Neural Networks Application on Emergency Department Load

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Neural Networks Application on Emergency Department Load
Neural Networks Application on Emergency Department Load Measurement
Edward Vitkin1,2, Boaz Carmeli1, Ohad Greenshpan1, Dorit Baras1, Yariv Marmor2
1
IBM Research – Haifa,
Haifa University Campus, Haifa 31905, Israel,
E-mail: [email protected] / [email protected] / [email protected] / [email protected]
2
Technion - Israel Institute of Technology,
Technion City, Haifa 32000 Israel,
E-mail: [email protected] / [email protected]
Abstract
The rising cost of healthcare services imposes pressure on healthcare providers to improve the
management of quality, efficiency and economics for their organisations. One of the most urgent
operational problems in hospitals is emergency department (ED) overcrowding. For optimizing the ED
operations one first needs to measure current crowding load level, which is very difficult task due to lack of
agreement on the major parameters and their contribution to the overall load.
This paper proposes Neural Networks based Load (NNL) measurement approach – an innovative
approach for measuring the real-time operational load within emergency departments targeting to overcome
the lack of agreement problem. NNL suggest a flexible framework—based on neural networks—that
calculates user-tuned load values, based on a set of well-defined operational and clinical indicators. The
operational load value is calculated by learning the weights of the raw operational indicators within a
particular emergency department without the need for implicit knowledge of true load values. We describe
the neural network structure used and explain the methods we used to calculate the ED operational load.
Major contributions of our work are the possibility to flexibly define user-specific function and the
innovative dynamic learning method used when no explicit calculation exist for creation of training set
Key words: Neural Networks (Computer), Operations Research, Workload, Emergency Department,
Machine Learning
1.
Introduction
The rising cost of healthcare services has been a subject of mounting importance and much discussion
worldwide. Ample explanations have been proposed, yet regardless of their cause, rising costs impose
pressure on healthcare providers to improve the management of quality, efficiency, and economics for
their organizations. Hospitals are one of the major players in the provisioning of health services and,
within hospitals, emergency department (ED) overcrowding is perhaps the most urgent operational
problem (Sinreich and Marmor 2005; Hall 2006; Green 2008). Overcrowding in hospital EDs leads to
excessive waiting times and unpleasant environments which, in turn, cause (1) poor service quality
(clinical, operational); (2) unnecessary pain and anxiety for patients; (3) negative emotions (in patients
and escorts) that sometimes escalate into violence against staff; (4) increased risk of clinical deterioration;
(5) ambulance diversion; (6) patients leaving without being seen (LWBS); (7) inflated staff workload; and
more (Derlet and Richards 2000).
To reduce overcrowding in hospital EDs and optimize ED operations, one first needs to understand the
current crowding load level. This means it is necessary to decide how the load on various resources
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should be defined, to whom it should be presented, and how it should be demonstrated. This task is
difficult for several reasons. First, there is no agreement about which parameters contribute to the load.
Second, there is no agreement regarding the level of contribution for these parameters, since the
conditions and the perception of each management team differ from hospital to hospital. Third, the ED is
a complex environment that involves various types of entities such as physicians, nurses, patients,
executives, etc.—each of whom may define the load function differently. Clearly, load has to be a usagedependent function. Moreover, the definition of load changes from time to time and needs to be updated.
Due to the large number of events and factors that change quickly and are critical to saving lives, it is
necessary to find a way to show a snapshot of the load in the system that is visible in real time and can be
easily interpreted.
1.1 Our Contribution
We present Neural Networks based Load (NNL) measurement approach – a novel approach based on
using neural networks to define and measure the emergency department operational load. NNL approach
deals with all the issues described earlier by providing a user-specific, yet useful, load definition. Tuning
towards user needs will results in a load score that directly reflects current ED situation as it is perceived
by this specific user. More so, optimization techniques using such load function definition are expected to
serve better than the generic functions for a specific ED setting, since NNL takes into account only the
items and optimization targets important for that specific ED. The system is based on artificial neural
networks (Haykin 1999) and enables a static mechanism for explicitly defining load functions. It also has
a dynamic learning mechanism, which enables the system to adapt to the specific ED settings and
perceptions of users with no explicit load function definitions (as in classic learning approaches).
