the ytem dynamic model.

5 The Ue of Sytem Dynamic N.B. Edited in thi hortened paper.* Variou healthcare ytem have been the object of previou imulation tudie. Here we briefly review the relevant work and the how the relevance of a tudy employing the ytem dynamic approach. The culture of the NHS lead undertandably to a focu on the handling of individual patient and thi generally predominate in tudie of A&E, 9-11 including thoe touching on waiting time. 12,13 It i therefore not urpriing that operational reearcher have frequently advocated the ue of a dicrete event imulation (DES) approach, which can generate detailed reult concerning the handling of different type of patient However, a conequence of conidering ituation at a micro-level ha been tudie whoe focu ha been on iolated area within a hopital or on the treatment hitorie of pecific type of patient Sytem dynamic modelling 25 can play a different role in probing the operation of healthcare ytem. A general dicuion of thi role may be found elewhere. 26 Model Focu: The Dynamic Hypothei In thi ection the main feedback procee that influence an A&E department are preented. An hypothei concerning the reulting dynamic behaviour i alo dicued. Together thee two element provide a focu for the tudy. A ytem dynamic model i a caual theory of how an oberved or deired behaviour i generated by a ocial ytem. 25,39-41 Such model need a clear focu and the tarting point for thi i a dynamic hypothei. Thi i a verbal and/or diagrammatic decription of a feedback tructure, combined with a reference mode, or decription of the oberved or deired ytem behaviour that the tructure i thought to generate. 42 A formulated and calibrated model can tet thi dynamic hypothei. The dynamic hypothei decribed below erved a a guide for model contruction and for the policy experiment decribed later. The tructural caue of waiting time are complex and no two A&E, or Caualty department will have exactly the ame et of problem. 1 However, the nature of the main factor i clear. There are two main patient group (emergency admiion and elective admiion) which interact to influence the availability of bed on the ward. The principal interaction are hown in Figure 2 a a caual loop diagram. 43 The main feedback loop are all balancing loop, that i, they are explicitly or implicitly goal-eeking, o that a change in the value of one of the variable in a loop tend to be counter-acted by the operation of that loop. (The model doe alo contain two reinforcing loop, repreenting crowding effect but thee are of le ignificance and are not hown here) Loop B1 act to drain the number of emergency patient in A&E by admitting them to hopital ward. A patient awaiting admiion increae o the rate of admiion increae, auming there i free bed capacity on ward. The total waiting time for a patient actually reult from the eparate delay involved in the variou activitie within A&E. Mot of the detail of the model therefore reide in the diaggregation of loop B1 into the eparate activitie decribed in the previou ection (Figure 1). Loop B2 act to limit the occupancy level on ward by the bed capacity. By retricting - and even hutting down - emergency admiion, loop B2 enure that patient are not admitted unle there i free capacity. Loop B3 ha the ame goal of controlling bed occupancy but act by influencing the rate of elective admiion. Again, bed capacity i a limiting variable. Loop B3 alo control loop B4 whoe two component together hare the goal of reducing the backlog of cheduled elective patient. Thi i achieved either by admiion to ward (loop B4a) or by cancellation (loop B4b). If there i room to accommodate all of the elective cheduled admiion then the elective admiion rate will equal the deired admiion rate (B4a), otherwie, a greater burden fall on B4b. The balance between B4a and B4b i itelf controlled by the balance between B2 and B3 and it i important to note that the operation of B2 ha priority over the operation of B3. The previou government claim that the quality of healthcare would not be affected by acute hopital bed cloure indicate a deired behaviour of the above ytem The cae might run a follow: decreaing the bed capacity increae the occupancy level of bed on the ward. Thi increaed utiliation of bed make up for the bed lot o that the hopital can accommodate the ame number of patient a before. Conequently the emergency admiion rate - and hence patient waiting time in caualty - remain unchanged. Or, in reference mode term: a downward tep in bed capacity yield upward adjutment in occupancy and no change in waiting time. We therefore have a ytem tructure (Figure 2) and the deired behaviour decribed above. Together, thee form the dynamic hypothei that i to be teted. * Thi plenary paper i a hortened verion of an LSE Working Paper. Thi ection ha therefore been reduced in length. For implicity and conitency, the reference relating to it (reference 27 to 38) have been retained. A later ection ha been removed, though it location i till indicated.

6 Arrival in A&E Patient in A&E o Patient Waiting Time in A&E B1 Emergency Admiion Rate o o B2 B3 Elective Admiion Rate Bed Capacity o Occupancy Level of Ward o o Dicharge Rate Elective Cancellation Rate B4a Deired Elective Admiion Rate B4b o Scheduled Elective Admiion o Figure 2 Caual loop diagram of the main effect determining waiting time in an A&E department. Formulation of Model Structure and Equation The ytem tructure decribed above ha been formulated a a quantitative model, the purpoe being to imulate the dynamic behaviour implied by the model aumption. 25,39,47 The key element of formulation are outlined here. The mot detailed egment of the model concern the A&E department itelf. An exhautive account of thee element of the model i not appropriate here. However, all of the procee decribed above are repreented, o that the feature of thi ub-ection of the model are a hown chematically in Figure 1. The model alo incorporate the handling of elective patient. The detail of thi ub-ytem i a conceptualied in the ection above on the management of elective patient, the map in Figure 3 being only a implified repreentation of the detailed formulation in the model. A patient are cheduled, they are modelled a flowing into a tock ('Scheduled Elective Admiion'). Individual waiting at home, travelling to the hopital and thoe who have tayed overnight in the hotel unit are all included in thi tock. Some patient are unable to keep their appointment ('Drop Out Rate'). Other have their treatment cancelled becaue the hopital doe not have bed available to admit them ('Elective Cancellation Rate'). The remainder are admitted onto a ward for treatment ('Actual Elective Admiion Rate'). Admiion and cancellation both on the day before treatment and on the actual day of treatment are brought together in thee two flow. The model wa contructed uing the ithink oftware, 28,29 on the Macintoh platform. With thi package a multiorder, non-linear ordinary differential equation model may be built which preent it main aumption to the uer via a graphical interface, or diagram. The model wa large; the core had nine tock and 160 other variable whilt nine tock and 16 other variable were ued to calculate variou performance meaure. To handle the complexity of the reulting diagram, the detailed repreentation of the activitie in A&E and of thoe concerned with elective admiion were built a ub-model. 48 Although the oftware allow all of thi tructure to be diplayed graphically, it wa overlaid with a implified, high level map (Figure 3). Thi format allow the ytemic interaction of the model to be effectively preented. For example, demand for A&E ervice can be een to depend on both emergency patient and on patient referred by their GP. Some patient are dicharged from A&E but thoe

