Easter 2007 in London

Keynote Speakers

Andrew Dillon Chief Executive, National Institute of Clinical Excellence, UK

Nigel Edwards Director of Policy, NHS Confederation, UK Professor Mike Pidd Associate Dean, Management School, University of Lancaster, UK

Professor Steve Gallivan Director of the Clinical Operational Research Unit, University College London, UK

Professor Nick Barber Head of Department of Practice and Policy, School of Pharmacy, London, UK

Professor Yasar Ozcan Department of Health Administration, Virginia Commonwealth University, USA

Professor Stephen Chick INSEAD, Fontainebleau, France

Call for Papers

We invite researchers in all relevant methodologies and problem domains to submit abstracts of 300-500 words to Lucy Nye at Lucy.Nye@ima.org.uk by 1 December 2006. Authors of accepted abstracts will be notified by 1 January 2007. Authors should indicate whether they wish to make an oral or a poster presentation. Poster presentations are particularly welcome as they stimulate discussion and feedback. We are also planning a special poster presentation session for PhD students to show their work in progress. Selected papers presented at the conference (whether orally or as a poster) will be published in the Springer journal Health Care Management Science.

THE INSTITUTE OF MATHEMATICS AND ITS APPLICATIONS

FIFTH INTERNATIONAL CONFERENCE ON

QUANTITATIVE MODELLING IN THE MANAGEMENT OF HEALTH CARE

http://www.healthcareinformatics.org.uk/qmmhealth2007 will be held at Goodenough College, central London on 2nd - 4th April 2007

Defining better measures of emergency readmission

Eren Demir, Thierry Chaussalet, Haifeng Xie chausst@wmin.ac.uk www.healthcareinformatics.org.uk

Who we are

People A bunch of academic staff including Christos Vasilakis A research fellow: Haifeng Xie A visiting professor (clinician): Peter Millard (Nosokinetics News) Four PhD research students including Eren Demir, Brijesh Patel and

Anthony Codrington-Virtue Research collaborators in and outside the UK and academia

What do we do? Application of Decision Support, Simulation, and Data Mining applied

to the process of care Problem domain: Length of stay and cost modelling in long-term

care, geriatric services; accident and emergency services Techniques: Markov/semi-Markov models, data mining, queuing

networks, simulation

Outline of presentation

Definition(s) emergency readmission. The importance of emergency readmission for

the National Health Service (NHS). A method for determining an appropriate time

window to classify a readmission as critical readmission.

Application of the methodology to the UK national dataset.

Discussions and Future Work.

Emergency Readmission (ER)

High level of emergency or unplanned (i.e. not scheduled) readmission is potentially associated with poor patient care“I take my car into a garage; if it needs to go back in a short time then that's obviously because they didn't do a good job“

(Clarke, 2003) Frequent readmissions are highly costly Readmission rate is an indicator in the performance rating

framework for NHS hospitals in the UK Currently the NHS defines readmission as an emergency or

unplanned admission (department) within 28 days following discharge

Lack of consensus in the literature on the appropriate choice of time interval in defining readmission.

Clarke, A. (2003). Readmission to hospital: a measure of quality of outcome. British Medical Journal 13, 10-11.

Definition of ER from different sources

Author Definition of readmission

(Anderson and Steinberg, 1984)

Readmission occurred when a patient was discharged from an acute care hospital within 60 days of discharge.

(Brown and Gray, 1998)

The definition of readmission is ranging from 2 weeks, three months, six months or one year from index admission.

(Reed et al., 1991)

Readmission to the hospital soon after discharge within 14 days

(Williams and Fitton, 1998)

Unplanned readmission within 28 days after a discharge.

Justifying a 28 days interval?

28 day interval has been justified by constructing a graphical output for the total number of readmissions (Sibbritt, 1995)

Each graph shows an exponential or lognormal shaped distribution

Justification relied solely on visual inspection Too crude and does not account of variations

Modelling framework

For each patient we observe the time between successive hospital admissions

We assume the population of readmitted patients comprises two groups High risk group ( ) Low risk group ( )

We do not know which group the patient belongs to

1c

2c

1( )c

2( )c

Community

high risk group

low risk group

Hosp

ital

dis

charg

e

Hosp

ital

adm

issi

on

Mixture distribution with probability density function (pdf)

1 2( ) ( ) (1 ) ( )f x pf x p f x

where is the probability of a patient being in group , and and are the pdf of time to admission for group

and respectively.