The dynamic learning mechanism allows the system to present different load values for the same
objective situation. This is particularly useful for understanding the differences in operational load as
perceived by physicians, nurses, patients, and ED management. For example, ED manager may want to
investigate the system from operational and from quality of service points of views. To cope with the first
point manager may give a high weight to the number of patients and their length of stay in the system,
while to cope with the second manager may seek to reduce the patient’s waiting time in the different ED
queues. The neural networks mechanism allows dynamic adaptation for a specific ED setting. Even more,
the system is able to track operational bottle-necks by calculating flexible combinations of various basic
input, throughput, and output indicators.
The paper is organized as follows. The Methods section describes our proposed solution together with the
technical details of how the system was built. In the Results section, we describe the main results
achieved in in-silico simulations from implementing our neural networks techniques for measuring ED
load. The Discussion section deals with the benefits of using the neural network based system in diverse
and dynamic environments for process optimization and planning. We conclude with a summary of the
approach, the benefits of system, and directions for future research and development.
2.
Methods
Calculating and presenting the operational load in emergency departments is both extremely important
and very complex. We studied the various difficulties that arise in defining ED load value and delved into
the different ways users perceive the importance of basic load indicators. NNL approach includes the
definition of raw indicators, a new neural network structure, and the incorporation of iterative learning
from user feedback.
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This section provides a short background on neural networks and discusses our approach in more detail.
2.1 Neural Networks – Theoretical Background
Artificial neural networks (Haykin 1999) are mathematical representations of complex mathematical
functions. They are composed of units named perceptrons (Figure 1a) and arranged as a multi-layered
feed-forward network (Figure 1b) in which the outputs of a layer are the inputs of the next layer. The
motivation for this type of learning machine comes from the brain structure. Neural networks are used
successfully in many applications such as pattern classification, dimensionality reduction, and function
approximation (Khan et al 2001; Hinton and Salakhutdinov 2006; Hornik et al 1989). Because of its
origin, the nodes in these networks are often called neurons. Their greatest advantage is their simplicity,
in both representation and learning. In these networks, the number of required training examples relative
to the network structure is not very high compared to other machine learning solutions.
x , x ,..., x n n
w , w ,..., wn
Each perceptron is composed of n inputs 1 2
,
weights 1 2
, and an activation
(
)
T
x = (1, x1 ,..., x n ), w = (b, w1 ,..., wn ) .
function ϕ (⋅) . The output of the unit is v( x, w) = ϕ x w , where
Examples of activation functions are: sign functions ( ϕ (u ) = sign(u ) ), linear functions ( ϕ (u ) = u ), and
−u
logistic functions ( ϕ (u ) = 1 / 1 + e ). The type of activation function affects the ability of the network to
(
)
learn and is application-dependent. The units in different layers are connected in a feed-forward style to
determine the network structure (see Figure 1b). The exact structure is also application-dependent, and in
many cases, domain knowledge can help determine this structure.
(X
,y
)
M
X ∈ ℜn
y ∈ℜ
i
i i −1
Given a training set of the form
where i
is the input to the network and i
is the
expected output (or target function) of the network, the back propagation algorithm (Haykin 1999) can be
used to find a set of weights that minimizes the mean square error (MSE) between the expected output
and the current calculated output. There are two types of learning: offline (or batch) learning and online
learning. In offline learning, the entire training set is given in advance. In each iteration of the back
propagation algorithm, all the examples are taken into account when updating the weights. In online
learning, the examples are given one after the other and each learning iteration depends only on the
current example. This is typically used when the environment changes over time and the network is
trained to fit those changes.
Figure 1: (a) Single perceptron; (b) Multi-layer network
Generally we can divide all the network neurons into three major classes: input layer, middle or hidden
layer, and output layer.
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2.2 Input Layer – Raw Indicators
Over the course of healthcare research history, several tens and even hundreds of different load indicators
have been defined, such as the number of people in the ED or the percentage of patients arriving in
ambulances. (For an example of comprehensive indicators and partial comparison research, see Solberg et
al 2003.) Using NNL approach, users have to choose a subset of such indicators relevant to their specific
ED setting. Other option is to take all the available indicators and allow the system to learn the relevant
ones dynamically by updating the appropriate weights on the edges (look in Section 2.5 for more details
on the learning process). We recommend applying all the indicators at the same time slot (last hour, last
30 minutes, etc.) to avoid inconsistencies. Each chosen indicator serves as a single input to a neuron node
that is created in the input layer. For example, '
average doctor'
s occupancy'indicator is highly relevant
while calculating physicians load at the ED. This indicator is less significant while measuring load on
nurses.
