K Silvester 190310 The maths behind a Hospital’s heart failure The maths behind a hospital’s...

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


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?


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


Flow, CostQuality

At the conference real data for the – Timeliness– Cost – Quality of care (death rate)

will be presented


The Deming Cycle

Plan

Check

DoAct


The NHS

Plan

Do


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!


Comparative Methods

What is the statistical significance of this?And what value does this add?What is the hypothesis?

The SHA performance management meetingMONTHLY


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


2nd Lesson

• ‘Assumptions are the things we don’t know we are making’

– Changing the mindset

• Act differently!


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


Av. Demand > Av. Capacity

For model go to www.steyn.org.uk/models/demand analysis.xls



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




If av. Demand = av. Capacity, variation mismatch = queue

time

Demand Capacity

Queue

Can’t pass unused capacity forward to next week


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


3rd Lesson

• The Flaw of Averages – NHS Plans are based on Averages

• Plan capacity to meet variation in demand


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




Erlang

20 40 80 10060 % utilisation

Service Failure:Waiting or Defaults


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


What have we achieved?March 2010

Check

Act

A&E performance Daily


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


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


Re-Run the NHS

1 2 3 4 5

Computer Model Demonstration

Go to www.steyn.org.uk/models/patflow.ppt



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

K Silvester 190310 The maths behind a Hospital’s heart failure The maths behind a hospital’s...

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