Post on 18-Jan-2016
K Silvester 190310The maths behind a Hospital’s heart failure
The maths behind a hospital’s heart failure.
Kate Silvester BSc MBA FRCOphthProgramme Lead for the Flow, Cost, Quality programme
The Health Foundation,
With thanks to Richard Steyn MS FRCSEd(C-Th) FIMCRCSEd MRCGP
Thoracic surgeon Heart Of England NHS Foundation Trust
K Silvester 190310The maths behind a Hospital’s heart failure
Objectives
• Run the NHS
• Back to reality!– What is going on in a hospital?– Learning in the real world
• Deming Cycle• Lessons
• Re-run the NHS
• A role for modelling?
K Silvester 190310The maths behind a Hospital’s heart failure
Run the NHS
1 2 3 4 5
Computer Model Demonstration
Go to www.steyn.org.uk/models/patflow.ppt
You can’t use these models for real life data
K Silvester 190310The maths behind a Hospital’s heart failure
Flow, CostQuality
At the conference real data for the – Timeliness– Cost – Quality of care (death rate)
will be presented
K Silvester 190310The maths behind a Hospital’s heart failure
The Deming Cycle
Plan
Check
DoAct
K Silvester 190310The maths behind a Hospital’s heart failure
The NHS
Plan
Do
K Silvester 190310The maths behind a Hospital’s heart failure
1st Lesson
• ‘A system is only as good as its feedback’– No feedback– Slow feedback– Faulty feedback
• Data distortion• Interpretation
– comparative v continuous statistics
• Check!
K Silvester 190310The maths behind a Hospital’s heart failure
Comparative Methods
What is the statistical significance of this?And what value does this add?What is the hypothesis?
The SHA performance management meetingMONTHLY
K Silvester 190310The maths behind a Hospital’s heart failure
Emergency & Elective Admissions -
8000
9000
10000
11000
12000
13000
14000
15000
16000
17000
05/0
4/20
09
12/0
4/20
09
19/0
4/20
09
26/0
4/20
09
03/0
5/20
09
10/0
5/20
09
17/0
5/20
09
24/0
5/20
09
31/0
5/20
09
07/0
6/20
09
14/0
6/20
09
21/0
6/20
09
28/0
6/20
09
05/0
7/20
09
12/0
7/20
09
19/0
7/20
09
26/0
7/20
09
02/0
8/20
09
09/0
8/20
09
16/0
8/20
09
23/0
8/20
09
30/0
8/20
09
06/0
9/20
09
13/0
9/20
09
20/0
9/20
09
27/0
9/20
09
04/1
0/20
09
11/1
0/20
09
18/1
0/20
09
25/1
0/20
09
01/1
1/20
09
08/1
1/20
09
15/1
1/20
09
22/1
1/20
09
29/1
1/20
09
06/1
2/20
09
13/1
2/20
09
20/1
2/20
09
27/1
2/20
09
03/0
1/20
10
10/0
1/20
10
17/0
1/20
10
24/0
1/20
10
31/0
1/20
10
07/0
2/20
10
14/0
2/20
10
21/0
2/20
10
28/0
2/20
10
07/0
3/20
10
14/0
3/20
10
21/0
3/20
10
28/0
3/20
10
Emergency
Elective (Voluntary Data Item)
Continuous methods
Is this statistically
significant?!!!!
Sept 09
Real life Results: SHA Sitrep reportA&E Total Attendances and % Seen Within 4 Hours
95%
95%
96%
96%
97%
97%
98%
98%
99%
99%
100%
05/0
4/20
09
12/0
4/20
09
19/0
4/20
09
26/0
4/20
09
03/0
5/20
09
10/0
5/20
09
17/0
5/20
09
24/0
5/20
09
31/0
5/20
09
07/0
6/20
09
14/0
6/20
09
21/0
6/20
09
28/0
6/20
09
05/0
7/20
09
12/0
7/20
09
19/0
7/20
09
26/0
7/20
09
02/0
8/20
09
09/0
8/20
09
16/0
8/20
09
23/0
8/20
09
30/0
8/20
09
06/0
9/20
09
13/0
9/20
09
20/0
9/20
09
27/0
9/20
09
04/1
0/20
09
11/1
0/20
09
18/1
0/20
09
25/1
0/20
09
01/1
1/20
09
08/1
1/20
09
15/1
1/20
09
22/1
1/20
09
29/1
1/20
09
06/1
2/20
09
13/1
2/20
09
20/1
2/20
09
27/1
2/20
09
03/0
1/20
10
10/0
1/20
10
17/0
1/20
10
24/0
1/20
10
31/0
1/20
10
07/0
2/20
10
14/0
2/20
10
21/0
2/20
10
28/0
2/20
10
07/0
3/20
10
14/0
3/20
10
21/0
3/20
10
28/0
3/20
10
% S
een
Wit
hin
4 H
ou
rs
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
50000
To
tal
Att
end
ance
s
% Seen Within 4 Hours
Target < 4Hrs = 98%
Total Attendances
K Silvester 190310The maths behind a Hospital’s heart failure
2nd Lesson
• ‘Assumptions are the things we don’t know we are making’
– Changing the mindset
• Act differently!