2.3 Middle Layer – Network Structure
Two major options can be considered to create the middle layer: (a) a standard hidden layer, where each
neuron of the previous layer feeds all the neurons in the following layer, and (b) a manually created
clustering structure based on an understanding of the problem. In the NNL approach we used the second
option, which reveals several important additional abilities relevant to the problem at hand. Specially, a
manually created tree-like hierarchy of clusters of indicators makes the system more meaningful and
usable since each internal neuron preserves its operational meaning. Moreover, the network has a tree-like
connectivity neuron operation, meaning that it remains independent from the edges'weight. This allows
the user to back-trace the system load bottle-necks and get meaningful alerts on local problems even
before they start to affect the entire system. For example, ED manager can get an alert from the internal
neuron when CT and X-Ray stations start to be overloaded. This indicator combines all the inputs from
imaging services may point a bottleneck at that section of the ED. The alert may urge the ED manager, to
solve the problem before it grows and affects other facilities and the overall load situation.
2.4 Output Layer – Load Score
The network has a single output node, which is the top-level node of the tree-like indicators hierarchy
created in the input and middle layers.. The top-level output node summarizes ED operational load into a
single number. There is a need to replicate the middle and output layers if the ED manager needs to look
separately on the different load scores for the same ED settings .
2.5 Network Weighting – Gradient Iterative Learning from User Feedback
As explained in Section 2.1, learning edges'weights requires true values for a bunch of vectors (training
set). However, current problem settings do not suggest how to create such a bunch, since we do not have
a clear load definition. Thus, we have a classic chicken–and-egg situation. To define the load, we must
have a load definition. We overcome this issue by the following 3 steps: (1) initializing network edges'
weights randomly or manually (according to some ranking system); (2) calculating the average output
load score over a defined time period; and (3) normalizing the received load score over the calculated
average. Thus, the resulting network output has 100% load when the system is assumed to be at average
load, 200% when the load is twice as large as the average, etc. We found this representation intuitive and
meaningful.
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After these 3 steps we have a random set of initial weights on the edges which produce some output load
value. Now we are ready to receive feedback from users to fix the edge weights toward the desired value.
Even if users do not have an explicit knowledge of the desired load function they still can feedback
regarding the load gradient. For example, if the current load is 170% of the average, users can give
feedback if they “feel” that the system does not truly reflect the actual load. In our system we
implemented four feedback buttons; namely, “significantly more”, “significantly less”, “slightly more”,
and “slightly less” for achieving better learning performance. Testing different granularity approaches is
out of the scope of our research. Receiving the desired function gradient in addition to the predefined step
size (which can be a function of the learned vectors number) allows us to calibrate the network edges'
weight and load estimation by using standard back-propagation algorithm (Haykin 1999).
Using such learning settings we allow NNL to learn load from implicit load functions and to provide to
the user, which is the NNL“teacher”, a simple and comfortable feedback scenario.
Clearly, several issues are still open for additional research, such as initialization of weights, granularity
values, step sizes, system status representation, and more. We discuss some of these aspects while
describing a sample approach implementation based on Solberg’s research in the Results section.
3.
Results
3.1 Harnessing the Power of Neural Networks to Calculate Load in the ED
To demonstrate the advantages of our methodology, we built a neural network that represents the
collective knowledge presented in the exhaustive load measurement indicators review paper (Solberg et al
2003) and used it as our basic network for the load calculation (see Figure 2). For input, we took the set of
indicators that were defined in the review paper and combined and ranked them hierarchically. The
hierarchy in the network consists of four main layers:
1) Indicators Layer: This layer is the set of inputs and consists of thirty-one nodes corresponding to
twenty indicators that appear in the review paper (Solberg et al 2003). Several indicators were spliced to
match their definition. For example, indicator “ED Throughput time” was spliced into two nodes: one for
admitted patients and one for discharged patients. Other indicators were totally omitted due to the lack of
appropriate input simulation data. We made minor modifications to the network suggested in the paper,
based on data we collected using a simulator presented by Sinreich and Marmor (Sinreich and Marmor
2005). This simulator, also used by Wasserkrug et al (Wasserkrug et al 2009) and is based on a canonical
ED model, which was generated based on real life observations within numerous hospitals.
2) Concepts Layer: The thirty-one indicators in the indicators layer are connected (each indicator to a
single concept) to the following six concepts: patient demand, patient complexity, ED capacity, ED
efficiency, ED workload, and hospital efficiency. The hospital capacity concept was omitted due to a lack
of appropriate simulation data. We divided the ED efficiency concept into two sub-concepts to serve the
input and the throughput separately. This modification was made to keep the tree-like structure of the
network, the importance of which is explained in other sections (see Section 2.3 and 3.3).
