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PREDICTIVE MODELING OF EMERGENCY
DEPARTMENT OPERATIONS:
EFFECT OF PATIENTS’ LENGTH OF STAY ON ED
DIVERSION
ALEXANDER KOLKER, PhD
Froedtert Hospital
Milwaukee, Wisconsin
Froedtert Hospital, Milwaukee WI
• Primary teaching Hospital for MCW
• Tertiary Referral Center
• Level 1 Trauma Center for SE Wisconsin
• 433 staffed acute care beds
• 23,617 admissions/ 47,176 ED Visits
• 454,780 Outpatient Clinic Visits
• Surgeries - Inpt: 9,034/ Outpt: 5,711
PROBLEM STATEMENT:
• Froedtert Hospital ED ambulance diversion has become unacceptably high
due to no ED beds (average ~21% of time in 2007)
•There are two big groups of patients:
(i) admitted to the hospital, and
(ii) treated, stabilized and discharged home
• Among factors that affect ED diversion patients’ Length of Stay (LOS) in ED is
one of most significant one.
The Goal of this work was:
• develop a methodology that could quantitatively analyze and
predict an impact of patients’ LOS on ED diversion (both for
admitted and discharged home patients’ groups).
• identify the maximum LOS limit that will result in significant
reduction or elimination ED diversion.
STEPS THAT HAVE BEEN PERFORMED:
• Collected data on
- patients arrival in ED: day of week and time of day
- mode of transportation: walk-ins or ambulance
- discharge disposition: home / expired or admitted in the Hospital
• Analyzed LOS distribution and its functional approximation for
(i) discharged home, and
(ii) admitted patients
• Developed an ED Process Model aimed at modeling different scenarios
of LOS upper limits that will result in significant reduction (or elimination)
ED diversion
• Summarized the basics of modeling methodology: What did we learn ?
What is the LOS distribution for admitted and discharged home patients ?
181512963
Median
Mean
5.04.94.84.74.64.54.44.3
1st Quartile 3.3833
Median 4.4667
3rd Quartile 5.9333
Maximum 20.4333
4.7761 4.9548
4.3667 4.5667
A-Squared 32.74
P-Value < 0.005
Mean 4.8654
StDev 2.1305
Variance 4.5389
Skewness 1.22735
Kurtosis 3.14050
N 2185
Minimum 0.4667
Anderson-Darling Normality Test
95% Confidence Interval for Mean
95% Confidence Interval for Median
24.521.017.514.010.57.03.50.0
Median
Mean
3.23.13.02.92.82.72.6
1st Quartile 1.6167
Median 2.6667
3rd Quartile 4.2000
Maximum 25.8167
3.1039 3.2099
2.6000 2.7167
A-Squared 146.60
P-Value < 0.005
Mean 3.1569
StDev 2.1225
Variance 4.5051
Skewness 1.84310
Kurtosis 8.14424
N 6155
Minimum 0.0667
Anderson-Darling Normality Test
95% Confidence Interval for Mean
95% Confidence Interval for Median
95% Confidence Intervals
Summary for LOS admitted, hrs
95% Confidence Intervals
Summary for LOS home, hrs
Total number for Jan 07: 1133
Feb 07:1052
Total number for Jan 07: 3255
Feb 07: 2971
DO THE SAME DAYS OF WEEK FOR DIFFERENT WEEKS HAVE A SIMILAR
ARRIVAL PATTERN ?
Take away:
Same days for different weeks have very different patient arrival pattern.
Therefore arrivals for all Mondays, all Tuesdays, and so on should not be combined
A dm T ime_1 /1 /2 0 0 7
Frequency
2400230022002100200019001800170016001500140013001200110010009008007006005004003002001000
8
6
4
2
0
A dm T ime_1 /8 /2 0 0 7
Frequency
2400230022002100200019001800170016001500140013001200110010009008007006005004003002001000
12
9
6
3
0
6
2
9
2
4
6
4
7
5
6
3
9
4
7
2
4
2
0
2
8
3
4
2
6
11
5
777
8
7
9
7
9
101010
12
6
222
0
3
2
4
1
Monday Adm Time_1/1/2007
Monday Adm Time_1/8/2007
ED structure and in-patient units
The high-level layout of
the entire hospital system:
Arrival pattern
wk, DOW, time
Mode of transp
Disposition
ED simulation model layout
Simulation
Digital clock
• ED diversion (closure) is declared when ED patients’
census reaches ED beds capacity.
