DEVELOPING SIMULATION DYNAMIC MODELS OF BREAST CANCER
SCREENING
Michael J Fett
Medical Advisor
Department of Health and Aged Care
PO Box 9849
CANBERRA ACT 2601
AUSTRALIA
michael.fett@health.gov.au
Within the health field, there appear to be few system dynamic models available for
examining major public policy options. In the field of breast cancer screening, the
results of several simulation models have been published'***>*, but none of the
models uses system dynamic modelling. This paper describes the development of two
system dynamic models of mammographic (X-ray) screening for breast cancer, and
illustrates their use.
The purposes of system dynamic models can be grouped under four headings:
1. Elucidating systems, their components and their inter-relationships
2. Developing cognitive and group processes (eg systems thinking, shared
understanding, team building)
3. Identifying information and knowledge gaps
4. Predicting and planning the future
For the first two purposes, models need not be based on data, although data-based
models can be used for these purposes. For the second two purposes, the quantity and
quality of data used in the model are crucial. Models that are heavily based on
empirical data (i.e. quantitative information) may be used for all four purposes, while
models that have a limited underpinning in data can only be used, reliably, for the first
two.
Here we present attempts to build models for mammography screening that rely
heavily on published data. If models can be constructed using published input data
and the results of these models can replicate published output data, then a case can be
made for using these models for health policy analysis. By ‘input data’, we mean data
that inform the workings of the model, and by ‘output data’, we mean the results that
the model calculates from the input data.
To examine the potential usefulness of system dynamic modelling for public health
policy analysis, the author attempted to build two data-based models of breast cancer
screening: The landmark trial of mammography known as the Swedish Two County
trial, which was conducted from the late 1970’s to late 1980’s,’ and the Australian
BreastScreen Program’, which is a national program offering mammographic
screening to all women aged 50-69 years. The models were build in Powersim
Constructor version 2.51 (4008) (Powersim AS, Isdalsto, 1998).
Breast cancer screening was selected as the topic for model building for three reasons:
the significance of breast cancer as a population health problem, the availability of
published research studies and extensive relevant Australian population data on breast
cancer, and the presence of a large national screening program in Australia which
might benefit from any policy analysis that could be undertaken with the models.
Breast cancer screening is well suited to system dynamic modelling because of the
presence of many time-related phenomena. These include: trends in breast cancer
incidence and mortality, trends in number of women screened, changing population
numbers, sojourn time of pre-clinical breast cancer (the time between a cancer being
detectable by screening and presenting clinically) and survival time following the
development of cancer.
Tables | and 2 shows the data stocks and flows, and their methods of calculation, for
both mammography models. Table 1 runs from the initial population to the
development of breast cancer. Table 2 runs from the stock of breast cancers to death
from breast cancer, the calculation of performance indicators and using the models for
policy analysis.
Stock or flow
Operation of Swedish trial model
Operation of Australian
screening program model
where it differs from
Swedish trial model
Population Initial population by (Study and A dynamic model of the
prior to Control) group and age’. Preclinical | Australian female population
development cases are subtracted from the initial by age from 1966 to 2015,
of breast population as they occur. The from Census and
cancer population ages each year. projections'*!'"3,
Developing Breast cancer-free population Australian population
preclinical multiplied by age-specific breast multiplied by age-specific
cancer cancer incidence rates for Sweden breast cancer incidence rates
1972-75". Incidence rate can be for Australia for 1983'°.
calibrated.
Cases of Population of preclinical cases ages
preclinical each year. Records number of years
cancer since preclinical cancer developed
(up to maximum: the sojourn
period’).
Detecting Number of preclinical cases Number of preclinical cases
cancer by multiplied by screening policies (age | multiplied by past
screening range and frequency), participation (historical) screening rates'’
by women"’, and screening and by possible future
sensitivity and specificity’. screening policies (age range
Overdiagnosis by screening can be and screening interval) using
calibrated. past or target'* participation
rates.
Detecting Preclinical cancers that reach the end
cancer of their age-specific sojourn time and
clinically after
sojourn time
have not been screen detected, are
detected clinically.
