What healthcare problems should we be tackling? How far have we progressed?

1. What healthcare problems should we be tackling?How far have we progressed? C a r d i f f Sheffield YHORG / Health SIG 26 February 2009 S h e f f i e l d Jeff Griffiths Professor of Operational Research Cardiff University griffiths@cardiff.ac.uk

2. OVERVIEW • Brief review of European & World Healthcare matters • The National Health Service in UK • What are we doing in Wales? Some modelling we are undertaking (or have undertaken) • Brief outlines of some models • More detailed description of a few models

3. Main causes of death worldwide

8. 60 YEARS OF THE NHS 1948-2008 • Scale of the NHS • NHS is the world’s largest publicly funded health service. • Nationwide, the NHS employs more than 1.5m people. About one half are clinically qualified, including some 90,000 hospital doctors, 35,000 GPs, 400,000 nurses and 16,000 ambulance staff. • Only the Chinese People’s Liberation Army, the Wal-Mart supermarket chain and the Indian Railways directly employ more people. • On average, the NHS deals with 1m patients every 36 hours - that’s 463 people a minute or almost 8 a second. • Each week, 700,000 will visit an NHS dentist, while a further 3,000 will have a heart operation.

9. Waiting List Targets for England and Wales The English plan set out the ambitious aim that, by December 2008, no one should wait more than 18 weeks from GP referral to hospital treatment. In Wales the target is that by the end of 2009 no one will wait more than 26 weeks from GP referral to treatment, including diagnostic tests. The waiting list targets for 2007/08 included that by the end of March 2008 nobody should have been waiting for admission as an in-patient or day case, or for a first outpatient appointment for over 22 weeks. By the end of March 2009, the target is to: • Reduce the maximum waiting time for inpatient or day case treatment to 14 weeks. • Reduce the maximum waiting time for a first outpatient appointment to 10 weeks.

13. 74,684 992,604 41,891 26,316 271,855 188,123 8,487

14. Modelling Waiting Times/Lists in NHS Hospitals Waiting Lists in Wales are much longer than in England. Why? • July 2004 – WAG commissioned members of OR Group at Cardiff University • Bi-weekly meetings with WAG and NHS Trust representatives during initial development phase • August 2004 – Workshop to inform all NHS Trusts in Wales of our requirements • Oct – Nov 2004 – Visits to all 14 NHS Trusts in Wales • Throughout 2005 – Further development & Trust visits. Monthly project group meetings • April 2006 – Delivery of initial phase of Model to all NHS Trusts

15. Referrals for an Outpatient Appointment ROTT Outpatient Clinic Leave system o o o o o o o o o o o o o o o o o o o o Outpatient Waiting List 2nd chance Daycase procedures not impacting on declared WL DNA Daycases in Main Theatre? Day Unit o o o o o o o o o o o o o o o o o o No Leave system Daycase Waiting List Direct Access Referrals Yes ROTT Main Theatre Beds Inpatient Leave system o o o o o o o o o o o o o o o o o o o o Inpatient Waiting List Process Map Emergency Inpatients Daycases Leave System

16. Number No of patients remaining on list: of Weeks Consultant 1 Consultant 2 Pooled 25 25 260 259 26 10 242 199 27 2 229 155 28 - 204 98 29 - 194 54 30 - 176 27 31 - 158 10 32 - 136 1 33 - 123 - 34 - 105 - 35 - 84 - 36 - 68 - 37 - 47 - 38 - 32 - 39 - 20 - 40 - 13 - 41 - 6 - 42 - 3 - 43 - - - 803 Total wait > 24 weeks 37 2,100

17. How are we doing in Wales? National Target Waiting list targets for 2007/08 include that, by the end of March 2008, nobody should be waiting for admission as an in-patient or day case, or for a first outpatient appointment for over 22 weeks.

19. Feb 2008 5565 Mar 2008 0

20. Modelling Activities at the Intensive Care Unit at University Hospital of Wales, Cardiff

21. Headline from British National Newspaper 16 June 2008 • Over 500 patients diverted from London CCU during last 12 months to hospitals as far as 400 miles away • The 20 London Hospital Trusts have collectively 508 CCU beds, which were working at over 90% bed-occupancy on average • The Intensive Care Society recommendation is that CCUs should aim for an average bed-occupancy of less than 70% • The problem is a mixture of shortage of CCU beds and CCU trained nurses

22. Some Facts about the Hospital • One of the largest hospitals in UK - covers the whole of Wales. • Full range of specialities – Regional Centre. • On occasions no beds available. • At the start of this investigation, ICU had 14 beds (which could be increased to 19). One nurse per bed required. • HDU had 9 beds. One nurse per two beds required. • Around 150 operations cancelled per year because no ICU bed available.