7 requiring admiion go on to interact with cheduled elective admiion, the outcome influencing both cancellation and patient on ward. Drop Out Rate Scheduled Elective Admiion ~ Scheduling Rate Actual Elective Admiion Rate to Ward Elective Cancellation Rate ~ Rate of Accepted Admiion via GP Major Treatment Area in A&E Patient on Hopital Ward Arrival Rate of Pot Regitrated Patient A&E Admiion Rate to Ward Ward Dicharge Rate ~ Self Referral Rate A&E Dicharge Rate ~ Occupancy Total Bed Capacity of Hopital Rate of Patient Ready for Dicharge Average Length of Stay in Hopital Figure 3 Stock/flow diagram of the A&E ytem dynamic model. Only the high level map i hown: the two boxe with vertical grill open to reveal the full, 194 equation model. The Bae Cae Simulation: calibration, analyi and model validation In thi ection the focu move to imulation output. Firt the calibration of the two patient arrival rate i decribed. We then report on how the completed imulation model wa ued to generate a Bae Cae, what ummary tatitic were recorded and of the broad-bruh analyi of the ytem that reulted. In the following two ub-ection we elaborate on ome point of formulation neceary to undertand adequately the functioning of the model. The ection cloe with comment on the validity of the model. Arrival rate calibration The model treat the arrival of emergency and elective patient into the A&E department a exogenou. The calibration of thee two rate i therefore crucial to the model realim. Below we decribe the ource of data ued to etimate them. Emergency admiion. In the mot recent year nearly 8,000 patient arrived without pre-arrangement at the St. Dane A&E department. Thi total wa known to be unevenly ditributed, depending on the time of day and day of week. However, at the time of thi tudy the hopital computer ytem had not been ued to record hourly data on thee emergency patient, only monthly total being available. Fortunately, the recently arrived Regitrar had tarted to compile more detailed information (in order to examine the appropriatene of the A&E doctor roter then in

8 place). We were therefore able to obtain written archival data which recorded A&E arrival at hourly interval for the period September to November 1995 (Figure 4). Thi data wa incorporated in the model after averaging over day of the week (ince day to day variation i dominated by within-day variation) and adjuting upward by 7% to reflect annual increae in uage. The reult wa a cycle which produced a total of 220 emergency patient per day, of whom about 40 would require hopital admiion and therefore a bed. Scheduling of Elective Admiion. Data for the average rate of cheduling elective patient for admiion wa obtained from the hopital Bed Manager. He etimated that each day 110 waiting lit patient were cheduled for admiion during the normal hour of 9:00 to 17:00, for treatment the following day. In the abence of more detailed information thi total wa aumed to be ditributed evenly over that period. Both emergency and elective admiion make ue of the finite bed capacity, taken to be 800 bed in the Bae Cae imulation. The relative prioritie afforded to A&E patient awaiting admiion and patient cheduled for elective admiion are affected by the extent of the backlog of each category of patient. The flow of admiion onto ward account for the relative prioritie o that, in practice, all other thing being equal, a the backlog of A&E patient rie, the free bed are increaingly allocated to A&E patient and more cheduled elective admiion are cancelled. Thi policy wa confirmed by all thoe we poke with and wa therefore repreented in the model Hour Figure 4 Average number of emergency patient arriving in A&E department in hourly interval. Thin line: arrival number for each of the day of the week. Bold line: hourly data averaged acro day of the week. Bae Cae output generation, performance meaure and preliminary analyi Thi ub-ection decribe how the imulation model wa ued to produce reult and what ummary tatitic were computed. Some preliminary analyi of the ytem i alo decribed. The model wa run for ix imulated 24 hour cycle to obtain teady tate data. Summary tatitic from thee run are hown in Table 1 and 2. Unle otherwie tated, thee performance meaure have been calculated from the teady tate region of the run, all initialiation tranient being excluded, and are average acro the daily cycle. Since the tarting point of the tudy wa delay experienced in A&E, the meaure calculated included daily average acro all patient type for the delay from regitration to: conultation with an A&E doctor; deciion to admit; and admiion to ward. The daily minimum and maximum of the lat of thee - the total waiting time - wa alo calculated. Other meaure track daily average figure for percentage of elective cancellation, proportion of A&E doctor time pent with patient and hopital bed occupancy. The output of the Bae Cae imulation wa alo ued to analye the functioning of the ytem in finer detail. Emergency patient go through many procedure in A&E (ee Figure 1) before it i poible to decide whether or not hopital admiion i required, and delay in thee activitie contribute to the total time pent in A&E. Figure 5 diplay thee delay experienced in reaching thee different tage. Such data may be preented in a variety of way; we have choen to how the average time taken to reach the completion of each tage, plotted againt the hour

