A System Simulation Model for Type 2 Diabetes in the
Saskatoon Health Region
Jin Zhang
Media Access and Production, University of Saskatchewan
28 Campus Drive, Saskatoon, SK S7N OX1
(306) 966-2500
Jin.Zhang@usask.ca
Nathaniel Osgood
Winfried Grassmann
Department of Computer Science, University of Saskatchewan
110 Science Place, Saskatoon, SK S7N 5C9
(306) 966-4898
grassman@cs.usask.ca and osgood@cs.usask.ca
Roland Dyck
College of Medicine
107 Wiggins Road, Saskatoon, SK S7N 5E5
(306) 966-7985
Roland.Dyck@usask.ca
Abstract
We describe a System Dynamics model for analysing and scenario analysis in regard to type 2
diabetes. The model has two parts, a normoglycemic part, and a hyperglycemic part. The
normoglycemic part is broken down according to weight into normal weight, overweight and
obese stocks, all indexed by age, sex and ethnicity, the last consisting of Registered Indian and
others. The hyperglycemic part consists of two streams, diagnosed and undiagnosed, both
divided according to the severity of hyperglycemia, starting with prediabetes. The model is
distinguished from many past models by its more detailed representation of weight, diabetes-
related cardiovascular risk, age, and ethnicity effects. The model was carefully calibrated, using
a methodology discussed here. Some projections and policy suggestions are presented.
Keywords: Vensim, Diabetes, Calibration, Health
Introduction
Diabetes Mellitus, colloquially referred as “diabetes”, is a chronic syndrome that results from
insufficient secretion or inefficient use of insulin. The prevalence of Diabetes Mellitus has
increased rapidly due to population aging, urbanization, and increasing prevalence of obesity.
An estimated 171 million people suffered from diabetes worldwide in the year 2000; the
estimated number grew to more than 180 million in the year 2006. The diabetic population is
projected to increase to 366 million by 2030 [1, 2]. In Canada, the prevalence of diabetes is
1
high and rapidly increasing. National Diabetes Surveillance System (NDSS) data estimated that
1.128 million people — about 4.8% of the total 20+ age population — were diagnosed with
diabetes during 1998-99. If one factors in the estimate of the undiagnosed diabetics
population, there were a total of 1.7 million Canadians with diabetes during 1998-99 [3, 4]. A
recent report from the NDSS shows that the prevalence of diagnosed diabetes increased to
approximately 1.783 million in the year 2004-05 [5]. The prevalence including undiagnosed
diabetics increased to more than 2 million and is expected to rise to 3 million by the end of the
decade [4, 6].
Saskatoon, a city in Saskatchewan, a Canadian prairie province, is not an exception to
Canadian’s high diabetes prevalence. Diabetes is the chronic disease with the third highest
mortality burden in the Saskatoon Health Region (SHR) demographically. Obesity is a well-
known risk factor of developing Type 2 diabetes. A high prevalence of obesity in the Saskatoon
Health Region makes a considerable contribution to the high diabetes prevalence. The cold
winters in Saskatchewan restrict outdoor physical activities and limited recreation facilities
restrict indoor physical activities. Many urban residents also find it difficult and costly to access
healthier food. Many people in the Saskatoon Health Region are overweight or obese. A total
of 30.63% of the residents in the Saskatoon Health Region were overweight and 16.88% were
obese in 2005 [8]. Partly as the consequence of the high prevalence of obesity, diabetes is
prevalent in the Saskatoon Health Region.
Aboriginal people are a higher risk ethnic group for having diabetes in North America [15,16].
About 8.7% of the populations of the Saskatoon Health Region are of aboriginal origin, and over
50% of those are Status Indians based on Statistics Canada 2001 data. This relatively high
percentage of aboriginal population when compared to other areas in Canada also contributes
to the elevated diabetes prevalence seen in the SHR.
With the limited budget available for preventing and treating diabetes and its complications,
cost-effective intervention policies are needed in order to slow the increase of prevalence of
diabetes and lower the burdens imposed by diabetes, and save as many lives as possible.