• ED stays in diversion until some beds become available
when patients are moved out of ED (discharged home,
expired, or admitted as in-patients).
• % ED diversion = % time ED is at full capacity
• upper LOS limits (simulation parameters) are imposed on
the baseline original LOS distributions:
LOS higher than the limiting value is NOT allowed in the
simulation run.
Baseline LOS distributions should be recalculated as
functions of the upper LOS limits.
MODELING APPROACH
Take-away:
MODELING APPROACH (cont.)
Given original distribution density and the limiting value of the random variable T,
what is the conditional distribution of the restricted random variable T ?
121086420
500
480
460
440
420
400
380
360
340
320
300
280
260
240
220
200
180
160
140
120
100
80
60
40
20
0
LOS, Hrs
Frequency
3-Parameter Gamma
Distributionof LOS_ home, Hrs
Imposed LOS limit 6 hrs
121086420
500
480
460
440
420
400
380
360
340
320
300
280
260
240
220
200
180
160
140
120
100
80
60
40
20
0
LOS, Hrs
Frequency
Re-calculatedboundeddistributionof LOS_ home, Hrs
dTTf
Tf
LOSTf
LOS
original
original
new


0
)(
)(
),(
LOSTif,0)( newTf
T, Hrs
LO
T, Hrs
Original unbounded distribution New re-calculated distribution
origTf )(
LOS limit
ED Simulation Run Example
Diversion time
& DOW
Diverted
Ambulance
Patients discharged Home
Patient admitted to the Hospital
• ED diversion could be negligible (~0.5%) if patients discharged home stay NOT more than 5
hrs and admitted patients stay NOT more than 6 hrs.
• Relaxing of these LOS limits results in low digits % diversion that still could be acceptable
SIMULATION SUMMARY & MODEL VALIDATION
Low single
digits
diversion
~4%24 hrs5 hrs3
Low single
digits
diversion
~ 2%6 hrs6 hrs2
Practically NO
diversion
~ 0.5 %6 hrs
Currently
24% with
LOS more
than 6 hrs;
5 hrs
Currently 17%
with LOS more
than 5 hrs;
1
Actual ED
diversion
was 21.5%
23.7%24 hrs24 hrsCurrent, 07
(Baseline)
NotePredicted ED
diversion, %
LOS for
admitted NOT
more than
LOS for discharged
home NOT more than
Scenario/option
Take-away:
Baseline ED census, January 2007
LOS <= 24 hrs. Capacity 30 beds.
Diversion 23.7 %
0
5
10
15
20
25
30
35
0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 384 408 432 456 480 504 528 552 576 600 624 648 672 696 720 744
time, hrs
EDcensus
ED census:
LOS_home<=6 hrs, LOS_adm<=6 hrs. Capacity 30 beds.
Diversion 1.8%
0
5
10
15
20
25
30
35
0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 384 408 432 456 480 504 528 552 576 600 624 648 672 696 720 744
time, hrs
census
Diversion is declared when ED census hits capacity limit.
The longer the census stays at capacity limit the higher is diversion %
What other combinations of upper limits LOS are possible to get low
single digits % ED diversion ?
Performed full factorial DOE with two factors (ULOS_home and ULOS_adm) at 6 levels each
using simulated % diversion as a response function.
Div %
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
2 45 6 8 1 81 0
1 2
1 21 8 1 08
6 ULOS_adm, hrs52 4ULOS_home, hrs
Surface Plot of Div % vs ULOS_adm, ULOS_home
We want to be here
ULOS_adm, hrs
MeanpredictedDiv%
241210865
24.0
22.5
21.0
19.5
18.0
16.5
15.0
13.5
12.0
10.5
9.0
7.5
6.0
4.5
3.0
1.5
0.0
5
6
8
10
12
24
ULOS_home, hrs
Simulated Div % as a function of upper LOS limits, hrs
What other combinations of upper limits LOS are possible to get low
single digits % ED diversion ?
