Re-thinking Bed management
Dr Rod Jones (ACMA) Statistical Advisor Healthcare Analysis & Forecasting Camberley, UK +(0)1276 21061 hcaf_rod@yahoo.co.uk
Re-thinking Bed Management
• • • • • • • • Randomness is very important Queuing theory is not complicated Why current bed planning is flawed Bed numbers, occupancy & turn-away Economies of scale High throughput has consequences Elective vs emergency flows Can you ‘plan’ medical bed occupancy?
Dr Rod Jones (2003) Tel: 0118 3773511
Randomness in healthcare
• Poisson randomness describes arrival events • Widely used in telecommunications, business and industry • Is the basis of queuing theory • Is the forgotten but controlling factor in most healthcare demand
Dr Rod Jones (2003) Tel: 0118 3773511
Poisson randomness
• Standard deviation equals square root of the average • Maximum variation is three times the standard deviation • But is a skewed distribution • Skew increases as size decreases
Dr Rod Jones (2003) Tel: 0118 3773511
Poisson randomness
P is o ra d me sfo a a e g a a ra o 1p rd y o s n n o n s r n v ra e rriv l te f e a
• You are expecting 1 per day but must be able to cope with 6 or 7 actual arrivals • On 37% of days your resources stand idle as there are no arrivals
4% 0 3% 5 3% 0 2% 5
re un y F qe c
2% 0 1% 5 1% 0 5 % 0 % F q ec re u n y
0 3% 7
1 3% 7
2 1% 8
3 6 %
4 2 %
5 0 %
6 0 %
Atul a rriv lsea hd y ca a a c a
Dr Rod Jones (2003) Tel: 0118 3773511
Poisson randomness
• At 5 per day need to be able to cope with 15 yet on 1% of occasions no arrivals • All outpatient referrals to consultants less than 10 per work day • Guaranteed 2 week cancer wait – almost impossible!
Randomness for an average of 5 arrivals per day
18%
16%
14%
Frequency of actual arriv als
12%
10%
8%
6%
4%
2%
0%
0
1 3%
2 8%
3
4
5
6
7
8 7%
9 4%
10 2%
11 1%
12 0%
13 0%
14 0%
Frequency 1%
14% 18%
18% 15% 10%
Dr Rod Jones (2003) Tel: 0118 3773511
Special & Common Combine
Standard deviation associated with healthcare demand
100,000 Emergency admissions Elective demand GP Referral A&E Poisson (Average^0.5)
Apparent standard deviation
10,000
1,000
100
10
1 1 10 100 1,000 10,000 100,000 1,000,000
Demand (admissions, FCE, GP referrals, A&E attendances)
Dr Rod Jones (2003) Tel: 0118 3773511
Elective demand
Total Elective Demand (ON + DC) in Surgical Specialties
22,500 22,000
Annual Demand
21,500
21,000
20,500 Poisson statistics suggests that one standard deviation should be 150, however, actual is higher than twice this value. The likelihood of deviation from the expected 'average' is high.
20,000
19,500
93
94
95
96
97
98
99
00
01
92 /
93 /
94 /
95 /
96 /
97 /
98 /
99 /
00 /
19
19
19
19
19
19
19
19
20
Dr Rod Jones (2003) Tel: 0118 3773511
20
01 /
02
Implications
• Size for financial stability - very much larger than any PCT • HRG’s - 95% have fewer than 1,000 p.a. thus unable to forecast prices • Why so much contract negotiation? • Size of A&E, bed pools, etc, etc • Not able to guarantee performance targets except with excess resources • Booked admissions initiative needs statistical support
Dr Rod Jones (2003) Tel: 0118 3773511
Queuing theory
• A.K. Erlang - line not available to next caller • Now widely used in industry
– supermarket, bank, petrol station queues, etc
• Healthcare applications
– A&E resources & waiting time – ICU beds – Turn-away experienced by any bed pool
Dr Rod Jones (2003) Tel: 0118 3773511
Turned-away or join the queue
• When arrivals exceed resources you either go elsewhere or join a queue • Hence - trolley waits, cancelled operations, borrowed beds, hidden queues • Best illustrated by plotting % occupancy vs bed pool size
Dr Rod Jones (2003) Tel: 0118 3773511
Throughput (per bed)
Dr Rod Jones (2003) Tel: 0118 3773511
Benchmarks - size
Dr Rod Jones (2003) Tel: 0118 3773511
Benchmarks – why?
