Transcript Application of phase-type renewal models and queueing

Interpretation of outputs
Health and Social Care Modelling Group
University of Westminster, London
Outline
Following the sequence of FLoSC reports
LoS – General Info
LoS – Summary Info
LoS – Fitted Results
Cost – General Info
Cost – Forecast Result
LoS – Technical Info
FLoSC: Report - LoS – General Info
First FLoSC summarises the data, after some basic
cleansing

FLoSC deletes records of patients moving from NC to RC
FLoSC: Report - LoS – Summary Info (1)
FLoSC provides a summary frequency table
FLoSC: Report - LoS – Summary Info (2)
FLoSC provides summary statistics on length-of-stay
(mean, standard deviation, etc), stratified by type of care
and by gender
FLoSC: Report - LoS – Summary Info (3)
■ Histograms (should) confirm the “exponential” shape of the
LoS distribution
The time labels are actually interval mid-points
LOS in nursing care
500
450
400
Number of residents
•
350
300
All
250
Female
200
Male
150
100
50
0
100
300
500
700
900
Time (days)
1100
1300
1500
1700
FLoSC: Report - LoS – Summary Info (4)
■ The table at the bottom summarises
the movement of residents
RC
NC
discharge
FLoSC: Report - LoS – Fitted Results (1)
•
•
•
More homogeneous group in RC than
in NC
High mortality in the first few months
in NC
Once past the early phase in NC,
residents “behave” like in RC
FLoSC: Report - LoS – Fitted Results (2)
Survival curve for residential care
1
0.9
Survival probability
0.8
0.7
Observed
0.6
Upper CI
0.5
Lower CI
0.4
Fitted
0.3
0.2
0.1
0
0
500
1000
1500
2000
2500
3000
Time (days)
•
•
Very good fit to data
Exponential shape
3500
4000
FLoSC: Report - LoS – Fitted Results (3)
Survival curve for nursing care
1
0.9
Survival probability
0.8
0.7
Observed
0.6
Upper CI
0.5
Lower CI
0.4
Fitted
0.3
0.2
0.1
0
0
500
1000
1500
2000
2500
3000
3500
4000
Time (days)
•
•
•
Very good fit to data
“Exponential” shape
Much sharper early decline captured
by the mixture of two exponentials
FLoSC: Report - Cost – General Info (1)
First FLoSC summarises the number of residents in the
care system (RC and NC) on the last date of the data
availability period (7 Sep 2007)
FLoSC: Report - Cost – General Info (2)
FLoSC provides other LoS statistics on those in care at
the last date of the data availability period
FLoSC: Report – Cost – Forecast Result (1)
First FLoSC summarises your cost input data
FLoSC: Report – Cost – Forecast Result (2)
Predict cost of known commitments quarterly

Known commitment: residents already in system
Estimated cost
4000
Estimated cost (thousands)
Costs amount to nearly
£7.5m to the end of the
current financial year (1
Apr 2008), and almost
£11m for the following
financial year
3500
3000
2500
2000
1500
1000
500
0
present to 200710-01
2007-10-01 to
2008-01-01
2008-01-01 to
2008-04-01
2008-04-01 to
2008-07-01
2008-07-01 to
2008-10-01
2008-10-01 to
2009-01-01
2009-01-01 to
2009-04-01
FLoSC: Report – Cost – Forecast Result (3)
Costs are also broken down by type of care
Estimated cost by type of care
2000
Estimated Cost (thousands)
1800
1600
1400
1200
RC
1000
NC
800
600
400
200
0
present to 2007- 2007-10-01 to
10-01
2008-01-01
2008-01-01 to
2008-04-01
2008-04-01 to
2008-07-01
2008-07-01 to
2008-10-01
2008-10-01 to
2009-01-01
2009-01-01 to
2009-04-01
FLoSC: Report - LoS – Technical Info
These are the parameters
used to derive
information on residents’
movements and costs
forecasts
THANK YOU
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