Low single digits
% diversion
Performed full factorial DOE with two factors (ULOS_home and ULOS_adm) at 6 levels each
using simulated % diversion as a response function.
% of patients that stay longer than the upper LOS limit
242220181614121086420
USL = 6 hrs
LSL *
Target *
USL 6
Sample Mean 4.86544
Sample N 2185
Location 1.49891
Scale 0.246641
Process Data
% < LSL *
% > USL 24.03
% Total 24.03
Observed Performance
24.521.017.514.010.57.03.50.0
USL = 5 hrs
LSL *
Target *
USL 5
Sample Mean 3.1569
Sample N 6155
Location 0.955823
Scale 0.39521
Process Data
% < LSL *
% > USL 16.83
% Total 16.83
Observed Performance
LOS_adm Jan and Feb, hrs
C alculations Based on Loglogistic Distribution Model
LOS_home Jan and Feb, hrs
C alculations Based on Loglogistic Distribution Model
~17% exceed LOS limit 5 hrs
~24% exceed LOS limit 6 hrs
More than X patients
waiting for a bed ?
Wait time greater
than Y hours ?
YES
YES CONSIDER
CLOSING
NO
NO
Bed
Available?
NO
1. Maintain Safe Patient Care
2. Decrease ED Diversions
3. Decrease Length of Stay
4. Decrease Left Not Seens
Objectives
ALTERNATIVE CLOSURE CRITERIA
Stay open
Questions to be addressed using Process Model
simulation:
• What should X and Y be to get low percent diversion ?
• Are X and Y correlated ?
Evaluate options to create beds
expedite discharges
move dispo’d pts to off floor bed
move stable pts to non-monitored bed
Advanced Nurse initiatives
Investigate LOS greater than 5 hours
Consult delays?
Radiology delays?
Lab delays?
• The lower max number of patients in the waiting room and max waiting time the
lower is ED diversion
• Locations of peaks of the max number of patients in Waiting Room is strongly
correlated to locations of peaks of the max waiting time (see next slides)
SIMULATION OF ALTERNATIVE CLOSURE CRITERIA
Take-away:
1 hr12~4%24 hrs5 hrs3
43 min10~ 2%6 hrs6 hrs2
35 min7~ 0.5 %6 hrs5 hrs1
3 hr 30 min3123.7%24 hrs24 hrsCurrent state,
(Baseline)
Waiting time
for admitted
patients in
Waiting Room
Max number of
patients in
Waiting Room
Predicted ED
diversion, %
LOS for
admitted NOT
more than
LOS for
discharged
home NOT
more than
Scenario/option
Number of patients in Waiting Room
ULOS_home=24 hrs, ULOS_adm=24 hrs
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 384 408 432 456 480 504 528 552 576 600 624 648 672 696 720 744
time, hrs
number
Wait_time_adm in Waiting Room, hrs
ULOS_home=24 hrs, ULOS_adm=24 hrs
0
0.5
1
1.5
2
2.5
3
3.5
0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 384 408 432 456 480 504 528 552 576 600 624 648 672 696 720 744
time, hrs
waittime,hrs
Number of patients in Waiting Room
ULOS_home=5 hrs, ULOS_adm=6 hrs
0
1
2
3
4
5
6
7
8
0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 384 408 432 456 480 504 528 552 576 600 624 648 672 696 720 744
time,hrs
number
wait_time_adm in Waiting Room, hrs
ULOS_home=5 hrs, ULOS_adm=6 hrs
0
0.1
0.2
0.3
0.4
0.5
0.6
0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 384 408 432 456 480 504 528 552 576 600 624 648 672 696 720 744
time, hrs
waittime,hrs
N_WR
Div%
3231302928272625242322212019181716151413121110987654321
25.5
24.0
22.5
21.0
19.5
18.0
16.5
15.0
13.5
12.0
10.5
9.0
7.5
6.0
4.5
3.0
1.5
0.0
Scatterplot of Div % vs N_WR
Take-away:
The number of patients in waiting room 11 or less corresponds to single digits
diversion less than 3%
Time_adm_WR, hrs
Div%
3.53.02.52.01.51.00.50.0
25.5
24.0
22.5
21.0
19.5
18.0
16.5
15.0
13.5
12.0
10.5
9.0
7.5
6.0
4.5
3.0
1.5
0.0
Scatterplot of Div % vs Time_adm_WR, hrs
Take-away:
Waiting time for admitted patients in waiting room 1 hr or less corresponds to
single digits diversion less than 3%
Time_adm_WR, hrs
N_WR
3.53.02.52.01.51.00.50.0
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
Scatterplot of N_WR vs Time_adm_WR, hrs
Take-away:
• The number of waiting patients and the waiting time for admitted patients is strongly
correlated to each other. Pearson linear correlation coefficient is 0.996 ! !.