9 of the day when that tage i completed. For example, at 6.00 the patient have waited about half an hour from regitration to firt conultation, from which we may deduce that they completed regitration around 5:30. Similarly, at 00:00 patient about whom a deciion to admit ha been made have pent nearly five hour from regitration to reach thi point, from which we may deduce that they completed regitration around 19:30 the previou day. The waiting time averaged acro all thoe emergency patient ubequently admitted to a ward i therefore given by the top line in Figure 5. At 24:00 patient admitted to a ward have pent more than ix hour from regitration to reach thi point. From thi we may deduce that they completed regitration before 18:00. We can ee that under normal condition patient pend at leat four and a much a eight and a half hour in the A&E department, depending on their time of arrival, before being given a bed. Note that patient who leave the department for hopital admiion early in the evening have therefore experienced the longet wait, while patient who are tranferred to bed on ward in early to mid-morning have pent relatively horter time in A&E Hour From regitration until patient leave A&E for ward admiion From regitration until a deciion to admit From regitration until conultation by pecialty doctor From regitration until referral to pecialty doctor From regitration until completion of conultation with A&E doctor Figure 5 Emergency patient waiting time to reach different tage in A&E (Bae Cae imulation output). According to the model reult, the current hopital reource produce an average daily occupancy level of 95% (Table 1). Neverthele, on average 16% of the cheduled elective admiion are cancelled to give room for emergency patient. Coniderable variation may be een in two component of total waiting time for emergency patient: the time from regitration until being een by an A&E doctor and the time waiting in A&E from the deciion to admit until leaving A&E for hopital admiion (Figure 5). The underlying reaon for thee two delay are analyed in more detail below. Average Average Total Average Average Average time to time to Waiting Time % Elective daily daily A&E Dr. DTA (min, avg, max) Cancell- hopital A&E Dr. Conult. ation Occupancy Util. [Hour] [Hour] [Hour] [%] [%] [%] Bae Cae 800 bed and normal demand , 5.9, Table 1 Performance meaure for the Bae Cae model run.

10 Waiting time from regitration until completion of A&E doctor conultation The graph for time waiting to be een, and then being een, by an A&E doctor (Figure 5) how a ingle deep trough in the morning and gentle afternoon and evening peak. Thi i only partly explained by the emergency patient arrival pattern. Another factor i the variation in the roter arrangement for doctor in A&E. At the time of thi tudy, the number of A&E doctor on duty at St. Dane ranged from a peak of even in the afternoon to a trough of two in the early hour of the morning. (The endogenou control of thi capacity i the ubject of an additional tudy 49 ). The trough in waiting time can now be analyed in relation to the proviion of A&E doctor. At midnight a backlog of pot-regitration patient ha built up and the four A&E doctor on duty are fully utilied (Figure 6, graph 1). Delay of nearly two hour reult. After midnight the number of doctor fall to three but further A&E arrival alo tail off (Figure 4). Conequently, the backlog fall and the delay reduce. Thi continue until 3:00, when patient are being een with a delay of only 25 minute (the aumed minimum time pent having a conultation with a patient) and doctor utiliation begin to fall away. Although the number of doctor reduce to two at 4:00, utiliation rie to compenate and the delay remain minimal. By 6:00 doctor utiliation i at it lowet. Utiliation and delay rie after thi but patient who arrive in caualty a late a 8:00 have waited on average only 25 minute for a conultation after regitration. Although the number of doctor tep up teadily from 7:00 until early-afternoon, there i a coniderable rie in emergency patient to contend with. Doctor utiliation, patient backlog and delay all therefore rie from 9:00 onward. Even with the maximum compliment of doctor in the early afternoon, there i inufficient capacity to keep up with the workload. The ituation i exacerbated by a crowding effect a the cubicle in A&E become full. It then become more difficult to adminiter the patient who are waiting, the time expended by a doctor finding and giving an initial conultation to a patient rie and o the backlog i drained le quickly. A&E doctor therefore work flat out for the ret of the day. Only in the late afternoon do they begin to catch up with the backlog of patient, and the reulting light dip in delay around 18:00 caue the afternoon peak. Thi perit only briefly a a econd, evening, ruh of arrival produce a new backlog of patient waiting to be een. During the evening, therefore, delay in conultation by doctor again rie, producing the econd peak. The waiting time from regitration to A&E doctor conultation and the aociated utiliation of A&E doctor i therefore een to reult from the combination of the pattern of arrival of emergency patient and the pecific A&E doctor roter : Bed Occupancy 1: A&E Doctor Utiliation : Ward Dicharge Rate 10 4: Scheduling Rate 5: Elective Admiion Rate 5 6: A&E Admiion Rate 0 6 3,4& Hour 3,4& Figure 6 Output from the Bae Cae run of the model.

11 Waiting time from deciion to admit until admiion to ward The longet wait experienced by patient are primarily attributable to delay in the ward admiion proce, thi delay diplaying a teep peak and trough pattern. Thi variability i not olely due to the backlog produced by the arrival pattern: the turnover rate of cleared bed and the management of elective patient combine to co-produce thi behaviour. We now conider the caue of thi delay in more detail (numbered graph refer to Figure 6). Patient are dicharged from the hopital from 9:00 until 17:00. In the model thee dicharge are taken to occur after an average tay of ix day, a figure which necearily aggregate a wide variety of urgical and medical cae. A tated previouly, there i a delay, the turnover interval, between patient dicharge and the time when a bed i ready for a new patient. Hopital taff etimated that in the late evening and early morning the turnover interval i relatively low (average one hour), while from midday until late in the afternoon thi interval i generally high (up to five hour). Thi difference i clearly generated by endogenou effect; procedure involving the interaction of adminitrative, cleaning and nuring dutie. However, for implicity thi effect wa repreented in the model a an exogenou time erie. During the daytime, thi component of waiting time i at it highet around 20:00 and relate to patient who regitered in A&E at 12:00. In fact, thi component rie from 8:00 onward (Figure 5). During the day there i interaction with the elective patient that have been cheduled for admiion, whilt increaed bed turnover time and a econd A&E crowding effect alo contribute to the rie in delay. Thee three effect are dicued further below. At 9:00 patient begin to be dicharged from ward (Graph 3). However, the turnover time on free bed tart to increae a the activitie of the day keep ward taff buy. Therefore, jut a more patient tart to arrive in A&E (Figure 4) and thoe requiring admiion begin to accumulate, the time to re-cycle a free bed tart to increae. Bed occupancy fall (Graph 2) and delay to A&E patient mount. We now conider another reaon for the rie in delay - crowding. An A&E patient mut be accompanied to a ward by a porter and a nure from A&E. A A&E become more preured during the late afternoon and early evening and more potentially urgent cae mut be attended to, it become increaingly difficult to pare nure to do thi. Conequently, although A&E patient have priority over elective patient for admiion, thi crowding effect limit the former ability to take up the opportunity of an available bed. Thee bed are napped up by elective patient, a long a they are eeking admiion. Elective patient intended for treatment the following day are cheduled to arrive throughout normal daytime hour (Graph 4) and thoe that can be admitted are a component of the elective admiion rate (Graph 5). However, from 9:00 to 12:00 priority i afforded to thoe elective patient held overnight whoe treatment are cheduled on thi day. Such patient make up the remainder of the elective admiion rate. After 12:00 uch patient cannot be prepped in time and their treatment i cancelled. Conequently, all of the elective admiion flow in the afternoon conit of patient intended for treatment the following day. Thi continue until 18:00, when ome will be held over in the hotel unit for admiion on the day of their treatment and the remainder are cancelled. During the evening and the early hour of the morning thee dynamic have a knock-on effect on the time pent by A&E patient awaiting an available bed. Although no patient are dicharged from ward during thi time, the delay reulting from the lengthened turnover interval mean that bed releaed by earlier dicharge are continuing to become available. In the abence at thee hour of elective patient eeking admiion, thee are filled by waiting A&E patient. There i a urge in uch admiion around 22:00 (Graph 6). Thi i aociated with the late evening reduction in turnover time and alo with the accumulated wave of A&E arrival, phae-hifted beyond the period of elective patient admiion. In conequence, through midnight and into the early hour we ee occupancy teadily riing and the lowet value of delay from deciion to admit and admiion (Graph 2 and Figure 5). Model Validation Previou ub-ection have decribed key apect of the Bae Cae imulation output. Here we outline the procee that were undertaken to validate the model. Two introductory remark are neceary. Firtly, model validity cannot be etablihed by a ingle tet, or at a ingle moment in a modelling tudy. Rather, ytem dynamicit - along with other imulator 50 - accept that validity, "accumulate gradually a the model pae more tet" (reference 51, p. 209). Therefore the treatment of the validity iue would ideally run in parallel with the decription of the model and it run. We have avoided uch a clumy tructure and have intead choen to conolidate the dicuion of validation at thi point. Secondly, becaue thi paper focue on the technical detail of the model and becaue validation and the modelling proce are the ubject of eparate, more detailed, publication, 52,53 the treatment here i brief. The validation tet pecific to a ytem dynamic model are well etablihed 39,51 and may be divided into thoe focuing on model tructure and thoe relating primarily to imulated behaviour. We firt outline the application of thee two type of tet to the A&E model and then decribe the team involved in performing them. Structure-baed validation tet. Thee validation tet are concerned with formulation and enure, firtly that the model i uitable for it purpoe and, econdly that it i conitent with the real ytem. To tet uitability for purpoe we focu inward on the model. Thee tet enure, firtly that the model i uitable for it purpoe and,