23. Intensive Care Resources • Beds • At the start of the investigation: • ICU had 14 beds (could be increased to 19) (HDU had 9 beds) • Each costs around £1800 per day to maintain • Up to £60,000 worth of specialist equipment around each bed • 2) Nurses • Required nurse : patient ratio of 1:1 • Specially trained intensive care nurses are in short supply Efficient management of these valuable resources is essential! • Under provision • Needy patients refused treatment - possible death • Cancellation of planned surgery - waiting lists increase • Over provision • Waste of scarce resources

24. Questions to be answered 1. How many beds/nurses should be provided in ICU and HDU ? If more than 14 beds are occupied in ICU, agency nurses have to be employed at a cost of 4 times that of the hospital’s own employed nurses. 2. Is it possible to reduce the number of cancellations of operations which result from the non-availability of an ICU bed? At the start of the study, about 148 operations were cancelled per year due to non-availability of an ICU bed, with the consequent distress to the patients and their families. 3. Is the ratio of ICU to HDU beds the optimal one? The ratio at the start of the study was 14 : 9, but there were 5 additional beds in storage which could be utilised in an emergency.

25. How many nurses should the ICU employ? The cost of care accounts for 71% of the daily cost of the ICU, which is equivalent on average to about £1,300 per bed per day. Thus, the total cost of care could be as high as £25,000 per day (19 x £1300) for ICU beds, plus £6,000 per day (4.5 x £1300) for HDU beds. Over a year this amounts to £11.3 million. The hospital employs a mixture of their own nurses (scheduled nurses), and when the need arises they also employ agency nurses (bank nurses). At that time the ICU employed 14 nurses per shift (one per bed). Agency nurses cost 4 times as much as scheduled nurses. Thus, we needed to seek a balance between the numbers of scheduled and agency nurses employed through the ICU.

26. Time - Dependent Arrivals No of Arrivals/ year

27. Bed Occupancy

28. Inter-Arrival Times: • Inter-arrival times may be represented by a negative exponential distribution: Pearson’s chi-square goodness-of-fit test.

29. Service Times / Lengths of Stay We tried a wide variety of distributions as fits to these data. The best fit was the hyper-exponential distribution.

30. Model Validation – (1) Length of Stay Distribution: Hyper-exponential

31. Steady-State Equations – M/H/c • LetP0(t)represent the probability that there are no customers in the system at time t. • Letrepresent the probability that there are j customers in the system at time t, with m of these customers occupying Branch 1 amongst the c service channels available, where j = 0, 1, … and m = 0, 1, … min(j, c). Steady-State equations:

32. Steady-State Equations - (2) For j = c For For For and Summary Measures: Define: L - mean number of customers in the system Lq - mean number of customers in the queue Q(j) - Prob j customers in the system Then:

33. Cost of employing Hospital (scheduled) / Agency (Bank) Nurses Current situation: 14 hospital nurses scheduled per shift From queueing theory: P(>14 customers in system) = 0.32 At least one agency nurse is required nearly 1/3 of the time! From queueing theory, mean number of agency nurses required per shift is 1.13 Cost of hospital nurse = x Cost of agency nurse = 4x Total nursing cost per shift =14x + (1.13*4x) =18.54x 16 hospital nurses should be employed per shift

34. Typical Investigations • Combining ICU and HDU into a single unit (CCU) • Incorporation of a rule which cancels elective surgery during busy periods • Evaluate the effect of admitting long-stay (>2 days) cardiac patients • Investigate the effect of reducing duration of stay of patients from the Ward, on introduction of an ‘outreach’ programme • Investigate the effect of introducing new therapies that save lives but increase duration of stay

35. What else have we been doing in Wales? • Brief details of modelling which we are undertaking (or recently have undertaken): • MRSA v MSSA mortality in ICU unit (UHW) • Alendronates v Etidronates in Bone Mineral Density (RG) • Effects of leucodepletion of large blood transfusions on length of stay in ICU (UHW) • Relationships between cell survival and prognostic markers in chronic lymphocytic leukaemia (SoM) • Risk factors in Type II Diabetes Mellitus (GSK) • Modelling Operating Theatre Performance at UHW (NHS) • Rehabilitation Hospital (Rookwood) 8. A randomised controlled trial of the effects of a web-based PSA decision aid (Cancer Research UK)

36. Questions? Questions ? QUESTIONS ? griffiths@cardiff.ac.uk Questions? Questions?