• Strong correlation indicates that either one or another criteria should be enough, not both.
Conclusions
• ED diversion could likely be negligible (less than 1 %) if patients discharged home stay
NOT more than 5 hrs and admitted patients stay NOT more than 6 hrs.
Currently:
-17% of patients discharged home stay above this limit up to 24 hrs;
-24 % of admitted patients stay above this limit up to 20 hrs.
This long LOS for large % of patients results in ED closure/diversion
• Some relaxing of these LOS limits will result in low single digits % ED diversion that still
could be acceptable
• Other combinations of LOS upper limits that result in low single digits % diversion
have been determined using full factorial DOE with two factors.
• An alternative diversion criteria could be used: the number of patients in waiting room.
The number of patients 11 or less corresponds to single digits diversion, less than ~3%
• All three components affect the flow of patients that the system can handle.
• A lack of the proper balance between these components results in the
system’s over-flow and closure/diversion
• Process Model Simulation methodology provides the only means of
analyzing and managing the proper balance
• Patient Throughput flow is an example of the general Dynamic Supply &
Demand problem .
Dynamic means that the system’s behavior depends on time (not a one-time snapshot)
• There are three basic components that should be accounted for in this type
of problems:
• The number of patients (or, generally, any items) entering the system at
any point of time
• The number of patients (any items) leaving the system at any point of
time
• Limited Capacity of the system which limits the flow of patients through
the system
What did we learn about simulation methodology?
APPENDIX
WHAT IS THE PROCESS MODEL ?
•It is a computer model that mimics the dynamic behavior of a real
process over the time in order to visualize and quantitatively analyze
its performance in terms of:
•Cycle times
•Throughput capacity
•Resources utilization
•Activities utilization
•It is a tool to perform ‘WHAT-IF’ analysis and play different
scenarios of the model behavior as conditions and process
parameters change.
This allows to make experiments on the computer model, and test
different solutions (changes) for their effectiveness before going to
the floor for the actual implementation.
WHAT ARE THE BASIC ELEMENTS OF THE PROCESS MODEL?
•Flow chart of the process: Diagram that depicts logical flow of a process
from its inception to its completion
•Entities: Items to be processed: patients, documents, customers, etc.
•Activities: Tasks performed on entities: medical procedures,
document approval, customer check out, etc
•Resources: Agents used to perform activities and move entities: service
personnel, operators, equipment, nurses, physicians.
•Connections:
•Entity arrivals: Define process entry points, time, and quantities of the
entities that enter the system to begin processing
•Entity routings: Define directions and logical conditions flow for entities
WHAT INFORMATION (DATA) IS REQUIRED TO FEED THE MODEL ?
•Entities quantities and arrival time: periodic, random, scheduled, daily
pattern, etc
•The time that the entities spend in the activities. This is usually not a
fixed time but a statistical distribution. The wider the time distribution the
higher the variability of the system behavior.
•The capacity of each activity, i.e. the max number of entities that can be
processed concurrently in the activity.