For this reason, a group was formed at the University of Saskatchewan, analyzing this problem,
which had the full support of the Saskatoon Health Region. One of the members of the group,
Dr. Roland Dyck, was a clinician with extensive experience with diabetes, and he has published
a number of papers in this area. It was decided to use a Systems Dynamics approach to analyze
this problem, and build a detailed model using Vensim. For details of the model, see [7]. When
constructing our model, we relied on some earlier studies. In particular, the U.S. Centers for
Disease Control and Prevention (CDC) started a modeling project in 2003 to construct a System
Dynamic model of diabetes [10]. The project team used the diabetes model to gain a better
understanding of the diabetes burden in the U.S. and to evaluate possible interventions. The
model simulates the diabetes onset process using the population at risk and the diabetes
progression. After calibrating the model with historical data, the project team forecasted
growth of diabetes and prediabetes prevalence through 2050 as the baseline for interventions
evaluation. Another study we used was done by Rees et al. at Synergia Limited who developed
a System Dynamics model to assist development of strategic diabetes policy for Manukau, a
large multi-cultural city in New Zealand [11]. For our studies, we relied on both models
extensively. However, we added considerable detail to the model, for instance, we indexed the
diabetes population according to age, refined the representation of the progression of
diabetes, and we adapted the model to the situation in Saskatchewan.
The Vensim Model
Like the CDC model and the New Zealand model, our model contains two core components: the
normoglycemic population and the hyperglycemic population. The normoglycemic population
section represents people in the SHR whose blood glucose levels lie within a normal range. This
population group is divided into three major subgroups by weight categories: normal weight,
overweight and obese (see Figure 1). Within a subgroup, the population is classified into
smaller scale subgroups by age, ethnicity and gender. There are 17 different age groups, using
commonly used 5-year age categories: 0 to 4, 5 to 9, 10 to 14, 15 to 19, 20 to 24, 25 to 29, 30 to
34, 35 to 39, 40 to 44, 45 to 49, 50 to 54, 55 to 59, 60 to 64, 65 to 79, 70 to 74, 75 to 79 and 80
plus. The ethnicity is Registered Indian (RI) and others, the non-RI. Age, ethnicity and gender
are represented using subscripts in equations in order to keep the model clean.
As one can see from Figure 1, there is a progression from the normal weight stock to the
overweight stock, and finally to the obese stock. All stocks have inflows through births, and
outflows through deaths of all causes.
= o © o 9
jormal weight being b ight ‘
being bor normal ms a eee eight! “Ybeal being bom obese A sece coe
weight pasa cas all causes
Normal Weight General] __sz_y,.| Overweight General |_s7__..! Obese General Population
Population becoming Population ieeaiecbee
overweight
normal weight overweight obese population
population aging population aging aging
Figure 1: Normoglycemic Population Structure
All normoglycemic subpopulations have a risk of developing hyperglycemia; young age groups
have lower risks, elderly age groups have higher risks; the population with lower BMI has lower
risks, and the population with higher BMI has higher risks. Reflecting these, a developing
prediabetes flow is associated with all general population stocks. Again, these outflows depend
on the age, the ethnicity, and the gender. Of course, the outflows are higher for overweight and
obese people. These outflows are omitted from Figure 1.
We now come to the component dealing with the hyperglycemic population (see Figure 2). Like
in the CDC model and in the New Zealand model, we have two streams, an undiagnosed (undx),
and a diagnosed (dx) stream. Each stream contains a progression of the severity of the
diabetes. It starts with prediabetes, continues with diabetes without complications, and
progresses to diabetes with early-stage macrovascular complications. The final stage is late
stage macrovascular complications which we assume is always diagnosed. Hence, for this last
stage, there is no undiagnosed stock. In summary, there an Undx Prediabetic Population a Dx
Prediabetic population, and Undx Diabetic population without complications, a Dx Diabetic
population without complications, and so on. The term diagnosis as used here means diagnosis
of the correct stage. Consequently, there is a flow from dx Prediabetic Population to the undx
Diabetes Without Complications population, meaning that though prediabetes is diagnosed,
diabetes is not. As in the component dealing with normoglycemia, all populations are also
classified by age, ethnicity and gender. As before, the progression to the next stage depends on
these characteristics. Also, at each stage, there are outflows due to deaths. They are omitted in
Figure 2.
