bahc 510 ltc planning
DESCRIPTION
BAHC 510 LTC Planning. Topics. LTC Capacity Planning Objectives Approaches LBH Deterministic Model Parameter Estimation Simulation Model Concept Data Optimization Comparisons Queuing Models and Capacity Planning What they are Why use them?. LBH Planning Case. - PowerPoint PPT PresentationTRANSCRIPT
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BAHC 510LTC Planning
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Topics LTC Capacity Planning
Objectives Approaches
• LBH Deterministic Model– Parameter Estimation
• Simulation Model– Concept– Data– Optimization
Comparisons Queuing Models and Capacity Planning
What they are Why use them?
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LBH Planning Case
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Simulation Based Planning and Survival
Analysis
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Overview
Goal: Develop a model to support long term care capacity planning decisions Model must forecast the annual bed requirements 2020
• Regional level• Facility level
Must allow sensitivity and “What if?” analysis This is a fundamental planning problem faced by all health system
planners Standard approach – Ratio based planning
Ratios of population 75 and older Usually between 75-90 beds per 1000 aged 75 or older
Our approach – Service criteria based planning Methods - simulation model, survival analysis, goal seeking Determine capacity levels to meet a service level standard
• For example 85% of clients wait less than 30 days for admission
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Model Overview
Tradeoff – excess capacity vs. long waits
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Model Inputs Demographics from BC Stats projections Arrival rate by age and gender in each LHA Historical length of stay by age and gender
In 2003 a significant change was made to admissions criteria for complex care that allowed only clients of higher acuity into care
This causes complications in models because we need different LOS models for pre-2003 clients.
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Simulation Logic
Preload clients at start of planning horizon Sample appropriate remaining lifetime distributions
Generate a case from the appropriate inter-arrival time distribution Allocate age and gender proportionally
Generate LOS from appropriate distribution Adjust LOS if desired Enter case into queue When case exits queue:
Record time in queue Record if service criterion has been met
Occupy “bed” for determined LOS Leave At the end of each year of simulation time:
Calculate the percentage of people served within the criteria and record
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Simulation Logic Schematic
Clients enter queue and then enter
care
Clients exit care
Create pre-load clients and waitlist
clients
Choose LOS
Create new clients Choose LOS Adjust LOS
Survival curves
Adjustment factors from
Excel
Clients loaded before simulation starts
Clients created as simulation progresses
Model operation and statistic collection
Pop’n estimatesand rates
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Arrival Rates Usually expressed as a rate per 1000 in a
particular age and gender group Relevant data may not be available!
In LBH setting, it is difficult to determine true arrival rate since arrivals are triggered by departures and so pure arrival process is not visible.
At VIHA we could only obtain a snapshot of the arrival list at a date.
We can do the best we can and then use sensitivity analysis to measure impact of arrival rate assumptions on capacity.
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Analyzing Length of Stay A key driver in capacity planning Data is censored; many clients remain in the system at the
end of the data period Ignoring censored clients seriously biases the estimates for LOS Censored cases tend to be those with long lengths of stay
Survival analysis takes into account clients still in the system when fitting LOS distributions A statistical technique for estimating LOS distributions accounting
for censored data. We will need whole distribution to generate LOS in simulation
model. Fit parametric models stratified by region with age group and
gender as covariates (Weibull).
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To examine the relationship between LOS and the age at admission
: random error with normal distribution : regression coefficients, to be estimated
from the data Data: All discharges from LB Home for the Aged –
1978 to 2008
Why not linear regression?
AgeLOS 10
10 ,
ID ResidentGende
rBirth Date
Admission
Discharge Status
1 **** **** Male 03-13-30 09-24-84 11-13-99DECEASED
2 **** **** Female 01-31-43 05-21-92 10-31-08Active
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NCSS Output
-2000.0
0.0
2000.0
4000.0
6000.0
-4.0 -2.0 0.0 2.0 4.0
Normal Probability Plot of Residuals of LOS
Expected Normals
Res
idua
ls o
f LO
S
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NCSS Output
0.0
2000.0
4000.0
6000.0
8000.0
50.0 65.0 80.0 95.0 110.0
LOS vs Age
Age
LOS
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Why Survival Analysis Linear regression is problematic because data is
skewed and censored Survival analysis takes into account clients still in
the system when fitting LOS distributions Parametric models provide the “whole distribution” so
that we can generate LOS in the simulation model We use models with age group, gender and region as
covariates (or strata) Questions
• Which models?• Interpretation?
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Sample Data and Censoring
Nov-03
Jan-0
4
Mar-04
May-04
Jul-0
4
Sep-04
Nov-04
Jan-0
5
Mar-05
May-05
Jul-0
5
Sep-05
Nov-05
Jan-0
6
Mar-06
May-06
Jul-0
6
Sep-06
Nov-06
Jan-0
7
Mar-07
Calendar Time
Clie
nts
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Kaplan-Meier CurvesAge_ Gr oup=85+
0. 00
0. 25
0. 50
0. 75
1. 00
LOS_year s
0. 0 0. 5 1. 0 1. 5 2. 0 2. 5 3. 0 3. 5 4. 0
STRATA: Gender =F Censor ed Gender =F Gender =M Censor ed Gender =M
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Why does this matter?