Table 1 Data stocks, flows and calculations to simulate the development of breast
cancer
Stock or flow
Operation of Swedish trial model
Operation of Australian
screening program model
where it differs from
Swedish trial model
Cases of
screen
detected and
clinically
detected breast
cancer
Population of clinical cases ages
each year. Records number of years
since cancer was detected.
Breast cancer cases
developing or detected each
year are summed into 5 y
age groups and divided by
population to calculate 5 y
age group incidence rates.
Applying
mortality
curves for
screen
detected and
clinically
detected
cancer
Use proportion dying each year from
breast cancer to calculate number of
breast cancer deaths each year.
Different mortality curves are used
for screen and clinically detected
cancer’’. Curves can be calibrated.
Breast cancer
deaths
Breast cancer deaths each year
summed to give cumulative breast
cancer deaths in Study and Control
groups.
Breast cancer deaths each
year are summed within 5 y
age groups and divided by
population to calculate 5 y
age group death rates.
Performance Cumulative number of deaths from Death rates and incidence
indicators are | breast cancer in Study and Control rates are calculated for each
calculated groups are divided by respective 5 y age group. These are
initial populations to calculate combined into age
simulated cumulative death rates standardised death rates and
over 15 y study period. incidence rates using a
Cumulative death rate of Study standard population.
group are divided by cumulative These simulated data are
death rate of Control group to compared with observed age
calculate simulated mortality rate standardised breast cancer
ratios. These simulated mortality death rates and incidence
data are compared with observed rates”.
mortality data’.
Model used Confirmed quantitative approach to | Vary age range and
for policy building system dynamic models of | screening interval to assess
analysis breast cancer screening. impact of different screening
policies on age standardised
breast cancer death rates.
Table 2 Data stocks, flows and calculations to simulate transition from cases of
breast cancer to death from breast cancer, calculation of performance indicators and
policy analysis
The listings of stocks and flows in Tables | and 2 show that the mammography
models are linear.
In the Swedish trial, communities were randomly assigned to either the Study or
Control group. At the start of the trial (the time of randomisation), women in the
Study group were offered breast cancer screening and those in the Control group were
not. After eight years, the trial ceased and women in the Control group were then
offered screening'*. Mortality in the two groups was followed for 14 years from the
time of randomisation. The Swedish trial simulation presented here is confined to
women aged 50 to 64 years at entry because of the availability of cumulative
mortality data for women in this age range *'. In the 50-64 y age group, there were
approximately 35,300 women in the Study group and 25,000 in the Control group.
Without calibration, there is quantitatively good agreement between the observed and
simulated cumulative breast cancer death rates (Figure 1). That is, the observed and
simulated rates are well within an order of magnitude and the Study/ Control death
rate ratios are similar for the observed and simulated data.
600,
1 Control group observed
< soo} mortality
_o 2 Control group simulated
gé mortality
£2 00 3 Study group observed
oo z mortality
ra} 4 Study group simulated
Bo 300} 1 mortality
5S
ve 24 Settings:
ZB 200]
B> Incidence calibrator 1.00
32
Ep Over-diagnosis factor 1.00
oO
£ Mortality curve calibration:
cD 1.00
SD 1.00
Years since randomisation
Figure 1 Observed and simulated cumulative breast cancer death rate Swedish trial
model - uncalibrated
Four parameters can be calibrated: the breast cancer incidence rate, the degree of
over-diagnosis of breast cancer by screening (whereby screening detects ‘cancers’ that
would not otherwise have become clinically apparent) and the mortality (survival)
curves for clinically detected and screen detected cancers. It should be noted that in
both the Study and Control groups, both clinically detected and screen detected
cancers occur, but in different proportions and at different times.
The survival curves that were subject to calibration come from an analysis of the
survival of women with breast cancer in South Australia’. The screen detected
mortality curve was derived from information on breast cancer tumour characteristics
w
of women with cancers that were diagnosed by the South Australian Breast X-ray
Service combined with information on survival by tumour characteristics from the
Swedish trial””*.
The clinically detected mortality curve was derived from information on breast cancer
tumour characteristics of women with breast cancer that was diagnosed outside the
South Australian Breast X-ray Service. An unknown proportion of these may have
been detected by mammography outside the screening program. Thus, this curve is
likely to be intermediate between the survival curves of cancers that are solely screen
detected and cancers that are solely clinically detected.