It is possible that persons having prediabetes may recover. This leads to three recovery
outflows from prediabetes: one to the Normal General Population, one to the Overweight
General Population, and one to the Obese General Population.
Gcvcoping a eal aaee
developing md betes a
emacs pednbtes abrtes i Die
Und Dibet without Say St
ame +e 2. | aeons
‘ation (Complication ‘the first major macrovascular
| Pogataion guess 5
developing Uhdx diabetes hee
predabetes "from dr ledabetes
a cat sage
compton agross
@sedweeusocececdocecsces Ee er foornn nnn nee ot
[Dx Diabetic with Early |Dx Diabetic with Late]
DaPredibeis [|__| EE See heace Shee ics
Population —F developing dx diabetes ‘Popa ee) Complication Comptcsion |
fiom dx predabates developing em stage] Person | dba strive oma the L__POP H
ation from dr first major macrovascalar '
'
Figure 2. Development of Hyperglycemia
The stages of diabetes are characterized as follows. Patients with early stage macrovascular
stocks start to develop macrovascular diseases caused by diabetes, such as coronary diseases
and cerebrovascular disease.
The population in the final diabetes progression stage is the population who survived from the
first attack of diabetes related macrovascular diseases, such as a heart attack or stroke. After
the first attack of macrovascular diseases, any undiagnosed macrovascular complication is
assumed manifest itself; hence, there is no undiagnosed population stock represented in the
final stage. Diabetic patients stay in this stage until their death.
The Determinations of the Parameter Values and the Initial Values
Because of indexing by age, ethnicity and gender, there is a great number of stocks: there are
10 progression stages, 17 age groups, 2 ethnicities and 2 sexes, which means that there are 680
stocks in total. All these stocks have to be initialized, that is, we had to find 680 initial values,
which had to be obtained from existing data bases or scientific papers, or, if they were missing,
which had to be inferred by using analogies or expert opinion. Finding initial value for
undiagnosed hyperglycemic stocks, in particular, posed a substantial challenge. There are also
a great number of flows between the stocks, and to find the rates of these flows, we used
numerous equations, and the parameter of these equations had to be obtained. Some of them
were available from our data sources, and others were determined by analogy and/or expert
opinion.
Our data sources can be grouped into four categories: local health authority reports, statistical
surveys and the Canadian Census, research papers, and experts’ opinion. We first consulted
data from local health authority reports. The Saskatoon Health Region Authority releases a
report every year summarizing health region operations in the previous year [8, 9, 12, 13].
These annual reports contain, among others, demographic information and its dynamics about
the health region. In particular, they provide detailed demographic information especially
regarding residents with Registered Indian status, who are at particularly high risk with respect
to diabetes [16]. Annual reports describe the health status of residents in the region by using
important health indicators; prevalence of diabetes is one of health indicators in the reports.
We were able to find the diabetes prevalence in the health region directly from the reports.
Besides the annual reports, the Saskatoon Health Region Authority released a detailed health
status report every five years [14]. This report listed some key indicators, including population
size, structure, birth rate, death rate and more, as attributes of overall health status of SHR
population. The values of many parameters in our model were drawn from in this report.
Statistical surveys are powerful instruments for collecting quantitative information ina
population. They obtain first-hand raw information directly from the targeted population. For
our research we obtained data from several statistical surveys, such as the National Population
Health Survey (NPHS), the Canadian Community Health Survey (CCHS) and Canadian Census,
collected by Statistics Canada and other agencies.
