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_1/1/2007

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ED structure and in-patient unitsThe 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 ?

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LOS, Hrs

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3-Parameter Gamma

Distribution of LOS_ home, Hrs

Imposed LOS limit 6 hrs

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Re-calculated bounded distribution of LOS_ home, Hrs

dTTf

TfLOSTf

LOS

original

originalnew

0

)(

)() ,(

LOST if ,0)( newTf

T, HrsLOT, 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 thanScenario/option

Take-away:

Baseline ED census, January 2007

LOS <= 24 hrs. Capacity 30 beds.

Diversion 23.7 %

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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

ED

cen

sus

ED census:

LOS_home<=6 hrs, LOS_adm<=6 hrs. Capacity 30 beds.

Diversion 1.8%

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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

cens

usDiversion 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 %

135791113151719212325272931

245 6 8 181012

1218 1086 ULOS_adm, hrs524ULOS_home, hrs

Surface Plot of Div % vs ULOS_adm, ULOS_home

We want to be here

ULOS_adm, hrs

Mea

n pr

edic

ted

Div

%

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22.5

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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, hrsC alculations Based on Loglogistic Distribution Model

LOS_home Jan and Feb, hrsC 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

NONO

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 bedsexpedite 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

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time, hrs

nu

mb

er

Wait_time_adm in Waiting Room, hrs

ULOS_home=24 hrs, ULOS_adm=24 hrs

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wai

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rs

Number of patients in Waiting Room

ULOS_home=5 hrs, ULOS_adm=6 hrs

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time,hrs

nu

mb

er

wait_time_adm in Waiting Room, hrs

ULOS_home=5 hrs, ULOS_adm=6 hrs

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time, hrs

wait

tim

e,

hrs

N_WR

Div

%

3231302928272625242322212019181716151413121110987654321

25.5

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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

%

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25.5

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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

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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