Using System Dynamics with Machine Learning for Modeling Patient Flow and Hospital Staffing Requirements

Abstract

Accurate forecasting is both art and science. For the science component, machine learning algorithms and tools have greatly advanced the ability to identify and dissect historical patterns in data. The art component, and the ability to insert tacit knowledge and domain expertise into the forecast has historically been a challenge. This paper will show how the combination of system dynamics modeling with machine learning gives data scientists and forecast modelers the ability to insert tacit knowledge into machine learning forecasts for improved accuracy and causal discovery. We will look at patient forecasts from Virginia Commonwealth University's Massey Cancer Center and its Bone Marrow Transplant (BMT) Clinic. From these forecasts we will examine underlying dynamics and estimate future staffing requirements.

Full text

Using System Dynamics with Machine Learning for Modeling Patient Flow and
Hospital Staffing Requirements
R. Jerome Dixon
Virginia Commonwealth University, School of Business,
Email: dixonrj@vcu.edu
ABSTRACT
Accurate forecasting is both art and science. For the science component, machine learning
algorithms and tools have greatly advanced the ability to identify and dissect historical patterns in
data. The art component, and the ability to insert tacit knowledge and domain expertise into the
forecast has historically been a challenge. This paper will show how the combination of system
dynamics modeling with machine learning gives data scientists and forecast modelers the ability to
insert tacit knowledge into machine learning forecasts for improved accuracy and causal discovery.
We will look at patient forecasts from Virginia Commonwealth University’s Massey Cancer Center
and its Bone Marrow Transplant (BMT) Clinic. From these forecasts we will examine underlying
dynamics and estimate future staffing requirements.
Keyword: Forecasting, System Dynamics, Causality, Machine Learning, Healthcare Analytics.
INTRODUCTION
This research started as a collaborative arrangement between Virginia Commonwealth
University’s (VCU) four schools and hospital. VCU’s School of Business, School of Engineering,
School of Arts, and the School of Medicine. Collaborators were collectively called the BEAM team.
VCU’s hospital (Medical College of Virginia (MCV)) would come up with quality improvement
initiatives and goals. The BEAM team would then review hospital initiatives, prioritize and allocate
resources between VCU’s four schools as deemed necessary. This project is a result.
Dr. McCarty (VCU’s Massey Cancer Center) requested a predictive model from historical data
that would estimate patient volume through the various clinical phases of the Bone Marrow
Transplant (BMT) process. This model would be used for capacity planning and resource
scheduling.
For understanding the Bone Marrow Transplant process, we will use process modeling with
Lean Six Sigma value stream and root cause analysis concepts for understanding. Process modeling
and initial analysis was performed by VCU’s School of Engineering. For predictive model
development we will use System Dynamics framework with machine learning to initiate and
calibrate our model. Here is our initial system dynamics model produced from process modeling for
Massey Cancer Center’s Bone Marrow Transplant Patient Flow.

Figure 1. Initial System Dynamics Model for Bone Marrow Transplant Forecasting
In our initial model, we have three structures. We have a structure for each type of transplant –
Allogenic and Autologous. We also have a structure to account for changing population age
demographics. Based on our research from the Federal Reserve Bank – Fifth District and the
University of Virginia’s Center of Public Policy, we expect increases in the age bands that are most
likely to require bone marrow transplants.
DOMAIN KNOWLEDGE AND RESEARCH
Our domain background was greatly influenced by meetings with Dr. McCarty, Dr. Catherine
Roberts, Judith Davis (RN), and Cheryl L. Jacocks-Terrell (MS). We also leveraged the Center for
International Blood and Marrow Transplant Research (CIBMTR), University of Virginia’s Weldon
Cooper Center for Public Service, and the Federal Reserve Bank of Richmond for additional reports
and statistics related to population health and metrics regarding changing local demographics.
From meetings with Massey Cancer Staff, we developed the below bone marrow process steps
that are performed by five (5) physicians, five (5) nurse practitioners/physician assistants at a
twenty-two (22) bed hospital facility.

Bone Marrow Transplant Process
Figure 2. Massey Bone Marrow Transplant Process
EXPLORATORY DATA ANALYSIS
We have electronic healthcare record (EHR) data for VCU’s Massey Cancer Center from January
2010 to February 2018. For exploratory data analysis we will use R/RStudio for data cleansing and
analysis, SAS Enterprise Miner for data visualization, forecasting, and analysis, and finally Tableau
for data visualization and analysis. Here are a few key visualizations for understanding and
developing our model parameters:

Tableau Output
Figure 3. Location of Bone Marrow Patients vs Census Age Distributions
Figure 3 is bone marrow patients overlaid over census age distributions. Our hypothesis is that since
bone marrow patients are of an older demographic (Figure 5) we should see more bone marrow
transplant patients in these older areas. Our hypothesis was incorrect. Our secondary hypothesis is
that we would see additional bone marrow patients in high growth areas (Figure 4). This hypothesis
was correct.
Figure 5. Age
Distributions by
Transplant Type
Figure 4. Age Distributions by Census Population Growth Areas

TIME SERIES FORECASTING
We perform a few minor data preparation steps in RStudio to prepare data for SAS Enterprise
Miner Time Series Analysis. We strip out extraneous columns and convert transaction column to
‘Numeric’ to capture bone marrow transplant single transaction counts. Our initial time series
forecasting results from SAS Enterprise Miner are below.
Figure 6. Allogenic Related Transplant Forecast
Figure 7. Allogenic Unrelated Forecast
Figure 8. Autologous Transplant Forecast