We reviewed some pioneering studies of the applications of the System Dynamics
methodology, which, aside from helping us greatly to build our model, also provided some
useful data. Two of these studies were specifically for diabetes and intervention: the CDC
model [10] and the New Zealand model [11]. These two models targeted a different population,
they maintained a similar structure, and required similar data, and we were therefore able to
use some common data (e.g. concerning disease progression rates) for the initial values of
parameters in our model.
We also consulted with some local diabetes experts. Their opinions and valuable suggestions
provided a good starting point for parameterization of the model. Their opinion also gave us
reasonable value ranges when we could not find accurate values for model parameters.
Though we spend a considerable time searching for data to find parameter values and initial
values, and we looked at all available data very carefully, there was no way to find all these
values in this fashion. To find the remaining values, we used calibration. Hence, we selected
additional historical time series, and for each of these historical series, we added the necessary
code to create the corresponding model. We then determined the unknown parameter in such
a way that the model series were as close as possible to the historical time series. We selected
the following five time series: the total population in the SHR, the normoglycemic population in
the SHR, the total mortality rate in the SHR, the prevalence rate of diabetes in the SHR and the
incidence rate of diabetes in the SHR. All these series were broken down according to age,
ethnicity and sex. We then minimized the squared relative differences between the model
series and the historical series, using the following formula:
h-m
discrepancy = aim |*
|
Here, h denotes the historical series, and m the model series.
In the first runs, we just added all discrepancies and minimized their sum. When doing this, the
results were unsatisfactory for the following reason. Some of the historical data had very small
sample sizes, whereas in other cases, the samples sizes were huge. For instance, the number of
registered Indians below 25 years of age with diabetes is very small, whereas the corresponding
population of the normoglycemic population of the SHR below 25 is large. The problem is now
that a better fit to some data tends to cause a worse fit for others. Data from small samples are
affected much more by random variations than data from large samples. When using equal
weights, calibration may try to adjust parameters to what are essentially random variations at
the expense of obtaining a good fit for data based on large samples. In our model, this led to
substantial distortions. For this reason, it was necessary to give data based on small samples a
smaller weight than the data based on large samples. Hence, before adding the discrepancies,
we multiplied them by some weight, were the weight reflected the sample size of the historical
data.
In this way, we could estimate unknown initial values, certain delays, and a number of
parameters affecting the rates of moving between the stocks by minimizing the squared
differences. Minimizing squared differences is, of course, well known from statistics, but it can
also be justified by other arguments. For instance, it avoids having very large deviations.
Using the Model to Predict the Diabetes Burden, and Find Policies for
Improvements
Our model is based on earlier models which we improved in several important aspects. One
important change over the New Zealand model was that we added the age structure to the
hyperglycemic stocks. Of course, our model is not perfect either. For instance, our simulation
does not consider immigration and emigration from and to the SHR. One reason for this is that
the migration patterns cannot predicted very well, and data are lacking.
Since it takes a long time for people to develop diabetes, we need a long time horizon for our
simulation to get reasonable results. Hence, we ran the model to simulate the diabetes burden
from year 2001 to year 2101 based on current conditions. To interpret the results of our
simulation, it is important to consider the population size and its age structure.
Figure 3 illustrates the trajectory of the total population in the SHR. The projection of the total
population slowly increases during the first 20 years of the simulation period. After the total
population reaches its peak level around the year 2025, it starts to decrease slowly due to the
low birth rates.
Total population
400,000
325,000
250,000
175,000 Pree
100,000
2001 2011 2021 2031 2041 2051 2061 2071 2081 2091 2101
Time (Y ear)
Total population : v3-27 Base Run 100 Y ears
Figure 3. Total Population
The diabetic population in the SHR is the most important indicator of diabetes burden. To
interpret the results obtained, note that due to the baby boomers, the population will get older
for some time, but after the bulk of the baby boomers has gone through, the average age in the
population will decrease. Since older people are more likely to get diabetes, this means that the
incidence of diabetes will at first increase, but it will decrease in the long run. Hence, the
prevalence of diabetes shows a similar pattern as the population. The total diabetic population
is, of course, the product of the two time series, which means that this pattern is even
strengthened as show in Figure 4.