With calibration, the correspondence between the observed and simulated cumulative
breast cancer death rates could be improved substantially by adjusting the survival
curves for clinically detected and screen detected breast cancers (Figure 2).
600-
1 Control group observed
< 500 mortality
io 2 Control group simulated
gs mortality
§ = 400. 3 Study group observed
oe a mortality
38 A 4 Study group simulated
8S 300 mortality
ae Setti
ge Si ettings:
22 200.
BS Incidence calibrator 1.00
a2
E £100 & Over-diagnosis factor 1.00
3 r
£ e Mortality curve calibration:
or cD 1.25
0 5 10 sD 0.60
Years since randomisation
Figure 2. Observed and simulated cumulative breast cancer death rate Swedish trial
model - calibrated
This calibration was performed by adjusting the values of the calibration factors and
observing by eye the degree of correspondence between the observed and simulated
rates. No calibration of incidence rate, nor calibration for over-diagnosis, was
required. The calibration factor of 1.25 for clinically detected cancers is consistent
with the possibility of the uncalibrated mortality curve for clinically detected cancers
being ‘contaminated’ with screen detected cancers and thus underestimating the death
rate for clinically detected cancers. The calibration factor of 0.6 for screen detected
cancers may be attributable to different survival expectations for screen detected
cancers in different settings. Alternatively, the calibration factors may be necessary to
compensate for the effects of the assumptions that have been made in constructing the
model or to adjust for integration errors in the model’s algorithms.
This model demonstrates that is it possible to use system dynamic modelling to
quantitatively replicate the results of clinical trials using information about
characteristics of the trial (such as number of subjects, their ages and screening
participation rates) and ‘intermediate’ statistical results (such as screening test
characteristics and mortality curves). Furthermore, models of trials can be used to
calibrate parameters, such as the intermediate statistical results, to improve the fit of
simulations with observed results, and thereby provide new information on the values
of the intermediate statistics. In effect, the model is suggesting what the actual
mortality curves may have been, in the absence of published data.
The capacity of system dynamic modelling to replicate a trial of breast cancer
screening suggested that replication of the Austrlian national breast cancer screening
program BreastScreen Australia may be practicable. There were doubts about its
feasibility, given the large amount of population data (e.g. numbers of women in each
age group each year over a 50 y period) and computation required. The first stage of
the BreastScreen model building process focussed on simulating breast cancer
incidence (i.e. the onset of breast cancer) for comparison with published breast cancer
incidence data. Figure 3 presents uncalibrated simulated incidence compared with
observed incidence. Two calibration factors were incorporated: baseline breast cancer
incidence calibrator and over-diagnosis calibrator. With these calibration factors set at
1 (ie. no calibration) there is a substantial difference between observed and simulated
incidence.
25
1 Observed breast cancer
incidence
2 20 2. Simulated breast cancer
e incidence
5 3. Index of number of
Ey a screening mammograms
Sg is
5 ana\e
Ss . ——
Su
7% 100. Settings:
a5 All| | Age 50-69
as mammography every 2 years Incidence calibrator 1.00
3 «1 _
Be so Over-diagnosis factor 1.00
=i _— ne Continuation of current
vo screening policy (age 50-69
ze | 3 every 2 years)
1980 1990 2000 2010
Calendar year
Figure 3 Observed and simulated breast cancer incidence rates in Australian breast
cancer screening program - uncalibrated
In contrast to the method of optimising the Swedish trial model, the simulated
incidence in the Australian program model was optimised by systematically searching
for values of the incidence and over-diagnosis calibration factors that would minimise
the sum of squares between the observed and simulated incidence. The simulated
incidence corresponding to this minimum is shown in Figure 4, along with the values
of the calibration factors.
250-
1 Observed breast cancer
incidence
2 20 2. Simulated breast cancer
g incidence
8 3 Index of number of
z 7 —_—2— _ screening mammograms
8
s
9 .