Probability of belonging to and can be determined from the posterior probability expressed via the Bayes’ theorem as

p 1c1( )f x 2 ( )f x

1c 2c

1c 2c

1 21 2

( ) (1 ) ( )( | ) and ( | )

( ) ( )

pf x p f xp c x p c x

f x f x

Modelling framework

General Framework: “time window”

Group membership of a patient with observed time to readmission : assign to if ; and to otherwise.

Optimal time window can be determined by solving

Or given by the time value where

that is, where the two corresponding curves intersect.

x1c 1 2( | ) ( | )p c x p c x

2c

1 2( ) (1 ) ( )pf x p f x

1 2( | ) ( | )p c x p c x

Given time to admission, this approach can be expressed as a mixture distribution in terms of the rates.

Where and are the pdf’s for high and low risk readmission, often assumed to be exponential.

1( )f x 2 ( )f x

General Framework - continued

0 50 100 150 200 250 300

0.0

00

0.0

02

0.0

04

0.0

06

0.0

08

0.0

10

0.0

12

days

Pro

ba

bili

ty d

en

sity

High riskLow risk

Optimal time window

Modelling Framework: Alternative approach

Empirical evidence suggests that risk of readmission substantially changes over time High soon after discharge Low after a period of time in the community

Assuming that all rates ( ) are constant, time to admission follows a Coxian phase-type distribution

10 12 20, and q q q

high risk of readmission

low risk of readmission

Community

Hospital

12q

10q 20q

Application to UK National Dataset

National dataset - Hospital Episode Statistics (HES) Admissions, Discharges; Geographical, Clinical

variables Dataset ranges from 1997 – 2004 (80 million records)

HES captures all the consultant episodes of a patient. First we focus our study on chronic obstructive pulmonary

diseases (COPD), one of the leading causes of early readmission

962,656 episodes from patients who had the primary diagnosis code corresponding to COPD (J40-J44)

After data cleansing process, a set of 696,911 completed spells were derived.

Using time window of 28 days as currently defined we observe: Increase in number of admissions between 1998-2003 Decreasing trend in percentage of readmissions within 28 day

interval

1998 1999 2000 2001 2002 2003

10

00

00

10

50

00

11

00

00

Year

No

. of a

dm

issi

on

s

1998 1999 2000 2001 2002 2003

10

15

20

25

30

Year

Pe

rce

nta

ge

of r

ea

dm

issi

on

s

Observations of calendar years

Strategic Health Authorities in London

15 20 25 30 35

01

02

03

04

05

0

Effects of readmissions on varying intervals for SHA's

days

pe

rce

nta

ge

of r

ea

dm

issi

on

s

NWLNELNCLSELSWL

NWLNELNCLSELSWL

NWLNELNCLSELSWL

Optimal time window for COPD patients

Nationally, the optimal time window is computed to be about 26 days

COPD Results for SHA’s in London

Fitted to COPD data from the 5 SHA’s in the London area.

Marked difference in the estimated optimal time window among the regions. Estimated time window is inline with the current 28 day interval for three out five SHA’s Additional information: Probability of belonging to high risk group can be used as alternative emergency readmission “indicator”

SHA’s in London: COPD and other

Fitted to data from the 5 SHA’s in the London area.

Again marked difference in the estimated optimal time window among the regions Estimated time window is no longer “inline” with current 28 days

Probability of belonging to high risk group is less variable

English Data set NWL NCL NEL SEL SWL

COPD26.0

(0.26)31.8

(0.30)28.2

(0.28)28.8

(0.29)26.9

(0.27)18.7

(0.21)

Stroke26.8

(0.193)39.5

(0.32)42.3

(0.34)34.0

(0.24)33.5

(0.22)43.5

(0.27)

Geriatrics30.0

(0.22)31.5

(0.24)33.0

(0.23)34.0

(0.22)34.0

(0.25)37.0

(0.26)

Summary and Future work

We developed a simple modelling approach to determining an “optimal” readmission time window

The approach takes account of variations across diseases, regions, etc.

Suggest alternative indicators: “high risk” probability The measures are “easy” to calculate More work needed test these indicators What do we do when mixture of two-phase Coxian do

not fit? More phases…but the meaning is “lost” Alternative: Use Mixture of Erlang and 2-phase Coxian

Model Extensions

What if mixture of two exponentials does not fit? More phases…OK if there looking for more than two readmission

risk groups

Alternative: Use Mixture of Erlang and 2-phase Coxian

phase 1

Hospital

phase 2 phase MHospital

phase 1 phase M-2 phase M-1 phase M

Hospital

Hospital phase 2

THANK YOU!

www.healthcareinformatics.org.uk