Total diabetic population
40,000
30.000
20,000
Ly
10,000
0
2001 2011 2021 2031 2041 2051 2061 2071 2081 2091 2101
Time (Year)
Total diabetic population : v3-27 Base Run 100 Years. ———H4H4HH——.
Figure 4. Diabetic Population
To highlight the importance of diabetes, let us consider relative figures. The population in the
SHR in 2001 was roughly 215,000, and it is forecast to increase to 220,000 by 2031. The number
of diabetes patients in 2001 was roughly 14,200, which is 6.9 percent of the population. This
increases to 28,800, which is 13.1 percent of the population by 2031. Hence, the diabetes
burden increases significantly. One reason for this increase is the prevalence of overweight and
obese people, which increases from 14.7% in 2001 to 19.4% in 2031. The increase of obesity
and the resulting increase in the diabetes burden make the introduction of policies ameliorating
the situation imperative. For this reason, we first conducted a sensitivity analysis to find which
parameters are most sensitive to changes, and we then tried a number of policies. We changed
a number of parameters by plus or minus 20% and observed the effects. We found that the
overweight incidence rate and the obesity incidence rate both have a strong impact on the
diabetes population, especially if they are combined. Also, the number of years to develop
diabetes from prediabetes has a strong effect. This affects two rates, the rate from undx
prediabetes to diabetes, and the rate from dx prediabetes to diabetes.
Intervention policies based on lowering the overweight incidence rate and the obesity
incidence rate - such as fitness classes, support for recreational facilities, and programs to make
nutritious food more affordable and accessible when compared with less nutritious food, can
10
help to lower the diabetes prevalence, as shown in the Figure 5. In this figure, the upper line
represents the projected diabetes prevalence in the base case, while the lower line represent
the projected diabetes prevalence resulting from lowering the overweight incidence rate and
obesity incidence rate fivefold. As one can see, these policies are very effective in slowing
down the rate at which the diabetic population and diabetes prevalence are rising, and with it
the diabetes related burdens.
These kinds of interventions will not lower the diabetic population from its original path
immediately since they are not intervening directly on the diabetic population directly. The
changes in the overweight and obese population will affect the diabetic population with levels
of delays and manifest their impacts in the long run.
total prevalence of diagnosed diabetes
Figure 5. Changes in Diabetes Prevalence from Lowering Overweight Incidence Rate and Obese
Incidence Rate Fivefold
If we implement an intervention policy to delay diabetes onset in the prediabetic population, it
could lower diabetes incidence and the diabetes prevalence greatly. Figure 6 illustrates the
improvement in the diabetes prevalence and the number of new incident cases by doubling the
average years to develop diabetes from undiagnosed prediabetes and the average years to
develop diabetes from diagnosed prediabetes. The diabetes prevalence and incident of new
cases (illustrated by bottom lines) are much lower than the baseline. Hence, using measures to
11
increase the time to pass from prediabetes to diabetes is effective in reducing the diabetes
burden.
total prevalence of diagnosed diabetes
Time (Year)
Figure 6. Changes in Diabetes Prevalence from Doubling Average Years to Develop Diabetes
from Diagnosed Prediabetes and Undiagnosed Prediabetes
Conclusions
In this paper, we discussed a model used to gain insight into the burden caused by diabetes. We
will continue to refine this model, and to use it to further our study in this important area.
Unfortunately, the policies we suggest only work over relatively long time scale, much longer
than the typical planning horizon of policy makers, and this may make the introduction of these
policies difficult.
REFERENCES
[1] S. Wild, G. Roglic, A. Green, R. Sicree and H. King. “Global Prevalence of Diabetes:
Estimates for the year 2000 and projections for 2030.” Diabetes Care, vol. 27, pp. 1047-
1053, Oct. 2004.