•The size of input and output queues for the activities
•The routing type or the logical conditions to take a specified routing.
•Resource Assignments: their number and availability, and/or resources
shift schedule

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ED conference presentation 2007

  • 1. PREDICTIVE MODELING OF EMERGENCY DEPARTMENT OPERATIONS: EFFECT OF PATIENTS’ LENGTH OF STAY ON ED DIVERSION ALEXANDER KOLKER, PhD Froedtert Hospital Milwaukee, Wisconsin
  • 2. Froedtert Hospital, Milwaukee WI • Primary teaching Hospital for MCW • Tertiary Referral Center • Level 1 Trauma Center for SE Wisconsin • 433 staffed acute care beds • 23,617 admissions/ 47,176 ED Visits • 454,780 Outpatient Clinic Visits • Surgeries - Inpt: 9,034/ Outpt: 5,711
  • 3. PROBLEM STATEMENT: • Froedtert Hospital ED ambulance diversion has become unacceptably high due to no ED beds (average ~21% of time in 2007) •There are two big groups of patients: (i) admitted to the hospital, and (ii) treated, stabilized and discharged home • Among factors that affect ED diversion patients’ Length of Stay (LOS) in ED is one of most significant one. The Goal of this work was: • develop a methodology that could quantitatively analyze and predict an impact of patients’ LOS on ED diversion (both for admitted and discharged home patients’ groups). • identify the maximum LOS limit that will result in significant reduction or elimination ED diversion.
  • 4. STEPS THAT HAVE BEEN PERFORMED: • Collected data on - patients arrival in ED: day of week and time of day - mode of transportation: walk-ins or ambulance - discharge disposition: home / expired or admitted in the Hospital • Analyzed LOS distribution and its functional approximation for (i) discharged home, and (ii) admitted patients • Developed an ED Process Model aimed at modeling different scenarios of LOS upper limits that will result in significant reduction (or elimination) ED diversion • Summarized the basics of modeling methodology: What did we learn ?
  • 5. What is the LOS distribution for admitted and discharged home patients ? 181512963 Median Mean 5.04.94.84.74.64.54.44.3 1st Quartile 3.3833 Median 4.4667 3rd Quartile 5.9333 Maximum 20.4333 4.7761 4.9548 4.3667 4.5667 A-Squared 32.74 P-Value < 0.005 Mean 4.8654 StDev 2.1305 Variance 4.5389 Skewness 1.22735 Kurtosis 3.14050 N 2185 Minimum 0.4667 Anderson-Darling Normality Test 95% Confidence Interval for Mean 95% Confidence Interval for Median 24.521.017.514.010.57.03.50.0 Median Mean 3.23.13.02.92.82.72.6 1st Quartile 1.6167 Median 2.6667 3rd Quartile 4.2000 Maximum 25.8167 3.1039 3.2099 2.6000 2.7167 A-Squared 146.60 P-Value < 0.005 Mean 3.1569 StDev 2.1225 Variance 4.5051 Skewness 1.84310 Kurtosis 8.14424 N 6155 Minimum 0.0667 Anderson-Darling Normality Test 95% Confidence Interval for Mean 95% Confidence Interval for Median 95% Confidence Intervals Summary for LOS admitted, hrs 95% Confidence Intervals Summary for LOS home, hrs Total number for Jan 07: 1133 Feb 07:1052 Total number for Jan 07: 3255 Feb 07: 2971
  • 6. DO THE SAME DAYS OF WEEK FOR DIFFERENT WEEKS HAVE A SIMILAR ARRIVAL PATTERN ? Take away: Same days for different weeks have very different patient arrival pattern. Therefore arrivals for all Mondays, all Tuesdays, and so on should not be combined A dm T ime_1 /1 /2 0 0 7 Frequency 2400230022002100200019001800170016001500140013001200110010009008007006005004003002001000 8 6 4 2 0 A dm T ime_1 /8 /2 0 0 7 Frequency 2400230022002100200019001800170016001500140013001200110010009008007006005004003002001000 12 9 6 3 0 6 2 9 2 4 6 4 7 5 6 3 9 4 7 2 4 2 0 2 8 3 4 2 6 11 5 777 8 7 9 7 9 101010 12 6 222 0 3 2 4 1 Monday Adm Time_1/1/2007 Monday Adm Time_1/8/2007
  • 7. ED structure and in-patient units The high-level layout of the entire hospital system:
