THE IMPACT OF DELAY ANNOUNCEMENTS ON HOSPITALNETWORK COORDINATION AND WAITING TIMES

Galit Yom-Tov (Technion – Israel Institute of Technology) Joint work with : Jing Dong (Northwestern University) Elad Yom-Tov (Microsoft Research)

Stochastic Networks conference, San Diego – June 20161

THE SERVICE ENTERPRISE ENGINEERING (SEE) LABSEELab: Environment for graphical EDA in real-time

Detailed operational histories (customers, servers), e.g.

1. *Bank Anonymous : 1 year, 350K calls by 15 agents - in 2000, which paved the way to:

2. *U.S. Bank : 2.5 years, 220M calls, 40M by 1000 agents

3. Israeli Cellular: 2.5 years, 110M calls, 25M calls by 750 agents

4. Israeli Bank: from January 2010-, daily-deposit at a SEESafe

5. Service Engineering internet site: click-stream data (2 years)

6. *Home (Rambam) Hospital : 4 years, 1000 beds, inter-ward flow

7. Emergency Department (ED) patient flow: � 5 EDs in Israel: 1-2 years, late David Sinreich, ED arrivals & LOS 1. ED in Seoul: 2 months, K. Song-Hee & W. Cha 2. ED in XY: 2 years� ED in Israel: 1 year of detailed processes

8. Hospital RTLS (Real-Time Location System): 1. 250K events/day: 1000 patients, 350 staff (1500 tagged entities)2. Infrastructure: 900 readers (sensors), many floors

9. Combination of medical and operational data in Hematology Ward: 5 year

10. Chat of an Aviation company: 3 month, 30K chats, 50 agents in 2016 (ongoing)

*Open & Free for research and teaching

LEADING CONCEPT

People are operating service systems and are operated by it. Hence, we need to understand their influence on the system and plan (operationally) accordingly

Understand = Data Analysis or Experiments

Plan = Queueing models

Today: combine the two to understand the impact of delay announcement on hospital network coordination

HOSPITAL PUBLISH ED WAIT TIMES

6/30/2015 Healthcare Providers in the Dallas-Ft. Worth and surrounding communities. - HCA North Texas | Irving, TX

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24/7 Emergency Care ­ PlanoDenton Regional Medical CenterER at BurlesonER at Grand PrairieGreen Oaks HospitalLas Colinas Medical CenterMedical Center AllianceMedical Center of ArlingtonMedical Center of LewisvilleMedical Center of McKinneyMedical City Dallas HospitalNorth Hills HospitalPlaza Medical CenterThe Medical Center of PlanoER at StonebridgeFlower Mound Emergency CenterMedical City Children’s Hospital

Wait times are an average and provided for informationalpurposes only. What does this mean?

Average ER Wait Time

Alliance

0Arlington

14Burleson

9Denton

5Flower Mound

0Grand Prairie

6Las Colinas

9Lewisville

2McKinney

5Medical City

5Medical City Children's Hospital

6North Hills

2North Plano

3Plano

3Plaza

4Stonebridge

0Edmond

3ER Oklahoma

0OU Childrens

9OU Presby

14OU Womens

0

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6/30/2015 About Our ER Wait Times - HCA North Texas | Irving, TX

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Home About Us About Our ER Wait Times 0

About Our ER Wait Times

ER wait times are approximate and provided for informational purposes only.  If you are having a medical emergency, call 9­1­1.

The ER wait time represents the time it takes to see a qualified medical professional, defined as a Doctor of Medicine (MD), Doctorof Osteopathy (DO), Physician Assistant (PA) or Advanced Registered Nurse Practitioner (ARNP).

ER wait times represent a four­hour rolling average updated every 30 minutes, and is defined as the time of patient arrivaluntil the time the patient is greeted by a qualified medical professional.  Patients are triaged at arrival and are then seen by aqualified medical professional in priority order based on their presenting complaint and reason for visit.

Any non­digital posting of HCA average ER wait times reflects the previous month’s average ER wait times defined as the time ofpatient arrival until the time the patient is greeted by a qualified medical professional.

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… AND PEOPLE SEARCH FOR THAT INFO

Google trend for searching the phrases: “Hospital wait time” and “ER wait time”

RESEARCH QUESTIONS

Do people take this information into account when deciding where to go?