12
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
{10]
World Health Organization. “Fact Sheet No312, Diabetes.” Internet:
http://www.who.int/mediacentre/factsheets/fs312/en/, Sep. 2006. [March 2007].
Health Canada. (Jan. 2003). Diabetes in Canada. (a4 Edition). [On-line] Available:
http://www. phac-aspc.gc.ca/publicat/dic-dac2/pdf/dic-dac2_en.pdf. [Mar. 2007].
Canadian Diabetes Association. “Diabetes Facts.” Internet:
http://www.diabetes.ca/Files/Diabetes Fact Sheet Mar04.pdf, Mar. 2004. [Mar. 2007].
National Diabetes Surveillance System. “Diabetes in Canada: Highlights from the
National Diabetes Surveillance System, 2004-2005.” Internet: http://www.phac-
aspc.gc.ca/publicat/2008/dicndss-dacsnsd-04-05/pwdd-iadd-eng.php, Apr. 23, 2008.
[June. 2011].
Canadian Diabetes Association. “The Prevalence and costs of diabetes.” Internet:
http://www. diabetes.ca/Files/prevalence-and-costs.pdf. [June 2011].
J. Zhang. A System Simulation Model for Type 2 Diabetes in the Saskatoon Health
Region, M. Sc. Thesis, Department of Computer Science, University of Saskatchewan,
July 2011.
Saskatoon Regional Health Authority. “2006-2007 Annual Report to the Minister of
Health Living Services.” Internet:
http://www.saskatoonhealthregion.ca/about_us/documents/shr annual report 2006 07.p
df, Jul. 2007. [June 2011].
Saskatoon Regional Health Authority. “2004-2005 Annual Report.” Internet:
http://www.saskatoonhealthregion.ca/about_us/documents/shr_annual_report_2004 _05.p
df, Jul, 2005. [June 2011).
J. Homer, A. Jones, D. Seville, J. Essien, B. Milstein and D. Murphy. “The CDC’s
Diabetes System Modeling Project Developing a New Tool for Chronic Disease
13
(11]
(12]
(13]
(14]
(15]
[16]
Prevention and Control,” in Proc. 22"¢ International Conference of the System Dynamics
Society. July 2004.
D. Rees and B. Orr-Walker. System Dynamics Modelling as a Tool in Healthcare
Planning. [On-line]. Available:
ftp://vps224.2day.com/assets/File/Publications/System% 20D ynamics% 20M odelling%20
as%20a%20T 001% 20in% 20Healthcare%20Planning.pdf. [June 2011].
Saskatoon Health Region. “2003-2004 Annual Report.” Internet:
http://www.saskatoonhealthregion.ca/about_us/documents/shr annual report 2003 04.p
df. Mar. 2004. [June 2011].
Saskatoon Regional Health Authority. “2005-2006 Annual Report to the Minister of
Health and the Minister of Healthy Living Services.” Internet:
http://www.saskatoonhealthregion.ca/about_us/documents/shr annual report 2005 06.p
df. Jul. 2006. [June 2011].
Saskatoon Health Region. “2004 Health Status Report.” Internet:
http://www.saskatoonhealthregion.ca/your_health/ps_public_health_profinfo.htm.
2004.[Sep. 2008].
P.W. Frank, H.C. Looker, S. Kobes, L. Touger, P.A. Tataranni, R.L. Hanson and W.C.
Knowler. “Gestational Glucose Tolerance and Risk of Type 2 Diabetes in Y oung Pima
Indian Offspring.” Diabetes, vol. 55, issue 2, pp. 460-465. Feb. 2006.
R. Dyck, N. Osgood, T.H. Lin, A. Gao, M.R. Stang. “Epidemiology of diabetes mellitus
among First Nations and non-First Nations adults.” Canadian Medical Association
Journal, vol. 182, no. 3, pp. 249-256. Jan. 18, 2010.
14