We see spikes in activity around July/August, a dip in activity in October with additional spikes in
activity November timeframe prior to the holidays.
SYSTEM DYNAMICS
System dynamics is a modeling methodology used to model complex systems by and using
differential equations with electrical engineering concepts to simulate real-world dynamic
problems. Jay Forrester invented this methodology in the 1960’s at MIT. The heart and soul of
system dynamics models are stocks and flows. A stock is something that stores an accumulation of
objects. A flow is something that depletes or increases a stock or accumulation of objects. These two
structures allow for complex feedback that is typically hard to capture for non-linear, dynamic
systems.
For our bone marrow patient flow model stocks will be patients at the various bone marrow
process steps, and flows will represent process cycle times and attrition rates that move patients
through the model.
Process Cycle Times
We use our electronic healthcare record data to calculate process cycle times for each step of the
process. We merge various datasets to form a longitudinal view of the patient from evaluation to
discharge and then calculate process cycle times as patient flows through various stages of the
transplant process.
Figure 9. Bone Marrow Process Cycle Times by Transplant Type
Figure 10. Bone Marrow Process Cycle Times Table Format

Attrition Rates
We use missing values (NAs) as a proxy for attrition rates from step to step. Initial count of Patients
in ‘Evaluations’ database is 2,408. Final number of patients receiving transplants is 1,334. We count
‘NAs’ through each process step to determine approximate attrition rates. Our results for cycle time
attrition rates are below.
Figure 11. Bone Marrow Attrition Rates
We also add the results from Figure 8 (Distribution of Patient Status after Transplant) to Step 6
(Att6) and our Follow Up timelines (+30, +60, +90, +180, +365) to calculate final model attrition
rates in our system dynamics model from Figure 1.
CAUSALITY/TACIT KNOWLEDGE
The Center for International Bone Marrow Transplant Research (CIBMTR) collects data from all the
bone marrow clinics in the United States and abroad. The data presented here is preliminary and
was obtained from the Coordinating Center of the Center for International Blood and Marrow
Transplant Research. The analysis has not been reviewed or approved by the Statistical or Scientific
Committees of the CIBMTR.
Figure 12. Center for International Blood and Marrow Transplant Research: United States 2010-2014

Here is a comparison of our Regional Virginia forecast with Massey Cancer Center forecast.
Figure 13. CIBMTR Regional Forecast vs Massey Cancer Center Local Forecast
We see the expected step increase in our Regional forecast but not in our local Massey forecast. This
is consistent with ‘the limits to growth’ system dynamics modeling structure. In our system, we
have bone marrow transplants reaching a certain carrying capacity and oscillating around that
number whereas the regional model is load-balancing transplants across all clinics. The regional
and local models both hit their peak for transplants in 2014 but then in 2015 both trend in opposite
directions. The period 2015 – 2016 is a point for additional causality research.
We implement our final forecast model with SAS Enterprise Miner Neural Network. We chose
this model due to the ability to scale up additional variables in future models. We use regional, local,
and seasonal data as input into our neural network. For a future iteration, we would like to include
diagnostic codes and genomics.
Figure 14. Final Patient Flow Forecast Model with SAS Enterprise Miner – HP Neural Network Node

FINAL MODEL
Figure 15. Final Patient Flow System Dynamics Model
After accounting for population growth with regional forecast model and aggregating transplant
types into an array, we have our final system dynamics model for calculating staffing requirements
during each phase of the bone marrow transplant process.
RESULTS AND IMPLEMENTATION
To implement the model’s results into hospital workflow we evaluated R’s deSolve package,
python’s PySD, and Microsoft Excel (MS Excel). Due to the granularity of our data we could develop
either mathematical models to simulate our results (deSolve or PySD) or use SAS Enterprise Miner
output data directly in a Microsoft Excel model. We decided to use Microsoft Excel due to our
client’s technology infrastructure and familiarity with Microsoft suite of tools.
We created an Excel dashboard that shows the time series forecast for all three types of
transplants (Autologous, Allogenic Unrelated, and Allogenic Related) by Quarter.
Figure 16. Forecasted Bone Marrow Transplants by Quarter

We then created a utility function in MS Excel for when user enters the first consult date and
Transplant Type, the model auto populates the remaining bone marrow process steps and
outpatient services based on our previously calculated BMT process cycle times.
Figure 17. Forecasted Staffing Requirements (dummy data)
Our table now contains projected staffing requirements for transplant date, length of stay,
outpatient plus 30 days, outpatient plus 60 days, and outpatient plus 90 days for planning Massey
Cancer Center staff requirements.
Next Steps
For project next steps, we would like to investigate further the policy or environmental change
that caused regional and local forecast to head in different directions for calendar year 2015. For
bone marrow transplant forecast accuracy, we would also like to evaluate nonlinear time series
forecasting methods for possible enhancements to our model. For staffing requirements, we would
like to add diagnostic data and additional clinical data (specifically genomic data) for any
improvements to bone marrow transplant cycle times, our staffing projections, and future cost
projections.
Medicaid expansion was recently approved for the state of Virginia. We would like to explore the
impacts of this further for what it means to Massey’s bone marrow transplant forecasts and
subsequent patient attrition rates.