This document discusses using machine learning and operations research methods to improve patient flow in hospital emergency departments. Specifically, it proposes using admission prediction tools at triage to help decide whether to board patients earlier than usual (called "BERT"). The goal is to balance reducing patient wait times with avoiding unnecessary boardings. A queueing model is developed and simulations are used to test policies for setting BERT thresholds. Future work may expand this approach to predict demand for different hospital units and help operations and control of the entire hospital system. The research is a collaboration between UNC and Harvard Medical School.

1. Nilay Tanık Argon
Department of Statistics and Operations Research
University of North Carolina
Chapel Hill, NC, USA
This research is supported by National Science Foundation Award CMMI1635574

2.  Relation 1:
Optimization Machine learning
 Relation 2:
Machine learning Complex decision making

3. Precision medicine
Public health
Healthcare operations
…

4. T
R
I
A
G
E

MAIN
HOSPITAL
EMERGENCY DEPARTMENT
Admission
Discharge

5. Triage Stage 1 Stage 2
ED work-up
Bed request
Boarding (if admit)
Total ED bed occupancy time
H

6. Triage Stage 1
Stage 2
H
Total ED bed occupancy time
Predict admission
and
BERT

7.  BERT is good:
 reduces the length-of-stay for the BERTed patient
 indirectly reduces the waiting times of consecutive
patients
 BERT is bad:
 hospital management does not like false bed
requests – waste of time/resources
 How to balance the good and the bad?

8. Tool 1: Estimate probability of hospital admission at
triage
Tool 2: Decide whether to BERT or not

9. 1. Admission Prediction Tool (APT):
 Logistic regression to estimate hospital admission
probability based on info at triage (e.g. chief complaints,
sex, age)
2. Decision to BERT Tool:
 Queueing control to determine when and who to BERT.
 Threshold on the hospital admission probability
 Constant or state-dependent threshold?

10. General approach:
 Develop a relatively simple mathematical model
that captures the basic trade-off and solve it.
 Use the solution to the mathematical model to
develop a policy that can actually be implemented
in practice.
 Test the performance of the policy using a realistic,
validated simulation model.

11. Focus on a queue for a single bed
S
BeRT No BeRT
Sequential Service
Bed
Parallel Service
ED Treatment
Bed Assignment
Process
ED Treatment
Bed Assignment
Process
Service time
Service time

12. Waiting cost per patient per unit time
Bed assignment and preparation “cost” with BeRT
Arrival rate (Poisson process)
Mean ED service time (iid exp. dist.)
Mean bed search and preparation time (iid exp. dist.)
Prob. of admission for patient k
Bed assignment and preparation “cost” without BeRT

13. Admission probability
and
Server Status
Number of
patients
waiting
Objective: Minimize the long-run average cost

16. So, now, how do we determine the optimal threshold function,
or maybe just a “good” threshold function?

19. Replace with where
OR

20.  Challenge 1: moving from single bed queue to multi-bed ED.
 Proposed approximation: single server pooled service
capacity.
 Challenge 2: moving from stationarity to non-stationarity.
 Proposed approximation: use time-dependent estimates.

21. ED census, i.e., number of patients in the ED
Hospital admission probability for the patient

22.  Ignore ED census. BeRT if and only if
Policy parameter.

23.  Developed and validated a simulation model based on UNC ED
data from 2012
Wards and bed capacities at UNC ED

26.  Scenario created based on CDC predictions.
 18 week period with a 6-week influenza period in the middle.

27. Entire eighteen-week period
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
420 470 520 570 620 670
Meannumberofdailyfalse
BeRTs
Mean length of stay (min.)
CTT
FT

28.  Predict the most suitable unit at the hospital for the
patient who is predicted to be admitted
 Predict the total number of patients who will need a
certain type of hospital bed
Predict the ED load on the hospital for the near
future.
 More generally…
 Hospital-level load predictions to improve hospital
operations…

30.  Prediction:
 Internal demand for each hospital unit using data collected
from patients currently at the hospital
 External demand for each hospital unit using historical data
 Control:
 Increase supply: expedite discharges, transfer to other
hospitals/skilled nursing facilities, etc.
 Reduce/delay demand: close the hospital or parts of it to
outside transfers, divert ambulances, reschedule elective
surgeries, etc.
Machine
Learning
Operations
Research

31. Harvard Medical School: Wanyi Chen, PhD
UNC Statistics and Operations Research: Nilay Argon, PhD;
Yufeng Liu, PhD; Serhan Ziya, PhD
UNC School of Medicine (Emergency Medicine): Abhi Mehrotra,
MD, MBA
UNC School of Nursing: Debbie Travers, PhD, RN; Ben Linthicum,
MSN, PhD
Roundtable Analytics: Thomas Bohrmann, PhD; Kenneth Lopiano,
PhD