Does the proportion of patients is large enough to have operational impact on the hospital network?

How sensitive patients are to ED wait times (gaps between two close hospitals)?

Do hospital announce the right information? Is there an operational significance for the forecasting methodology used?

Methodology: Data analysis and numerical analysis

DELAY ANNOUNCEMENTS

Delay announcement impact:� Customer abandonment (Mandelbaum and Zeltyn 2013, Yu et al. 2014, Munichor and Rafaeli (2007))� Customer satisfaction (Larson 1987, Carmon and Kahneman 1996, Munichor and Rafaeli 2007)� What to announce? (Munichor and Rafaeli 2007, Alon et al. 2011)

Estimating/Forecasting delays (Ibrahim and Whitt 2009, 2011, Senderovich et al. 2014, Plambeck et al. 2014)

Use as an operational tool: Call back (Armony and Maglaras 2004), Amusement parks (Kostami and Ward 2009), Patience (Huang et al. 2015)

DELAY ANNOUNCEMENTS IN A NETWORK

If all customers would Join the Shortest Queue (JSQ) the efficiency of the network could be improved to be almost like that of a fully pooled system (Foley and McDonald 2001).

Even when the fraction of customers choosing a server by the JSQ policy is small, this policy is still advantageous (Reiman 1984, Turner 2000).

=> Reduced delays

=> Improve quality of care (Chaln et al. 2007) and decrease mortality (Bennidor and Israelit 2015).

Can wait time announcement achieve this in reality?

ARE PEOPLE INFLUENCED BY DELAY ANNOUNCEMENT? IF YES, TO WHAT EXTENT?

DATA GATHERED210 hospital EDs.

3 month of delay announcements (3-6/2013)

All use the same method: 4 hour moving average estimator

Some don’t not present the delay info (13%), some only their own info (49%) and some also others (38%)

Exposure Information - Queries to Bing during that time to those pages (including location information) (10% explicitly looked at multiple hospitals)

Demographic information: Income, Age, Usage of internet, etc.

Environment information: Population, No of hospitals/EDs in area, etc.

BASIC IDEA: SYNCHRONIZATION OF QUEUEING NETWORKS WHEN CUSTOMER CHOOSE THE SHORTEST WAIT

All patients join the shortest wait Patients join hospitals randomly

THE THEORETICAL IMPACT OF PARTIAL JSW ACTIVATION => SUGGEST A NEW MEASUREMENT FOR THE LEVEL OF POOLING IN A NETWORKMultinomial Logit Model (MNL): The utility for being served in hospital iwith reported delay ri is Ui=βi-αri+εi . The probability to choose Hospital 1 is:

Partial synchronization occur with customer choice𝜌 = 0.85 𝜌 = 0.9 𝜌 = 0.95

CORRECTING FOR SMOOTHING AND DIURNAL EFFECTS

The effect of averaging using a moving window is akin to convolving wi(t) with a rectangular window W of length 4.

The reported wait times are: where

The cross-correlation is where

In the matrix form

We can recover the original correlation by the Moore-Penrose pseudo-inverse:

CORRECTING FOR SMOOTHING AND DIURNAL EFFECTS

Separate the wait time to a diurnal trend and a transient effect

Allow us to separate the effect of the trends and transient components in the data on the correlation.

We call the detrended wait data Residual Waiting Times (RWT)

Wait time patterns of three load clusters

EMPIRICAL ANALYSIS: HIGH VARIATION IN SYNCHRONIZATION LEVELS

Synchronization could be negative!

Range: [-0.2,0.8]. Detrended: [-0.1-0.2]

Only close by pairs (up to 50 km apart)

EMPIRICAL ANALYSIS: PEOPLE USE THE DELAY INFORMATIONCluster of close hospitals only (<25km apart)

As more hospital publish waits, synchronization increases

Younger population (<42) use information more

Effect of exposure to information (# of customers query) is not linear and depends on demographics. For areas with kids synchronization increases with queries; for areas with no kids synchronization decreases with queries.

Model checks:

Leave-one-out cross-validation method show that the Spearman correlation between predicted and actual average RWT correlations is 0.525 (P=0.002).