Length of Stay (years)
1.00
0.75
1.5 2.0 2.5 3.0 3.5 4.00.23 1.18
0.50
0.25
0.00
0.0 0.5 1.0
Median
Uncensored
CensoredProbability of Survival
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Survival Distributions In order to simulate LOS, a distribution is required Several distributions are commonly used in
survival analysis: Weibull Exponential – a special case of Weibull Gompertz, log-normal, log-logistic
Weibull is most common & was used for our simulations
Two parameters required: Shape, α Scale, β
2020
Weibull Distribution PDF and CDF
Two parameters Shape: Scale: β=1 is the exponential with mean 1/α
t
t
etF
ettf
1
1
)!1()(
)]11()21([dev std
)11(mean
0
1
22
xordtetx tx
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Various Weibull Distributions
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Fitting Parameters Finding a suitable model involves
regression Ordinary regression problematic
• Length of stay times are not normally distributed• Data has large percentage of right censoring
Models are fit by maximizing the likelihood function When censoring exists this becomes the product of the likelihood for
each type of data (censored & uncensored)
Requires analyst involvement!
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Type III Analysis of Effects WaldEffect DF Chi-Square Pr > ChiSq Agroup 4 33.9101 <.0001Ggroup 1 156.4401 <.0001LHA 11 66.7901 <.0001 Analysis of Parameter Estimates Standard 95% Confidence Chi-Parameter DF Estimate Error Limits Square Pr > ChiSq Intercept 1 5.4206 0.3097 4.8136 6.0275 306.42 <.0001Agroup 0 1 0.0530 0.1819 -0.3035 0.4096 0.08 0.7706Agroup 1 1 0.1909 0.1351 -0.0739 0.4558 2.00 0.1576Agroup 2 1 0.2362 0.0837 0.0721 0.4002 7.96 0.0048Agroup 3 1 0.2822 0.0503 0.1837 0.3807 31.50 <.0001Agroup 4 0 0.0000 . . . . .Ggroup 0 1 0.5936 0.0475 0.5006 0.6866 156.44 <.0001Ggroup 1 0 0.0000 . . . . .LHA 061 1 0.6501 0.3090 0.0444 1.2558 4.43 0.0354LHA 062 1 0.7035 0.3283 0.0601 1.3469 4.59 0.0321LHA 063 1 0.9557 0.3161 0.3362 1.5752 9.14 0.0025LHA 064 1 0.2955 0.3415 -0.3738 0.9648 0.75 0.3868LHA 065 1 0.2329 0.3194 -0.3930 0.8588 0.53 0.4658LHA 067 1 0.2346 0.3262 -0.4047 0.8740 0.52 0.4720LHA 068 1 0.6631 0.3137 0.0483 1.2780 4.47 0.0345LHA 069 1 0.6593 0.3165 0.0391 1.2795 4.34 0.0372LHA 070 1 0.6176 0.3271 -0.0234 1.2587 3.57 0.0590LHA 071 1 0.5475 0.3174 -0.0746 1.1697 2.98 0.0846LHA 072 1 0.3302 0.3281 -0.3128 0.9733 1.01 0.3141LHA 085 0 0.0000 . . . . .Scale 1 1.4992 0.0193 1.4618 1.5375Weibull Shape 1 0.6670 0.0086 0.6504 0.6841
SAS Output
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Interpretation of coefficients
39.76433.1*73.574)5.1(1*574.73 mean 0.671/1.50
1/SCALE574.13
exp(6.35)0.65) 0 0.28 exp(5.43
LHA061) Ggroup1 Agroup3 ept exp(Interc
For example, the estimated parameters for males in LHA061 who are 75-84 years old would be determined as follows:
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More on coefficient interpretation A female of the same age and in the same
location as a male will have a mean time in long term care that is exp(0.59) = 1.80 times greater than that of a male
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Using Simulation to Determine Capacities
A simulation optimization approach is adopted
Capacities are determined by iteratively running the simulation and adjusting resource levels Stopping conditions are determined by the service
criteria The service criteria we used was that 85% of
clients are placed within 30 days.
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Bisection Search
0
Ser
vice
Lev
el
100%
85%
# Beds
Upper Bound:
Lower Bound:
1000 0
# Beds to choose: 500
1000 500
750 500 750
625
750 625
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Simultaneous Search
0
Ser
vice
Lev
el
100%
85%
Year2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020
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Some Plans
2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020
Year
Res
ourc
e S
ize Base case
LOS increased
LOS decreased
Arrival rate increased
LOS down, arrival rate up
Bed
s
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Comparison to Ratio Based Approachin two regions
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Comparison of Service Based Approach to Ratio Approach: two metrics
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Comparison of Simulation Approach to LBH Approach
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Comparison to other methods
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Some Observations These are important and costly decisions
In depth analysis is required Ratio based plans and service base plans differ
Improved ratios do not give reliable service levels We recommend using simulation optimization to
determine “how many beds”. Managers should not relax acuity standards if
there is excess capacity Will extend LOS and invalidate planning assumptions Capacity is usually added in discrete blocks which
necessitates some further analyses