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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 [email protected] 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 [email protected] 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