Sequential forward feature selection (DHS) show that the best correlation is 0.662 (P=10^{-6}).

Hospitals that provide network information exhibit higher correlation only if other hospitals are close (<8km).

EMPIRICAL ANALYSIS: THE EFFECT OF INFORMATION PROVIDED

USING NUMERICAL STUDY FOR DEEPER UNDERSTANDING

SIMULATING A HOSPITAL NETWORK: CALIBRATING MODELED size: 10-40 beds (Hospitals website)

ED capacity differ between day and night by No. of physicians.

Average service time (LOS in ED): 108 minutes for low acuity patients (Average in US hospitals, Medicare)

Time-Varying arrival rate of a real hospital

Announcement using 4 hour moving average

Exposure proportion in the population and cost-of-waiting vary

SIMULATING A HOSPITAL NETWORK

Simulation fit reality: � Wait times are similar to data in values and patterns� Trended and detrended correlation fit data in their ranges. Including negative values!!!

The effect of cost-of-waiting and exposure proportion is similar.

Low exposure Medium exposure High exposure

Detrended

With trend

Data wait time pattern

HOW MUCH SYNCHRONIZATION CAN BE ACHIEVED?Setting: Time-homogeneous, perfect information, symmetric network

Depends on patients’ sensitivity to wait:� As delay sensitivity increases, synchronization increases.� Most of the operational impact is achieved with low cost of waiting (i.e., small proportion of ”strategic”

patients).

Depends on hospital loads:� The higher the load, the higher the synchronization is (for every alpha).

𝜌 = 0.85 𝜌 = 0.9 𝜌 = 0.95

HOW MUCH SYNCHRONIZATION CAN BE ACHIEVED?

Depends on the network structure:� The more asymmetry between hospitals, the less synchronization is expected.

(asymmetry either in patients preference or in hospital capacity)� As long as the differences are small both hospitals will experience reduction in waiting times. If

difference are large, the more loaded hospital (preferred , smaller) will experience wait reduction. The less loaded hospital (less-preferred, larger) may experience a small increase in wait times.

Synchronization with differentpatient preferences asymmetry

Low asymmetry High asymmetry

HOW MUCH SYNCHRONIZATION CAN BE ACHIEVED?

Depends on forecast accuracy:� The more accurate the delay estimator is, the higher the synchronization is.

Depend on the forecasting methodology:� The higher the delay in the forecasting algorithm, the lower the synchronization achieved.� If delay is too long and customers are highly delay-sensitive, self oscillation occur

Correlation with inaccurate forecast

4 hours moving average 0.5 hour moving average Head of the line

ANNOUNCING 4-HOUR MOVING AVERAGE…

Synchronization reduces with cost of waiting to a negative value

Synchronization Wait times

ANNOUNCING 4-HOUR MOVING AVERAGE…Load alternates between queues

Time-Lag reduces with the length of averaging window

Similar results in control theory: self oscillation

Announcement time-lag Wait time in the two hospitals

CONCLUSIONS

We developed a new performance measure to estimate the level of pooling in a queueing network.

Patients use ED wait time announcement to decide where to go.

There is a trend in seeking such information which suggests this will phenomena will grow.

ED delay announcements can reduce waiting time in a hospital network and increase coordination.

BUT the 4-hour moving average is problematic and reduce the operational improvement potential.

Combining all the above: As we observe still a positive correlation for most networks, it seems that the cost of waiting is still low or that a relatively small proportion of the population is influenced by that info. But as trends of using such info grow, a change in policy is needed.

WHAT’S NEXT?Concern 1: No agreement on effective methodology

� Building correct wait time estimators to ED (special features: Network, non FCFS) (with A. Mandelbaum and N. Carmeli)

�What announcement to publish? (Time to triage vs. Length-of-stay)

� Robustness of estimators vs. Operational influence

� The influence of driving time. Forecasting wait for time t?

Concern 2: Urgent patients might delay their visit

� Risks benefit analysis

� Estimating hospital preferences and cost of waiting for a real network of hospitals (with IMoH).

Concern 3: Theoretical understanding (with J. Dong)

� Analysis of the connection between methodology and pooling

� Analysis of the JSQ/JSW with customer choice

THANK YOU