12 econdly that it i conitent with the real ytem. To tet uitability for purpoe we focu inward on the model, teting that all variable and output of equation have enible dimenion and that equation hold true for extreme input value. In thi way we confirmed that the model wa well poed. Teting that the model tructure i conitent with the real ytem involve judging the model repreentativene. 50 The cloe link with St. Dane' allowed u to dicu the tructure with people familiar with the A&E ytem. Coniderable time wa pent on chooing variable name and on documenting the aumption in algebraic formulation. Validity wa further enhanced by confirming the correpondence of model parameter to information available. Behaviour-baed validation tet. Thee tet ue model imulation to probe further the validity of it contruction. The paucity of recorded data made it impoible to perform a full behaviour reproduction tet54,55 and o a proce of triangulation involving ubjective, qualitative time erie analyi and objective, quantitative ummary data wa ued. Graph of all of the model variable were preented to our collaborator (Figure 5 & 6 how example). Thi output, along with the performance indicator, wa judged to be realitic and convincing by thoe with day-to-day experience of the real ytem. A brief comment hould be made on one of the quantitative validation point, 'average percentage elective cancellation', which i the ratio of thoe patient cancelled to thoe cheduled. Thi performance meaure correpond to the only available data, which wa obtained from the relevant Health Authority, converted into the appropriate form and then cro-checked with etimate from the St. Dane' Bed Manager. Some adjutment i neceary becaue, in ituation of great demand preure, adroit bed management allow ome bed temporarily vacated by patient undergoing urgical treatment to be ued by new patient pending only a brief time in the hopital for ome clinical treatment. Thi bed doubling effectively boot the actual occupancy of bed, though to a trictly limited extent. However, the Regitrar and the Bed Manager felt that a atifactory accounting of model behaviour had been achieved without an explicit modelling of bed doubling. One might alo oberve that the inight generated by the model reult, eentially, from enitivity analyi and that the qualitative inight that flow from thi would not be altered by uing adjuted data. The above judgement were made from the Bae Cae. However, model validity wa further enhanced by applying tet to the policy analyi run decribed below. Thee cenario can be een a extreme condition tet, 51 the diagnoi of urprie behaviour 56 and the generation of inight. 39,51 The group proce ued to create the model meant that thee imulation could be tudied and judged reaonable by our collaborator. The modelling team. For a model to be valid, one mut be confident that it i, uitable for it purpoe and the problem it addree... [and]... conitent with the lice of reality it trie to capture (reference 39, p. 312). To make uch judgement both experienced modeller and individual with knowledge of the actual ytem are needed. The core team for thi tudy conited of the author (acting a modeller and facilitator) and taff from St. Dane'. Our collaborator from St. Dane' included: the Regitrar in the A&E department, other phyician from A&E, the Bed Manager, the Site Nure Practitioner, other nure and taff from other pecialim and from the tet laboratorie. In addition, apect of the model formulation were checked with taff from the Southwark Community Health Council and we alo benefited from the experience of taff in Caualty Watch, the London Ambulance Service and the Emergency Bed Service. The detail of how thi team worked to create the model are recorded elewhere. 53 Here we merely comment that thi pread of individual gave u acce to both hopital databae and a range of judgmental etimate. However, it wa the LSE team and the Regitrar of St. Dane' who were reponible for checking each model aumption, element of formulation and parameter value ued. By conducting the tet decribed above we aimed to enure that the model accurately incorporated the variable, parameter and feedback effect neceary to analye the underlying reaon for long wait in A&E. The model preented here wa the reult. We might alo comment that it wa a model which our collaborator at St. Dane' ued with confidence (and enjoyment) to tudy the real ytem. Policy Analyi: Exploring cenario uing model imulation The initial motivation for the reearch decribed in thi paper wa to tet the hypothei that retriction of bed capacity would not lead to increaed waiting time in A&E. However, in the coure of developing the model it became evident that waiting time i only one of a number of meaure of ytem performance. Similarly, dicuion with our collaborator indicated that other imulation experiment might be of interet. The developed model wa therefore ued to conduct a range of imulation experiment for comparion with the Bae Cae. The value of the key performance meaure for thee cenario are hown in Table 2. The cenario are dicued in turn below.