  • 8. Arrival pattern wk, DOW, time Mode of transp Disposition ED simulation model layout Simulation Digital clock
  • 9. • ED diversion (closure) is declared when ED patients’ census reaches ED beds capacity. • ED stays in diversion until some beds become available when patients are moved out of ED (discharged home, expired, or admitted as in-patients). • % ED diversion = % time ED is at full capacity • upper LOS limits (simulation parameters) are imposed on the baseline original LOS distributions: LOS higher than the limiting value is NOT allowed in the simulation run. Baseline LOS distributions should be recalculated as functions of the upper LOS limits. MODELING APPROACH Take-away:
  • 10. MODELING APPROACH (cont.) Given original distribution density and the limiting value of the random variable T, what is the conditional distribution of the restricted random variable T ? 121086420 500 480 460 440 420 400 380 360 340 320 300 280 260 240 220 200 180 160 140 120 100 80 60 40 20 0 LOS, Hrs Frequency 3-Parameter Gamma Distributionof LOS_ home, Hrs Imposed LOS limit 6 hrs 121086420 500 480 460 440 420 400 380 360 340 320 300 280 260 240 220 200 180 160 140 120 100 80 60 40 20 0 LOS, Hrs Frequency Re-calculatedboundeddistributionof LOS_ home, Hrs dTTf Tf LOSTf LOS original original new   0 )( )( ),( LOSTif,0)( newTf T, Hrs LO T, Hrs Original unbounded distribution New re-calculated distribution origTf )( LOS limit
  • 11. ED Simulation Run Example Diversion time & DOW Diverted Ambulance Patients discharged Home Patient admitted to the Hospital
  • 12. • ED diversion could be negligible (~0.5%) if patients discharged home stay NOT more than 5 hrs and admitted patients stay NOT more than 6 hrs. • Relaxing of these LOS limits results in low digits % diversion that still could be acceptable SIMULATION SUMMARY & MODEL VALIDATION Low single digits diversion ~4%24 hrs5 hrs3 Low single digits diversion ~ 2%6 hrs6 hrs2 Practically NO diversion ~ 0.5 %6 hrs Currently 24% with LOS more than 6 hrs; 5 hrs Currently 17% with LOS more than 5 hrs; 1 Actual ED diversion was 21.5% 23.7%24 hrs24 hrsCurrent, 07 (Baseline) NotePredicted ED diversion, % LOS for admitted NOT more than LOS for discharged home NOT more than Scenario/option Take-away:
  • 13. Baseline ED census, January 2007 LOS <= 24 hrs. Capacity 30 beds. Diversion 23.7 % 0 5 10 15 20 25 30 35 0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 384 408 432 456 480 504 528 552 576 600 624 648 672 696 720 744 time, hrs EDcensus ED census: LOS_home<=6 hrs, LOS_adm<=6 hrs. Capacity 30 beds. Diversion 1.8% 0 5 10 15 20 25 30 35 0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 384 408 432 456 480 504 528 552 576 600 624 648 672 696 720 744 time, hrs census Diversion is declared when ED census hits capacity limit. The longer the census stays at capacity limit the higher is diversion %
  • 14. What other combinations of upper limits LOS are possible to get low single digits % ED diversion ? Performed full factorial DOE with two factors (ULOS_home and ULOS_adm) at 6 levels each using simulated % diversion as a response function. Div % 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 45 6 8 1 81 0 1 2 1 21 8 1 08 6 ULOS_adm, hrs52 4ULOS_home, hrs Surface Plot of Div % vs ULOS_adm, ULOS_home We want to be here
  • 15. ULOS_adm, hrs MeanpredictedDiv% 241210865 24.0 22.5 21.0 19.5 18.0 16.5 15.0 13.5 12.0 10.5 9.0 7.5 6.0 4.5 3.0 1.5 0.0 5 6 8 10 12 24 ULOS_home, hrs Simulated Div % as a function of upper LOS limits, hrs What other combinations of upper limits LOS are possible to get low single digits % ED diversion ? Low single digits % diversion Performed full factorial DOE with two factors (ULOS_home and ULOS_adm) at 6 levels each using simulated % diversion as a response function.