3) Operational Stages Layer: The seven concepts are connected (one concept for each operational stage)
to the input, throughput, and output operational stages.
4) Load Score Layer: This output layer consists of a single node representing the total load function
score.
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Figure 2 – ED neural network view: the triangle is a total neuron, hexagons are the stage neurons,
rectangles are the concept neurons, and diamonds are input indicator neurons
As described in Section 2.1, we can learn the target function using either the static or dynamic method.
Both methods require knowledge of the true target function values on some set of input vectors. This
means that we have to present each such vector to an expert user and receive the desired function value in
return. However, this flow cannot be used because input vectors are often too long for human perception
and embedding. Moreover, the desired value of the target function cannot be explicitly calculated. In the
following paragraph we describe how we overcome both challenges.
Instead of presenting the input vector itself, we presented the current ED status using a patient-centric
dashboard (Figure 3). The patient-centric dashboard provides ED staff with information about the status
of each patient in the ED. Patient status is usually presented as a row within a table-like view. (This
approach is commonly used in several EDs around the world.) By working with the patient-centric
dashboard, the ED staff gained total insight regarding the operational ED load. We used this insight to
provide feedback to the back-propagation algorithm, which allows it to learn the required load function.
Figure 3 Dashboard snapshot. Load value (black line) is calculated as the percent of the average (green
line)
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The user provides feedback using the dedicated feedback buttons. For example, if users feel that the
represented load is far below the desired value, they push the bigger ‘+’ button and the system updates the
current load, increasing it by 10%. A similar update process (+1%, -1%, -10%) works for other feedback
buttons. Clearly, such feedback system can be easily implemented in any existing dashboard without
significant changes.
3.2 Learning Rate
To check our method’s learning ability, we defined a user profile based on Solberg et al 2003, who
measure ranks of “Early Warning”. This model assumes that the input, throughput, and output stages have
the same weight. The training process simulates the system run and receives user feedback. Evaluation is
then performed by calculating the MSE over 100 randomly sampled time points. Initially, all the network
weights were randomly generated, and on average, the network received feedback on every 10th vector.
The feedback was received as a push on one of the four buttons mentioned earlier. After receiving all of
the feedback, a total MSE over the testing set was calculated. Network demonstrated quick convergence
into the desired function as a function of the amount of feedback received by the system (Figure 4).
0.5
Test MSE
0.46
0.42
0.38
0.34
0.3
1
26
51
76
101
126
151
Number of User Clicks
176
Figure 4 – Average MSE on the test set
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3.3 Tracing Load and Bottlenecks
In our system, every neuron has an explicit operational meaning. Our network design keeps the tree-like
neuron hierarchy instead of the usual all-to-all connections. This allows each neuron to preserve its
operational meaning during the learning process. Conserving the tree-like structure allows the user to
track the current load back into the network and to gain a deeper understanding of the current load status
(Figure 5). Moreover, we can get an alert from any hierarchy level in the system if a certain neuron
becomes overloaded. For example, if the current system load is only 40% of the average but the CT room
is overcrowded, the appropriate neuron’s status will reach the high mark and can alert the user if the
neuron is preconfigured accordingly.
Figure 5 – Tracing load: Green line indicates total load, orange line indicates throughput. The rise in the
total load is caused by increasing the load on the throughput neuron. Tracing it further, we can deduce
that the peak in throughput was caused by elevation of the ED workload concept neuron
4.
Conclusion
In this paper, we introduced NNL – a novel approach to learning functions that cannot be explicitly
defined, such as the load in Emergency Departments. The neural network development approach
stemmed from understanding that the ED load is influenced by a large number of factors that are difficult
for humans and machines to consider together. The system was validated in-silico on the comprehensive
research by Solberg et al 2003. While Solberg provides a comprehensive set of load measures and
concept categories, he does not suggest a straightforward way to use these measurements in real-life
scenarios. Our experience shows that it is not practical to establish a standard operational load model that
fits all EDs due to the inherent differences between them. Hence, we are suggesting an adaptive approach
based on neural networks. We showed that any existing load definition can be easily calculated by
adapting the edge weight of a single basic indicator, or a combination of several. Moreover, our approach
allows defining target- or user-oriented load functions, which can be useful for further optimization
purposes. Its implementation is straightforward and can be easily integrated in any current ED dashboard.
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5.
References
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