13 Average Average Total Average Average Average time to time to Waiting Time % Elective daily daily A&E Dr. DTA (min, avg, max) Cancell- hopital A&E Dr. Conult. ation Occupancy Util. [Hour] [Hour] [Hour] [%] [%] [%] Bed Capacity Scenario 700 bed , 5.9, bed (Bae) , 5.9, bed , 5.9, Demand Pattern Scenario Demand Increae 0% , 5.9, % , 6.0, % , 6.2, % , 6.3, % , 6.6, % n/a n/a n/a Combined Scenario 700 bed and 7% increae in demand , 7.1, (+ A&E Dr repone) Table 2 Conolidated performance meaure for the variou policy analyi run of the model. Bed Capacity Scenario Sytem behaviour wa imulated for level of bed capacity between 700 and 900, the range choen by our collaborator to be of interet. Thee cenario were aimed at invetigating whether the government wa right in it aertion that cloure of hopital bed would not affect the tandard of ervice provided to the community. The effect that change in hopital bed number have on A&E performance i hown in Table 2. The performance meaure, and analyi of the variou output of the run, reveal the extreme imilarity of the three imulation; there are only trivial difference in output graph. Thi urpriing, counter-intuitive reult 57,58 might appear to upport the hypothei that the model wa built to tet, namely that reduction in bed capacity can be compenated by increae in occupancy o that A&E waiting time do not increae. However, the performance meaure reveal that average daily occupancy i increaed only lightly a bed number are reduced (Table 2), and uch change are quite inufficient to ubtitute for the lot bed. The explanation for thi apparent paradox lie in the figure for elective cancellation. Thi meaure i far more enitive to bed capacity. Thee reult indicate that a hopital bed are removed more elective patient have their treatment cancelled. In order to deliver approximately the ame waiting time to emergency patient with 100 bed le, cancelled non-emergency treatment almot double in abolute term. Thi repone can be explained uing the caual loop diagram of Figure 2. Balancing Loop B1, B2 and B3 together control the flow of patient onto ward. Specifically, B3 control the balance between B4a and B4b. By hifting greater weight to B4b and cancelling elective admiion, the hopital manage - even with reduced bed number - to keep ward occupancy at a level which leave virtually unaffected the waiting time for emergency patient. The elective cancellation afety valve remove the expected ditortive effect on B2, and hence B1. Patient will not experience additional delay in the variou A&E activitie a a reult of reduced bed number in hopital ward. The operation of loop B1 i unaffected by the change in bed capacity and o no more patient will occupy trolley in caualty than previouly.

14 The repone of the hopital occupancy performance meaure ha a le complex explanation, the low decline indicating that the variou proceing capacitie involved in the different admiion activitie reult in a limited ability to take advantage of further bed. Demand Pattern Scenario The repone of the model to change in the number of emergency patient preenting wa alo examined in two way. By applying permanent change we conidered poible future demand environment for the A&E department; and by tudying the model repone to a harp tranient increae we both teted it ability to reproduce pat behaviour in a plauible way and explained the ytem repone to a crii event. Permanent change in demand. The aim of thee cenario i to explore how the ytem - with today taff number and bed reource - would behave in ituation of increaed load. Thee might be caued either by the permanent cloure of a caualty unit in a nearby hopital, or imply by a generalied increae in demand. (Further increae in emergency arrival and admiion would be in line both with hort term experience - a 7% rie in the previou year - and long term trend 59 ). Reduction in demand were deemed unrealitic and therefore irrelevant by our collaborator. For reaon explained below, the model wa imulated for permanent change in emergency demand of up to 5%. The reult are hown in Table 2 and Figure 7, with data for demand reduction plotted only for comparion purpoe. Elective cancellation once again increae but to a maller extent than in the previou et of cenario. Thi i becaue only a mall fraction of A&E patient actually require admiion and o increaing thi fraction add only lightly to the total number of all patient eeking admiion. However, mall change in demand do have appreciable effect on patient total waiting time, primarily becaue of the increae in delay before conultation with an A&E doctor. With a 4% increae, patient pend an average of three quarter of an hour more in A&E. Higher level of arrival alo produce increae in the daily averaged utiliation of A&E doctor. However, with increae up to 4%, there i till free doctor capacity at certain hour of the day, though thi decreae teadily. Although patient experience delay for conultation there i jut ufficient taff to cope with the workload over a 24 hour cycle. Note, however, that with a 4% increae in demand doctor utiliation virtually reache 100%. Beyond 4%, thi gradually deteriorating balance collape. There i no lack A&E doctor capacity to cope with the extra arrival, a backlog of patient awaiting initial conultation accumulate without bound and, even with taff working at maximum capacity, the waiting time ecalate from hour to hour. The ytem therefore fail to reach a teady tate and the performance meaure can no longer be calculated. Interetingly, the caue of thi collape i not bed capacity, but rather inufficient proviion of A&E doctor Avg Wait befor completion of A&E Dr Conultation Avg Total Wait Avg A&E Dr Util. Avg % Elective Cancellation % Change in Demand w.r.t. Bae Cae Figure 7 Spiderplot howing the proportional effect of permanent demand change on a election of performance meaure.