  • 16. % of patients that stay longer than the upper LOS limit 242220181614121086420 USL = 6 hrs LSL * Target * USL 6 Sample Mean 4.86544 Sample N 2185 Location 1.49891 Scale 0.246641 Process Data % < LSL * % > USL 24.03 % Total 24.03 Observed Performance 24.521.017.514.010.57.03.50.0 USL = 5 hrs LSL * Target * USL 5 Sample Mean 3.1569 Sample N 6155 Location 0.955823 Scale 0.39521 Process Data % < LSL * % > USL 16.83 % Total 16.83 Observed Performance LOS_adm Jan and Feb, hrs C alculations Based on Loglogistic Distribution Model LOS_home Jan and Feb, hrs C alculations Based on Loglogistic Distribution Model ~17% exceed LOS limit 5 hrs ~24% exceed LOS limit 6 hrs
  • 17. More than X patients waiting for a bed ? Wait time greater than Y hours ? YES YES CONSIDER CLOSING NO NO Bed Available? NO 1. Maintain Safe Patient Care 2. Decrease ED Diversions 3. Decrease Length of Stay 4. Decrease Left Not Seens Objectives ALTERNATIVE CLOSURE CRITERIA Stay open Questions to be addressed using Process Model simulation: • What should X and Y be to get low percent diversion ? • Are X and Y correlated ? Evaluate options to create beds expedite discharges move dispo’d pts to off floor bed move stable pts to non-monitored bed Advanced Nurse initiatives Investigate LOS greater than 5 hours Consult delays? Radiology delays? Lab delays?
  • 18. • The lower max number of patients in the waiting room and max waiting time the lower is ED diversion • Locations of peaks of the max number of patients in Waiting Room is strongly correlated to locations of peaks of the max waiting time (see next slides) SIMULATION OF ALTERNATIVE CLOSURE CRITERIA Take-away: 1 hr12~4%24 hrs5 hrs3 43 min10~ 2%6 hrs6 hrs2 35 min7~ 0.5 %6 hrs5 hrs1 3 hr 30 min3123.7%24 hrs24 hrsCurrent state, (Baseline) Waiting time for admitted patients in Waiting Room Max number of patients in Waiting Room Predicted ED diversion, % LOS for admitted NOT more than LOS for discharged home NOT more than Scenario/option
  • 19. Number of patients in Waiting Room ULOS_home=24 hrs, ULOS_adm=24 hrs 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 384 408 432 456 480 504 528 552 576 600 624 648 672 696 720 744 time, hrs number Wait_time_adm in Waiting Room, hrs ULOS_home=24 hrs, ULOS_adm=24 hrs 0 0.5 1 1.5 2 2.5 3 3.5 0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 384 408 432 456 480 504 528 552 576 600 624 648 672 696 720 744 time, hrs waittime,hrs
  • 20. Number of patients in Waiting Room ULOS_home=5 hrs, ULOS_adm=6 hrs 0 1 2 3 4 5 6 7 8 0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 384 408 432 456 480 504 528 552 576 600 624 648 672 696 720 744 time,hrs number wait_time_adm in Waiting Room, hrs ULOS_home=5 hrs, ULOS_adm=6 hrs 0 0.1 0.2 0.3 0.4 0.5 0.6 0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 384 408 432 456 480 504 528 552 576 600 624 648 672 696 720 744 time, hrs waittime,hrs
  • 21. N_WR Div% 3231302928272625242322212019181716151413121110987654321 25.5 24.0 22.5 21.0 19.5 18.0 16.5 15.0 13.5 12.0 10.5 9.0 7.5 6.0 4.5 3.0 1.5 0.0 Scatterplot of Div % vs N_WR Take-away: The number of patients in waiting room 11 or less corresponds to single digits diversion less than 3%
  • 22. Time_adm_WR, hrs Div% 3.53.02.52.01.51.00.50.0 25.5 24.0 22.5 21.0 19.5 18.0 16.5 15.0 13.5 12.0 10.5 9.0 7.5 6.0 4.5 3.0 1.5 0.0 Scatterplot of Div % vs Time_adm_WR, hrs Take-away: Waiting time for admitted patients in waiting room 1 hr or less corresponds to single digits diversion less than 3%
  • 23. Time_adm_WR, hrs N_WR 3.53.02.52.01.51.00.50.0 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 Scatterplot of N_WR vs Time_adm_WR, hrs Take-away: • The number of waiting patients and the waiting time for admitted patients is strongly correlated to each other. Pearson linear correlation coefficient is 0.996 ! !. • Strong correlation indicates that either one or another criteria should be enough, not both.