Region Average Number of Acute Beds per NHS Trust 425 440 390 330 260 350 380 370 Average weighted Occupancy 80% 80% 82% 85% 87% 87% 85% 88% Average weighted Turn-away 0.8% 1.4% 2.0% 4.4% 4.7% 4.9% 5.3% 6.5%
Trent Northern South & West North Thames Anglia & Oxford West Midlands North Western South Thames
Dr Rod Jones (2003) Tel: 0118 3773511
Let’s sweat those assets
Dr Rod Jones (2003) Tel: 0118 3773511
Medical bed planning
Dr Rod Jones (2003) Tel: 0118 3773511
Medical bed planning
Dr Rod Jones (2003) Tel: 0118 3773511
Bed days
• Is a fundamental time-related unit of healthcare demand • Can be diminished by shifts to other healthcare settings and new methods • Can be converted to beds by adding the appropriate occupancy
Dr Rod Jones (2003) Tel: 0118 3773511
Is 75% day case achievable?
Specialty General Surgery
ON EM ON EM ON EM
LOS (days) 0 1
7% 8% 4% 16% 8% 9% 25% 20% 15% 18% 24% 22%
2
25% 16% 26% 13% 17% 12%
Urology
T&O
Dr Rod Jones (2003) Tel: 0118 3773511
Hidden Gain
• 0 LOS patients increase daytime occupancy leading to that part of A&E trolley waiting due to unavailable beds • 1 day LOS can potentially be treated as day case – the hidden consequence of insufficient day case resources • 2 day LOS are potential day case candidates if intensive input is available • Short stay emergency imply need for streaming of patients • The above do not save overnight beds but reduce daytime occupancy to the point that the ‘system’ (including A&E) starts to work again
Dr Rod Jones (2003) Tel: 0118 3773511
HRG-based LOS variation
HRG F82
700 600
500
This is probably as good as it gets in terms of iso-resource. Annual average LOS still varies between 2.33 to 2.75 days via variation in total beddays
Frequency
400
Average LOS = 2.5 days
300
200
100
0 0 1 2 3 4 5 6 7 8 9 10 >10
LOS (days)
Dr Rod Jones (2003) Tel: 0118 3773511
Controlling LOS
• Are the clinicians responsible?
– Studies in USA show that clinicians take on the LOS of the hospital where they work – By implication it is the ‘system’ rather than the clinician per se that is responsible – Change the system, provide the resources and the clinicians will deliver on LOS & day case rates
• All within the context of variation in LOS
– Concentrate on the system and be very clear about how the LOS distribution will change – Never measure success by average LOS always use the LOS distribution – An increase in day case rate should increase average LOS!
Dr Rod Jones (2003) Tel: 0118 3773511
Optimum efficiency
• Gain benefits of scale
– L&D hospital only has 2 bed pools – ‘surgical’ and ‘medical’
• Analyse daily occupancy by HRG to create specialty pools within the larger pool • Remove all 0 LOS patients to other settings • Make the shift to 75% DC sooner rather than later
Dr Rod Jones (2003) Tel: 0118 3773511
Hot & Cold Sites?
• Forfeits economy of scale • Elective demand is just as variable as emergency demand • Implies adequate bed provision on both sites • Ignores realities of medical bed demand • Same effect if an elective factory opens nearby
©Dr Rod Jones (2009) hcaf_rod@yahoo.co.uk
Conclusions
• Understanding randomness is important • A little bit of queuing theory goes a long way to explaining a lot of things • Some things are mathematically impossible - unfortunately they are part of your performance targets! • If planning was that easy we would all have been doing it years ago
Dr Rod Jones (2003) Tel: 0118 3773511