7B 10 Settings:
os Age 50-69
oe every2 years —-‘INcidence calibrator 1.17
ae =a —————* Over-diagnosis factor 1.24
g
rae Continuation of current
om 3 screening policy (age 50-69
20 ° every 2 years)
1980 1990 2000 2010
Calendar year
Figure 4 Observed and simulated breast cancer incidence rates in Australian breast
cancer screening program - calibrated
The optimum incidence calibration factor is 1.17 (i.e. an incidence rate 17% greater
than that originally chosen). The optimum over-diagnosis factor is 1.24, suggesting
that in the Australian program, screening may detect 24% more cancers in screened
women than would have become clinically apparent without screening. A substantial
proportion of these cancers may be in situ cancers, most of which do not become
invasive, but which, once detected, need to be treated because of their invasive
potential.
Using simulated incidence optimised to correspond most closely with observed
incidence (Figure 4), the second stage of simulating breast cancer mortality was
undertaken. With optimised incidence simulation but without calibration of the
mortality curves for clinically and screen detected breast cancer, there is again a
substantial difference between the observed and simulated results (Figure 5).
60 1 Observed breast cancer
mortality
_ so. poor Simulation:
e
£ 2 Simulated breast cancer
4 40. mortality
s ai ES 3. Index of number of
8 2
Q_ 30 ee ae screening mammograms
su
a8 Simulation settings:
Lo
BE 2 All| | Age 50-69 .
os mammography || every 2 years Up. tercaeany
26 RE
£% 10 From 1998 on: Age 50-69
og ny 3 every 2 years
zs
0 Mortality curve calibration:
1980 1990 2000 2010 cD 1.00
sD 1.00
Calendar year
Optimal incidence calibration
Figure 5 Observed and simulated breast cancer death rates in Australian breast
cancer screening program - uncalibrated
Systematically searching for mortality calibration factors to minimise the sum of
squares between observed and simulated age standardised death rates yielded values
of 1.52 for the clinically detected cancer mortality calibration factor and 1.04 for the
screen detected cancer mortality calibration factor. The optimised simulated age
standardised mortality rate for the Australian BreastScreen program is shown in
Figure 6. The value of 1.52 is consistent with the observation in the Swedish model
that the clinically detected survival curve may underestimate the true clinically
detected survival curve because of contamination by screen detected cancers. The
small degree of calibration required of the screen detected mortality curve (1.04)
suggests that the South Australian curve may be representative of the survival
experienced by Australian women with screen detected cancer.
60- 1 Observed breast cancer
mortality
_ sors 3 Simulations:
¢
£ Up to 1997: All
$40 "Gipecneraes mammography
° '
3 aaureent From 1998 on:
~ 30- All screening
sy 2 50-69 y every 2 years
fh licies y every 2 y!
o3 mammography | | _P' » 3 40-69 y every 2 years
BE 2 4 40-49 y every year and
as 50-69 y every 2years
ee
ae 46 5,6,7 Respective index of
Eo —— number of screening
£2 ru mammograms
Ors + + Simulation settings:
1980 1990 2000 2010
Mortality curve calibration:
cD 1.52
sD 1.04
Calendar year
Figure 6 Observed and simulated breast cancer death rates in Australian breast
cancer screening program - calibrated
Figure 6 also presents expected future age standardised mortality rates under different
screening policies. These curves provide an indication of the policy uses that could be
made of this model: As the quantity of screening increases (by including women in
their forties in the program) the breast cancer mortality rate drops. Moving from the
current policy of screening women aged 50 - 69 y every two years by adding biennial
screening of women in their forties produces an increase in the amount of screening
required and a reduction in the death rate from breast cancer. Shortening the
screening interval for women in their forties from two to one year requires a similar
increase in the quantity of screening but yields a proportionately smaller decrease in
the death rate. This suggests that the marginal cost-effectiveness of adding biennial
screening of women in their forties is greater than moving to annual screening of
women in their forties.
This model demonstrates that system dynamic modelling can be used to quantitatively
simulate significant public health programs and their impact on population health.
This model has also enabled estimation of the extent of over-diagnosis of breast
cancer in the Australian screening program and estimation of the expected timing and
degree of mortality reduction from BreastScreen. It can also be used to investigate the
impact of different screening policies on program costs and the number of lives saved.
The model also leaves significant computational capacity unused, allowing for further
development of the model. These developments could include modelling type of
cancer and cancer stage and their respective survival curves, incorporating stochastic
processes and confidence bands, automation of sensitivity testing and optimisation,
and duplication of the basic model to allow head-to-head comparisons of different
screening policies in terms of cost and health gain.
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