K Silvester 190310The maths behind a Hospital’s heart failure
Mental Model
Queues = Bottlenecks
= more capacity
& reduce demand
= demand management
Heart failure• Irregular pulse• Oedema• Reduce variation
– Steady the pulse
• Drain the backlog– Get the patient to pee
K Silvester 190310The maths behind a Hospital’s heart failure
Av. Demand > Av. Capacity
For model go to www.steyn.org.uk/models/demand analysis.xls
You can’t use these models for real life data
K Silvester 190310The maths behind a Hospital’s heart failure
Variation Mismatch
0
10
20
30
40
50
60
70
80
90
100
1 21 41 61 81 101
121
141
161
181
201
week
wai
ting
0
5
10
15
20
25
30
35
40
45
50
dem
and/
was
te
demand waiting list waste
For model go to www.steyn.org.uk/models/demand analysis.xls
You can’t use these models for real life data
K Silvester 190310The maths behind a Hospital’s heart failure
If av. Demand = av. Capacity, variation mismatch = queue
time
Demand Capacity
Queue
Can’t pass unused capacity forward to next week
K Silvester 190310The maths behind a Hospital’s heart failure
Hospital emergency admissions & discharges Daily variation mismatch
Emergency admission and emergency discharges
0102030405060708090
2008
-11-
01
2008
-11-
05
2008
-11-
09
2008
-11-
13
2008
-11-
17
2008
-11-
21
2008
-11-
25
2008
-11-
29
2008
-12-
03
2008
-12-
07
2008
-12-
11
2008
-12-
15
2008
-12-
19
2008
-12-
23
2008
-12-
27
2008
-12-
31
2009
-01-
04
2009
-01-
08
2009
-01-
12
2009
-01-
16
2009
-01-
20
2009
-01-
24
2009
-01-
28
date
nu
mb
er o
f p
atie
nts
discharges
admissions
K Silvester 190310The maths behind a Hospital’s heart failure
3rd Lesson
• The Flaw of Averages – NHS Plans are based on Averages
• Plan capacity to meet variation in demand
K Silvester 190310The maths behind a Hospital’s heart failure
Planning the right capacity
0
10
20
30
40
50
60
70
80
90
100
1 21 41 61 81 101
121
141
161
181
201
week
wai
ting
0
5
10
15
20
25
30
35
40
45
50
dem
and/
was
te
demand waiting list waste
For model go to www.steyn.org.uk/models/demand analysis.xls
You can’t use these models for real life data
K Silvester 190310The maths behind a Hospital’s heart failure
Erlang
20 40 80 10060 % utilisation
Service Failure:Waiting or Defaults
K Silvester 190310The maths behind a Hospital’s heart failure
0
10
20
30
40
50
60
70
80
2007
-04-
0120
07-0
4-23
2007
-05-
1520
07-0
6-06
2007
-06-
2820
07-0
7-20
2007
-08-
1120
07-0
9-02
2007
-09-
2420
07-1
0-16
2007
-11-
0720
07-1
1-29
2007
-12-
2120
08-0
1-12
2008
-02-
0320
08-0
2-25
2008
-03-
1820
08-0
4-09
2008
-05-
0120
08-0
5-23
2008
-06-
1420
08-0
7-06
2008
-07-
2820
08-0
8-19
2008
-09-
1020
08-1
0-02
2008
-10-
2420
08-1
1-15
2008
-12-
0720
08-1
2-29
2009
-01-
2020
09-0
2-11
2009
-03-
0520
09-0
3-27
2009
-04-
1820
09-0
5-10
2009
-06-
0120
09-0
6-23
2009
-07-
15
Em Adms
Mean
Mean + 1sd
Mean + 2sd
All emergency admissions April 07 to July 09
K Silvester 190310The maths behind a Hospital’s heart failure
What have we achieved?March 2010
Check
Act
A&E performance Daily
K Silvester 190310The maths behind a Hospital’s heart failure
Daily A&E performance Sept 07 to 28/02/10:
The canary in the healthcare system
Daily A&E % Seen Within 4 Hours
0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
70.0%
80.0%
90.0%
100.0%
01-Sep 01-Oct 01-Nov 01-Dec 01-Jan 01-Feb 01-Mar 01-Apr 01-May 01-Jun 01-Jul 01-Aug 01-Sep 01-Oct 01-Nov 01-Dec 01-Jan 01-Feb
Community Referral hub
Closing down of 40 community beds
Opening of newHsp ward 29/11/09
X-mas and New Year
Change to the acute medical Take system Mon to Fri
Pull system At discharge Hub
A&E ‘crashes’ againWhy? Lots of outliersElective activity is trying to pick upOther contributing factors?What is happening elsewhere?
What happened here?
X-mas and New Year
K Silvester 190310The maths behind a Hospital’s heart failure
The System:
GP Hsp
Intermediate care
Community Hsp
CareHomes
Home
Death
% Attendances through A&E in <4 hours
70%
75%
80%
85%
90%
95%
100%
08/04/
2007
08/05/
2007
08/06/
2007
08/07/
2007
08/08/
2007
08/09/
2007
08/10/
2007
08/11/
2007
08/12/
2007
08/01/
2008
08/02/
2008
08/03/
2008
08/04/
2008
08/05/
2008
08/06/
2008
08/07/
2008
08/08/
2008
08/09/
2008
08/10/
2008
08/11/
2008
08/12/
2008
08/01/
2009
08/02/
2009
08/03/
2009
08/04/
2009
08/05/
2009
08/06/
2009
08/07/
2009
08/08/
2009
08/09/
2009
08/10/
2009
08/11/
2009
08/12/
2009
08/01/
2010
% in 4 Hours
Flow through A&E is a very sensitive indicator of flow through the whole system
K Silvester 190310The maths behind a Hospital’s heart failure
Re-Run the NHS
1 2 3 4 5
Computer Model Demonstration
Go to www.steyn.org.uk/models/patflow.ppt
You can’t use these models for real life data
K Silvester 190310The maths behind a Hospital’s heart failure
Summary
Plan
Check
DoAct
Access to continuous data (Statistical Process Control)Verification of ‘The Model’
Teaching principlesThe Flaw of Averages Little changes quickly
Simple to use modelsPaper + pens = Gantt charts