  • 24. Conclusions • ED diversion could likely be negligible (less than 1 %) if patients discharged home stay NOT more than 5 hrs and admitted patients stay NOT more than 6 hrs. Currently: -17% of patients discharged home stay above this limit up to 24 hrs; -24 % of admitted patients stay above this limit up to 20 hrs. This long LOS for large % of patients results in ED closure/diversion • Some relaxing of these LOS limits will result in low single digits % ED diversion that still could be acceptable • Other combinations of LOS upper limits that result in low single digits % diversion have been determined using full factorial DOE with two factors. • An alternative diversion criteria could be used: the number of patients in waiting room. The number of patients 11 or less corresponds to single digits diversion, less than ~3%
  • 25. • All three components affect the flow of patients that the system can handle. • A lack of the proper balance between these components results in the system’s over-flow and closure/diversion • Process Model Simulation methodology provides the only means of analyzing and managing the proper balance • Patient Throughput flow is an example of the general Dynamic Supply & Demand problem . Dynamic means that the system’s behavior depends on time (not a one-time snapshot) • There are three basic components that should be accounted for in this type of problems: • The number of patients (or, generally, any items) entering the system at any point of time • The number of patients (any items) leaving the system at any point of time • Limited Capacity of the system which limits the flow of patients through the system What did we learn about simulation methodology?
  • 27. WHAT IS THE PROCESS MODEL ? •It is a computer model that mimics the dynamic behavior of a real process over the time in order to visualize and quantitatively analyze its performance in terms of: •Cycle times •Throughput capacity •Resources utilization •Activities utilization •It is a tool to perform ‘WHAT-IF’ analysis and play different scenarios of the model behavior as conditions and process parameters change. This allows to make experiments on the computer model, and test different solutions (changes) for their effectiveness before going to the floor for the actual implementation.
  • 28. WHAT ARE THE BASIC ELEMENTS OF THE PROCESS MODEL? •Flow chart of the process: Diagram that depicts logical flow of a process from its inception to its completion •Entities: Items to be processed: patients, documents, customers, etc. •Activities: Tasks performed on entities: medical procedures, document approval, customer check out, etc •Resources: Agents used to perform activities and move entities: service personnel, operators, equipment, nurses, physicians. •Connections: •Entity arrivals: Define process entry points, time, and quantities of the entities that enter the system to begin processing •Entity routings: Define directions and logical conditions flow for entities
  • 29. WHAT INFORMATION (DATA) IS REQUIRED TO FEED THE MODEL ? •Entities quantities and arrival time: periodic, random, scheduled, daily pattern, etc •The time that the entities spend in the activities. This is usually not a fixed time but a statistical distribution. The wider the time distribution the higher the variability of the system behavior. •The capacity of each activity, i.e. the max number of entities that can be processed concurrently in the activity. •The size of input and output queues for the activities •The routing type or the logical conditions to take a specified routing. •Resource Assignments: their number and availability, and/or resources shift schedule