15 A crii event. N.B. Removed in thi hortened paper. Combined Scenario In the final cenario a ituation wa imulated with a combination of change from the Bae cae, namely 700 hopital bed and a 7% increae in demand for A&E ervice. However, the imulation decribed above ha hown that A&E doctor would be overwhelmed by demand increae above 4%. To bridge thi gap we applied an increae of 3% to the conultation rate. Thi crudely imulate A&E doctor working fater in repone to the increaed demand (poible deleteriou effect on the quality of their ubequent diagnoe are not conidered). Debottlenecking thi component of the model wa neceary if the behaviour of the other activitie wa to be examined. Thi cenario therefore explore ytem behaviour under reaonable prediction of annually increaed demand if, at the ame time, a policy of further reduction in bed number to achieve NHS economie wa to be implemented (Figure 8 and Table 2). 10 Combination 5 Bae Cae Hour Figure 8 Comparion of total waiting time under normal condition (Bae Cae) and in the cenario of combined demand increae and bed reduction, with illutrative decompoition into tage of waiting. A might have been expected, total waiting time for patient increae. The greatet contribution to increaed waiting time occur in the morning, the experience of patient arriving on ward around 7:00 exemplifying the effect (Figure 8). In thi cenario, thee emergency patient entered A&E around 00:30 and have therefore waited ix and a half hour before admiion. Thi compare with the Bae Cae in which patient only waited four and a half hour, having entered A&E jut before 3:00 the ame day. Thi increae ha a ingle main component, the delay before obtaining a firt conultation, which ha increaed fivefold, reaching three hour. The analyi of the Bae Cae and of the cenario with permanent change in demand allow u to ee that thi reult from the loading on A&E doctor capacity caued by the demand increae. The increae in total waiting time in the afternoon and evening i maller. Patient admitted to ward at 20:00 have waited le than half an hour extra in total. Thi increae i largely in the delay prior to firt conultation, with a mall contribution from the delay between deciion to admit and actual admiion (Figure 8). From the previou bed capacity cenario and analyi of thi run, we can determine that thi latter change i aociated with the mall increae in patient needing bed, rather than the reduction in bed capacity. Patient arriving on ward at 20:00 have waited almot nine hour ince arriving in A&E but during thi period (from 11:00) the afety valve of elective patient cancellation i ued to cope with the reduced bed capacity. Thi i evidenced in the harp increae in elective cancellation hown in Table 2, up to 32.5% acro a 24 hour cycle. At time when loop B4b i available (Figure 2) it i ued to control waiting time and the penalty of a mimatch between demand and reource i ubtantially tranferred to a different performance meaure.

16 Comment and concluion The development of the model of an A&E department reported in thi paper, and the imulation run which have been carried out, offer leon at a number of different level. Firtly, there are direct, practical implication from the Bae Cae and the policy analyi run; econdly, there are more general leon a to the connectedne of the ytem of which A&E i a part; and finally there are propoal for the elaboration and further ue of the model. Leon from the Simulation Certain concluion can be drawn from the Bae Cae and policy analyi run decribed in the previou ection; thee are detailed below, againt the cenario which give rie to them. Although they apply formally only to ituation comparable to thoe tudied at St. Dane, their wider applicability i quite evident. The Bae Cae. The analyi indicate that much of the waiting time experienced before admiion i inevitable: the contituent procee (Figure 1) are many and imply take time. However, at St. Dane the retricted A&E doctor capacity in the morning and the limited availability of bed in the afternoon produce avoidable additional delay. The average daily occupancy level of 92% - above the 80-85% recommended by the Britih Aociation of Accident and Emergency Medicine 60 - and the high A&E doctor utiliation indicate an intenive ue of reource. Neverthele, capacity i inufficient to deal with demand: waiting time are high and elective patient are regularly cancelled. Thi i a ytem with little room for manoeuvre and with few efficiencie waiting to be queezed out. Bed capacity cenario. The bed occupancy meaure wa hown to be relatively inenitive to total bed capacity. Thee cenario clearly indicate that without change in both A&E and ward taffing, there are limit to how fat new patient and ued bed can be made ready. Thee imulation demontrate that enhanced bed occupancy level cannot compenate for further bed reduction. Intead, the burden i borne elewhere: it i the afety valve of elective cancellation that i ued to a greater extent to compenate for any bed lo. The rapid increae in thee cancellation a bed capacity fall i what prevent a further rie in daytime A&E delay. It follow that the appropriate choice of indicator i crucial in judging the performance of the ytem. Taking an holitic view of the healthcare ytem within which A&E i embedded, it become evident that delay to patient in both caualty and elective cancellation mut be aeed - they are linked and compenating meaure. Demand pattern cenario. Scenario with permanent demand change how that depite increaed elective cancellation, bed occupancy and utiliation of A&E doctor approach 100%. Eventually the ytem collape, though it i the earliet proce - conultation with an A&E doctor - which i overwhelmed firt. Combined cenario. Thi cenario erve to emphai the error of the dynamic hypothei - that bed occupancy level can aborb a relative increae of demand preure on reource. There i even le lack in thi ytem, and it can reaonably be inferred that it i highly expoed to a crii event or to a reduction in taff capacity due to illne. General policy concluion The principal meage of thi tudy i that, while A&E waiting time may in practice be excellent meaure of the effectivene of acute hopital, uing them alone to judge the effect of bed reduction i ytemically naive. Recent development in multiple performance indicator 61 recapitulate an old idea: complex ytem mut be monitored uing a correponding variety of ignal. 62 In the context of A&E the obervation ha been made before: "tudie hould be baed on appropriate outcome meaure" (reference 11, p. 41). By providing a rigorou decription of the complexity of an A&E department, our model act a a formal platform from which concluion may be drawn which addre the complexity of the ytem ignal. By concentrating on A&E delay - important a thee are - the original dynamic hypothei provide mileading, indeed dyfunctional guidance to policy. The hypothei encourage policymaker to look in the wrong place for healthcare improvement becaue it implicitly dicount the effect of cancelling elective patient. However, thi afety valve i not without it cot. Even with current bed number, headline uch a Girl heart urgery cancelled five time (Guardian, ) are all too numerou. Patient waiting on lit for elective admiion are the victim in the battle for bed on ward, becaue of the priority necearily allotted to emergency patient. In the light of thi, and of the low amount of lack at St. Dane' and elewhere, the conequence of a further reduction in bed mut be to increae cancellation and puh hopital cloer to being mere 'emergency ward'. Thi tudy reveal the interconnectedne of A&E ervice level, bed proviion and the experience of patient on waiting lit. Bringing that interconnectedne to life via imulation can, in principle, alo provoke a dicuion on appropriate meaure of performance. A&E department do not exit in iolation. Policy mut be baed on an

