Transcript A method for determining an emergency readmission time window

Easter 2007 in London
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
Keynote Speakers
Andrew Dillon
Nigel Edwards
Professor Mike Pidd
Professor Steve Gallivan
Professor Nick Barber
Professor Yasar Ozcan
Professor Stephen Chick
Chief Executive, National Institute of Clinical Excellence, UK
Director of Policy, NHS Confederation, UK
Associate Dean, Management School, University of Lancaster, UK
Director of the Clinical Operational Research Unit, University College London, UK
Head of Department of Practice and Policy, School of Pharmacy, London, UK
Department of Health Administration, Virginia Commonwealth University, USA
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.
Defining better measures of
emergency readmission
Eren Demir, Thierry Chaussalet, Haifeng Xie
[email protected]
www.healthcareinformatics.org.uk
Who we are
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People
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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?
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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
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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)
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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)
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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, The definition of readmission is ranging
1998)
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?
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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
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High risk group ( c1)
Low risk group (c2)
We do not know which group the patient belongs to
Community
high risk group (c1 )
low risk group (c2 )
Hospital admission
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For each patient we observe the time between
successive hospital admissions
We assume the population of readmitted patients
comprises two groups
Hospital discharge
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Modelling framework
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Mixture distribution with probability density function (pdf)
f ( x)  pf1 ( x)  (1  p) f 2 ( x)
where p is the probability of a patient being in group c1,
and f1 ( x) and f 2 ( x) are the pdf of time to admission for group
c1 and c2 respectively.
Probability of belonging to c1 and c2 can be determined
from the posterior probability expressed via the Bayes’
theorem as
pf1 ( x)
(1  p) f 2 ( x)
p(c1 | x) 
and p(c2 | x) 
f ( x)
f ( x)
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General Framework: “time window”
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Group membership of a patient with observed
time to readmission x: assign to c1 ifp(c1 | x)  p(c2 | x) ;
and to c2 otherwise.
Optimal time window can be determined by
solving
p(c1 | x)  p(c2 | x)
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Or given by the time value where
that is, where the two corresponding curves
intersect.
pf1 ( x)  (1  p) f 2 ( x)
General Framework - continued
0.012
0.006
0.008
0.010
High risk
Low risk
0.002
0.004
Optimal time window
0.000
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Given time to admission, this approach can be expressed
as a mixture distribution in terms of the rates.
Where f1 ( x) and f 2 ( x) are the pdf’s for high and low risk
readmission, often assumed to be exponential.
Probability density
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0
50
100
150
days
200
250
300
Modelling Framework: Alternative approach
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Empirical evidence suggests that risk of readmission
substantially changes over time
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High soon after discharge
Low after a period of time in the community
Community
high risk of
readmission
q10
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q12
low risk of
readmission
q20
Hospital
Assuming that all rates (q ,q and q ) are constant, time
to admission follows a Coxian phase-type distribution
10
12
20
Application to UK National Dataset
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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.
Observations of calendar years
Using time window of 28 days as currently defined we observe:
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25
20
15
10
100000
105000
Percentage of readmissions
110000
30
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Increase in number of admissions between 1998-2003
Decreasing trend in percentage of readmissions within 28 day
interval
No. of admissions
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1998
1999
2000
2001
Year
2002
2003
1998
1999
2000
2001
Year
2002
2003
Strategic Health Authorities in London
50
Effects of readmissions on varying intervals for SHA's
30
20
10
0
percentage of readmissions
40
NWL
NEL
NCL
SEL
SWL
15
20
25
days
30
35
Optimal time window for COPD patients
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Nationally, the optimal time window is computed to be
about 26 days
COPD Results for SHA’s in London
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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”
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SHA’s in London: COPD and other
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Fitted to data from the 5 SHA’s in the London area.
English Data set NWL
NCL
NEL
SEL
SWL
COPD
26.0
(0.26)
31.8 28.2
(0.30) (0.28)
28.8
26.9
18.7
(0.29) (0.27) (0.21)
Stroke
26.8
(0.193)
39.5 42.3
(0.32) (0.34)
34.0
33.5
43.5
(0.24) (0.22) (0.27)
Geriatrics
30.0
(0.22)
31.5 33.0
(0.24) (0.23)
34.0
34.0
37.0
(0.22) (0.25) (0.26)
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marked difference in the estimated optimal time window
among the regions
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Estimated time window is no longer “inline” with current 28 days
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Probability of belonging to high risk group is less variable
Summary and Future work
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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?
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More phases…but the meaning is “lost”
Alternative: Use Mixture of Erlang and 2-phase Coxian
Model Extensions
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What if mixture of two exponentials does not fit?
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More phases…OK if there looking for more than two readmission
risk groups
Hospital
phase 1
phase M
phase 2
Hospital
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Alternative: Use Mixture of Erlang and 2-phase Coxian
Hospital
phase 1
phase 2
phase M-2
phase M-1
phase M
Hospital
THANK YOU!
www.healthcareinformatics.org.uk