17 undertanding of how they relate to pre-hopital circumtance, to the ret of the hopital and to care in the urrounding community, 1 and a et of performance meaure reflecting thi broad view hould therefore inform policy making. Poible elaboration of the model Any model ha limitation, and the model reported in thi paper i no exception: it concentrate on hort timecale effect, aggregate patient attribute and ha a implified repreentation of a hopital. Thee limitation appeared, both to the tudy team and it collaborator, to be appropriate to the quetion which were being addreed. Neverthele, there are a number of model elaboration that could throw light on a range of related iue. i) De-bottlenecking. The imulated ytem collape provoked by inadequate proviion of A&E doctor mak other effect. With few change, the model can be run with thi capacity caled up in order to reveal the effect of increaed demand on other ytem element. Thee run could be ued to inform judgement on prioritie for the proviion of additional reource. ii) Longer timecale effect. Model operating with a longer timecale might have the potential to explore a range of effect. Scenario in which taff operate at permanently high utiliation could incorporate the effect of worker burnout, a downward piralling productivity erve to exacerbate individual workload and o further degrade productivity. 63 It might alo be poible to invetigate the longer term effect of cancelling elective admiion, ince thoe o dilodged cycle back into an ageing chain, emerging with a higher priority, either becaue of the duration of their wait or becaue they become emergency cae. High occupancy level and/or high demand level can lead to great preure to free up bed, leading to inappropriately early dicharge. Modelling thi effect would allow the conideration of the extra demand created by the ubequent relape of ome of thee patient. 64 Latly, there are intereting ytemic interaction involving the phenomenon of o-called bed blocking caued by the low proviion of community care ervice for elderly people. 8 The addition of new care capacity would merit tudy ince it might have the effect of increaing effective bed capacity in hopital. iii) Hopital cluter. To tet the ability of A&E ervice to repond to demand urge, it would be deirable to conider the reilience of a network of hopital acro which a demand urge would be hared. (Poible ource of uch a urge include a major accident, or the cloure of A&E to admiion at one or more hopital within the network). Such a 'Cluter Model' i currently under development. iv) Feedback control of A&E doctor roter. In it current form the model timulate a complex ytem with input in order to undertand the nature of the repone mechanim. The ytem dynamic approach prompt u to ee how endogenou feedback effect might be improved; to thi end we have been developing improved policie for controlling the rotering of A&E doctor. 49 In concluion, we would ay that the ytem dynamic model reported in thi paper helped our collaborator to conider the interconnectedne of factor affecting the performance of A&E at an appropriate level of detail and to explore the effect of change in parameter value. We hope that the model attract wider attention. We believe that it offer thoe involved with the planning and proviion of health ervice an opportunity to bae their deciion on a ytemic analyi and o improve the quality of the healthcare that i delivered. Acknowledgement - We would like to offer our thank to taff at Caualty Watch, London Ambulance Service, the Emergency Bed Service, Southwark Community Health Council, the Department of Health and particularly all of the taff at the collaborative hopital for the time that they contributed to thi tudy. Without the acce that they afforded u, and their peronal involvement, thi work would not have been poible. Reference N.B. Reference 25,39,42,43 and 58 have been republihed by Productivity Pre, Portland OR; See Reference 65, 66 and Audit Commiion (1996). By Accident or Deign: Improving A&E Service in England and Wale. HMSO: London. 2 Department of Health (1996). The Patient Charter. HMSO: London. 3 NHS Confederation/Royal College of Phyician (1997). Tackling NHS Emergency Admiion: Policy into practice. NHS Confederation: Birmingham.

18 4 Department of Health (1998). Outpatient and Ward Attender, England: Financial year HMSO: London. 5 Hadfield, J, Yate, D and Berry, A (1994). The Emergency Department and the Community: A model for improved cooperation. Journal of the Royal Society of Medicine 87: Woltenholme, EF (1993). A cae tudy in community care uing ytem thinking. Journal of the Operational Reearch Society 44: Lane, DC (1994). Sytem dynamic practice: a comment on a cae tudy in community care uing ytem thinking. Journal of the Operational Reearch Society 45: Audit Commiion (1997). The Coming of Age: Improving care ervice for older people. Audit Commiion Publication: Abingdon. 9 Derlet, RW, Nihio, DA, Cole, LM and Silva, J (1992). Triage of patient out of an emergency department: three year experience. American Journal of Emergency Medicine 10: Dale, J, Green, J, Reed, F and Gluckman, E (1995). Primary care in the accident and emergency department: I. Propective identification of patient. Britih Medical Journal 311: Leydon, GM, Lawrenon, R, Meakin, R and Robert, JA (1996). The cot of alternative model of accident and emergency care: a ytematic review. Report to North Thame Regional Health Authority: 12 Meilin, HW, Coate, SA, Cyr, J and Valenzuela, T (1988). Fat track: Urgent care within a teaching hopital emergency department: can it work? Annal of Emergency Medicine 17: Middleton, EL and Whitney, FW (1993). Primary care in the emergency room: a collaborative model. Nuring Connection 6: Davie, R (1985). An aement of model of a health ytem. Journal of the Operational Reearch Society 36: Davie, R and Davie, H (1994). Modelling patient flow and reource proviion in health ytem. Omega 22: Paul, R (1995). Outpatient Clinic. OR Inight 8: O Kane, PC (1981). Simulation model of a diagnotic radiology department. EJOR 6: Riley, J (1995) Viual Interactive Simulation of Accident and Emergency Department. In: Katelein, A, Vier, J, van Merode, GG and Deleie, L (ed). Proceeding of ORAHS 21: Managing health care under reource contraint. Eindhoven Univerity Pre: Maatricht, pp Huang, X-M, Taylor, C and Stewart, I (1995). Computer imulation of an A&E department. OR Inight 8: Altinel, IK and Ula, E (1996). Simulation Modelling for Emergency Bed Requirement Planning. Annal of Operational Reearch 67: Romanin-Jacur, G and Facchin, P (1987). Optimal planning of a pediatric emi-intenive care unit via imulation. EJOR 29: Worthington, D (1991). Hopital waiting lit management model. Journal of the Operational Reearch Society 42: Davie, R (1995). The growing need for renal ervice. OR Inight 8: Mejia, A, Shirazi, R, Beech, R and Balmer, D (1998). Planning midwifery ervice to deliver continuity of care. Journal of the Operational Reearch Society 49: Forreter, JW (1961). Indutrial Dynamic. MIT Pre: Cambridge, MA. 26 Taylor, KS and Lane, DC (1998). Simulation Applied to Health Service: Some experience o far and opportunitie for applying the ytem dynamic approach. Journal of Health Service Reearch and Policy, to appear. 27 Richardon, GP (1991). Feedback thought in ocial cience and ytem theory. Univ. Pennylvania: Philadelphia. 28 Richmond, B (1985) STELLA: Software for bringing ytem dynamic to the other 98%. In: Anderen, DF, Forreter, NB and Warkentin, ME (ed) International Conference of the Sytem Dynamic Society: Volume II. Sytem Dynamic Society: Boton, MA, pp Richmond, BM, Vecuo, P and Peteron, S (1990). ithink Software Manual. High Performance Sytem, 145 Lyme Road, Hanover, NH 03755, USA.: Hanover, NH. 30 Morecroft, JDW (1988). Sytem dynamic and microworld for policymaker. EJOR 35: Lane, DC (1992). Modelling a learning: a conultancy methodology for enhancing learning in management team. European Journal of Operational Reearch 59: Vennix, JAM (1996). Group Model-building: Facilitating team learning uing ytem dynamic. Wiley: Chicheter. 33 Forreter, JW (1992). Policie, deciion and information ource for modelling. EJOR 59: Senge, P (1990). The Fifth Dicipline: The art and practice of the learning organization. Doubleday/Currency: New York. 35 Senge, P and Sterman, JD (1992). Sytem thinking and organizational learning: acting locally and thinking globally in the organization of the future. EJOR 59:

19 36 Lane, DC (1993). The road not taken: oberving a proce of iue election and model conceptualization. SDR 9: Lane, DC (1995). On a reurgence of management imulation and game. Journal of the Operational Reearch Society 46: Lane, DC (1997) Diary of an Oil Market Model: How a ytem dynamic modelling proce wa ued with manager to reolve conflict and to generate inight. In: Bunn, DW and Laren, ER (ed). Sytem Modelling for Energy Policy. Wiley: Chicheter, pp Richardon, GP and Pugh, AL ({1981} 19--). Introduction to Sytem Dynamic Modelling with DYNAMO. Productivity: Cambridge, MA. 40 Sterman, JD (1988) A keptic guide to computer model. In: Grant, L (ed) Foreight and National Deciion. Univerity Pre of America: Lanham, MD, pp Lane, DC and Smart, C (1996). Reinterpreting generic tructure : evolution, application and limitation of a concept. SDR 12: Rander, J (1980) Guideline for model conceptualiation. In: Rander, J (ed) Element of the Sytem Dynamic Method. MIT Pre: Cambridge, MA, pp Goodman, MR (1974). Study Note in Sytem Dynamic. MIT Pre: Cambridge, MA. 44 Tomlinon, B (1992). Report of the inquiry into London health ervice, medical education and reearch. HMSO: London. 45 King Fund Commiion (1992). London Health Care 2010: Changing the future of ervice in the capital. King Fund: London. 46 Department of Health (1993). Making London Better. HMSO: London. 47 Homer, JB (1996). Why we iterate: cientific modelling in theory and practice. SDR 12: Peteron, S (1994) Software for model building and imulation: an illutration of deign philoophy. In: Morecroft, JDW and Sterman, JD (ed). Modeling for learning organization. Productivity Pre: Portland, OR, pp Monefeldt, C and Lane, DC (1997). A&E Model: Initial invetigation of improved rotering policie. LSE Reearch Note 50 Lane, DC (1995) The Folding Star: a comparative reframing and extenion of validity concept in ytem dynamic. In: Shimada, T and Saeed, K (ed). Proceeding of the 1995 International Sytem Dynamic Conference: Volume I - Plenary Program. Gakuhuin Univerity and the International Sytem Dynamic Society: Tokyo, pp Forreter, JW and Senge, PM (1980) Tet for building confidence in ytem dynamic model. In: Lagato, AA, Forreter, JW and Lynei, JM (ed). Sytem Dynamic: TIMS Studie in the Management Science. North- Holland: Oxford, pp Monefeldt, C and Lane, DC (1997). A&E Model: Validation note. LSE Reearch Note 53 Monefeldt, C and Lane, DC (1997). A&E Model: Collaboration meeting note. LSE Reearch Note 54 Lane, DC (-). Can We Have Confidence In Generic Structure? Journal of the Operational Reearch Society, to appear. 55 Sterman, JD (1984). Appropriate ummary tatitic for evaluating the hitorical fit of ytem dynamic model. Dynamica 10: Sterman, JD, Repenning, N and Kofman, F (1997). Unanticipated ide effect of ucceful quality improvement program: exploring a paradox of organizational improvement. MS 43: Ma, NJ (1991). Diagnoing urprie model behavior: a tool for evolving behavioral and policy inight (1981). Sytem Dynamic Review 7: Forreter, JW (1970) Counterintuitive behaviour of Social Sytem. In: Collected Paper of Jay W. Forreter. Wright-Allen Pre: Cambridge, MA, pp Fry, L (1960). Caualtie and caual. Lancet 1: Royal College of Surgeon of England (1993). Britih Aociation for Accident and Emergency Medicine Directory Royal College of Surgeon of England: London. 61 Kaplan, RS and Norton, DP (1992). The balanced corecard - meaure that drive performance. HBR Jan./Feb.: Ahby, WR (1956). An Introduction to Cybernetic. Methuen: London. 63 Homer, JB (1985). Worker Burnout: A Dynamic Model with Implication for Prevention and Control. Sytem Dynamic Rev. 1: Audit Commiion (1992). Lying in Wait: The Ue of Medical Bed in Acute Hopital. HMSO: London. 65 Lane, DC (1997). Invited Review and Reappraial: Indutrial Dynamic by Jay W. Forreter. Journal of the Operational Reearch Society 48: Lane, DC (1997). Four Invited Book Review. Journal of the Operational Reearch Society 48: Lane, DC (1997). Invited Review on Sytem Dynamic. Journal of the Operational Reearch Society 48: