This document describes a study that used Monte Carlo simulation to model childhood dental decay in Australia. Key points: - Monte Carlo simulation was used to model the prevalence and incidence of dental decay for 275,000 12-year-olds in Australia based on 2005-2006 data and population probabilities. - Five runs of the simulation found results within 5% of reported population data for average DMFT and DMFT of highest 10% of sample. - The simulation was based on socioeconomic status and Indigenous heritage, known to be strongly linked to dental decay. It generated individual records that could then be analyzed. - The study demonstrated that Monte Carlo simulation can be successfully applied to model childhood dental decay at a population

1. International Dental Journal 2013; 63: 39–42
ORIGINAL ARTICLE
doi: 10.1111/idj.12003
A dental public health approach based on computational
mathematics: Monte Carlo simulation of childhood dental
decay
Marc Tennant and Estie Kruger
Centre for Rural and Remote Oral Health, The University of Western Australia, Nedlands, WA, Australia.
This study developed a Monte Carlo simulation approach to examining the prevalence and incidence of dental decay
using Australian children as a test environment. Monte Carlo simulation has been used for a half a century in particle
physics (and elsewhere); put simply, it is the probability for various population-level outcomes seeded randomly to drive
the production of individual level data. A total of five runs of the simulation model for all 275,000 12-year-olds in
Australia were completed based on 2005–2006 data. Measured on average decayed/missing/filled teeth (DMFT) and
DMFT of highest 10% of sample (Sic10) the runs did not differ from each other by more than 2% and the outcome was
within 5% of the reported sampled population data. The simulations rested on the population probabilities that are
known to be strongly linked to dental decay, namely, socio-economic status and Indigenous heritage. Testing the simu-
lated population found DMFT of all cases where DMFT<>0 was 2.3 (n = 128,609) and DMFT for Indigenous cases
only was 1.9 (n = 13,749). In the simulation population the Sic25 was 3.3 (n = 68,750). Monte Carlo simulations were
created in particle physics as a computational mathematical approach to unknown individual-level effects by resting a
simulation on known population-level probabilities. In this study a Monte Carlo simulation approach to childhood den-
tal decay was built, tested and validated.
Key words: Dental public health, computational mathematics, Monte Carlo
National data on childhood decay is often difficult to late every occurrence in a population. The results of all
obtain except on occasional childhood dental sur- the individual applications of the population probabili-
veys1,2. This is particularly the case in countries with ties are accumulated to provide the specific data for
extremely distributed populations or in those still devel- testing.
oping a large-scale public dental service. Often surveys Over the last 30 years the prevalence of dental
focus on measuring the oral health of subsets of the decay in children in Australia has reduced significantly.
children and leave the reader to extrapolate the results Currently, 60–70% of all 12-year-olds suffer no decay
to the wider community. However, this approach faces and only about 10% of children have more than two
many difficulties, including (in countries with popula- decayed teeth1. This quite exceptional outcome has
tion fluoride programmes) the problem of a small resulted fundamentally from the near-universal popu-
cohort of disease spread in a large population, or more lation-level coverage of fluoride exposure (be it water
importantly, where economics prevents large-scale or toothpaste)2. Notwithstanding this outstanding
survey research. A parallel problem was faced nearly achievement, a small but persistent level of decay still
half a century ago in particle physics. In their case, put exists within Australian children, causing them signifi-
simply, the probability for various population level cant pain and suffering. The challenge in dental public
outcomes for neutron movement was known but the health now is to find a way to target these children
specific data on the penetration of individual neutrons with additional preventive strategies. Historically,
remained unknown. The solution came with the devel- school-based dental services with universal coverage
opment of a computational mathematical approach have been the norm in Australia. However, it is clear
called Monte Carlo simulations3,4. This is where that the massive resources required to continue such
general population probabilities are applied to simu- services, against a population background of only a
© 2013 FDI World Dental Federation 39

2. Tennant and Kruger
small number of cases of childhood dental decay, is remote-dwelling children suffering poverty. Therefore,
brought into question. Ways to find and target services the usage of socio-economics as a driver in part
at those who need care is vital to the future health of accommodates variation in population by location of
Australian children. residence. Despite this, further additions to the model
The present study took a Monte Carlo simulation are possible. This study aimed to show that the meth-
approach and, for the first time, applied it to an entire odology was appropriate and that other variables can
population’s dental health. Although we used Austra- be added in the future. Statistical local areas are a
lia as a model, the development of the approach was geographic clusterings of people and used a basis of
targeted at facilitating dental public health research census data reporting. Australia is divided into just
and analysis in areas where robust data are not so over 1300 SLAs with no gaps and no overlaps.
readily available. The hypothesis tested was that the Clearly, within any geographic region variables can be
Monte Carlo method can be successfully applied to heterogeneous, but for modelling purposes the socio-
dental health and can provide opportunities to exam- economic variable for the geographic region (in this
ine population-wide childhood decay variables that case SLA) was applied equally to all. This is a reason-
are, in many cases, not attainable by survey. able assumption for higher-level models. At more
granular levels higher resolution of all variables would
need to be applied.
METHODS
All data was from open sources and therefore no
Population data
ethics was required for the study5–8. In addition, all
data collected and reported is for 12-year-olds unless The numbers of children and the proportion of Indig-
otherwise stated. Based on previous studies it is enous children was collected from the census that
accepted that dental decay in Australia children is most closely matched the most recently available data
strongly linked to socioeconomic strata, with poorer for childhood oral health (the 2006 census) from the
children suffering greater levels of decay. In addition, ABS website6. The total number was 275,000 with
it has been previously clearly identified by us (and 5% being of Indigenous heritage. It is noted that 5%
others) that Indigenous children suffer greater levels is higher than the wider population average but Indig-
of decay than other children9–14. Against this back- enous people, as a population, are younger than the
drop these two factors (socio-economics and Indige- rest of the population. Adjustments for the level of
nous status) were chosen as the drivers of the poverty that Indigenous children suffer compared with
Monte Carlo simulations. Gender does not play a their non-Indigenous counterparts were made7.
large role in variation in the distribution of decay in Although this specific figure was not publicly available
12 year-olds and was not used as a driver of the it was assumed, based on various sources of available
model. However, the opportunity exists for others to data (and extrapolations), that 25% would not be
replace/add more variables in the future. At this stage unreasonable7. Importantly, a series of five smaller
this approach was chosen as fundamentally a proof of pilot Monte Carlo simulations using only 3000 chil-
outcome. dren were run in Excel and this established that
within the range 20–30% there was little difference in
the outcome for this assumption.
Socioeconomic strata
The nationally agreed stratification of socioeconomic
Probabilistic data
disadvantage (IRSD – Index of Relative Socio-eco-
nomic Disadvantage) designed and maintained by the The prevalence of decay for each socioeconomic
Australian Bureau of Statistics (ABS) was used stratum, the incidence of decay and the difference
thoughtout this study5. The ABS presents the IRSD in incidence for Indigenous and non-Indigenous chil-
data in decile clusters, each 10% of the total Austra- dren was obtained from previously published works
lian population in each decile. The deciles were clus- contemporaneous to the population data1,7,8.
tered into pairs to provide five levels (0–4) with 0
being the poorest 20% of the population, and 4 being
Preliminary calculations
the wealthiest. This was applied to each statistical
local area (SLA) as defined by the ABS. This approach The decay prevalence data for each socioeconomic
meant that local variation in populations was stratum was fitted to a line, based on the mid-point
accounted for at a level that was more specific that IRSD strata and the low-point. This fitted line function
that nation- or state-wide. It is also noted that socio- simplified further calculations in the Monte Carlo
economics has a linkage to the type of location where simulation. This allowed the translation of the quartile
children live, with greater proportions of rural- and (previously reported data) into quintiles appropriate
40 © 2013 FDI World Dental Federation

3. Remote area dental services
for the modelling. At each socioeconomic stratum The output is 275,000 individual records of data that
(0–4) the incidence ‘curves’ were calculated based on can then be analysed. Each child’s data is simulated
the residual prevalence [i.e. after taking out the from two randomly seeded calculations (that are con-
decayed/missing/filled teeth (DMFT) = 0 proportion]. strained by known population-level constraints). The
In short, caries incidence ‘curves’ were calculated for first random seed generates to IRSD score. The second
each socioeconomic stratum (0–4) for non-Indigenous seed is used to generate the incidence of caries depend-
children, giving a total of five separate curves. A sim- ing on the relevant distribution, based on the selection
ple best-fit linear function that adjusted the incidence of one of the 10 curves calculated from the population
curves for Indigenous status was based on the data level statistics. The data presented by the simulation
presented by Jamieson et al. 20077 which reported sig- can then be treated in a similar form as population
nificantly higher caries in Indigenous children across data to test its validity and to test other public
socio-economic strata. The highest and the lowest health measures. For example, DMFT of all children
score in the previously published work was used in with caries was 2.3 (n = 128,609) and DMFT for
forming the best-fit linear function. Application of this Indigenous children only was 1.9 (n = 13,749).
function to the five non-Indigenous probabilities (one Another commonly reported statistic in the literature
for each socio-economic quintile) produced five addi- is the SiC25 and from this simulation was determined
tional probabilities specific for Indigenous children. to be 3.3 (n = 68,750).
The constraints of these probabilities (socioeconomic An additional four runs of the simulation were
and Indigenous) were used to control the boundaries completed to test the sensitivity of the model to ran-
of the randomly generated DMFT score. dom seed change, each time with new random seeds
applied. The data from all five runs did not differ by
more than 2%, as measured by change in overall
Monte Carlo simulation
DMFT or SiC10, and therefore no further runs to test
Trial Monte Carlo simulations were run on Excel this effect were carried out.
(Microsoft, Redmond, WA, USA) but it was found Once a full simulation of a population is available
that it would not be possible to run large-scale (over an alternative statistical analysis can be completed.
50,000 children) simulations with Excel. Personally For example, this simulation found that the average
developed software (Visual Basic 6.0; Microsoft) was DMFT for those with a DMFT of greater than 3 (not-
employed to run the large-scale Monte Carlo simula- ing that 6 was given as a nominal score for all those
tions. All resultant data was outputted to CSV with scores of 6 and above as the capacity to calculate
(comma separated values) format and imported into exact scores above 6 was limited by the assumption
MySQL (Community edition; Oracle, Atlanta, GA, data cut-off being 6) was 4.13 (n = 42,088).
USA) for analysis. Analysis included average overall
DMFT, Significant Caries index (SiC), SiC25, DMFT
DISCUSSION
of caries-affected children and DMFT of Indigenous
children. These outputs from each SLA were cumu- The application of Monte Carlo simulations to public
lated to a total population level and compared with dental health can provide a new and innovative
previously reported data. approach to looking at oral health where sampling at
population levels is available. This approach rests on
the previously reported population-level probabilities
RESULTS
but then extends these to construct a theoretical full
A Monte Carlo simulation model for 275,000 chil- population data set. The full population dataset (in
dren (with 5% being Indigenous) was undertaken. this example all Australian children aged 12 years old
From the full run of the simulation it was found that in 2005) provides a real opportunity to interrogate
the overall DMFT was 1.08 while the DMFT of the dataset in interesting ways.
highest 10% of sample (Sic10) was 4.76. Both these Clearly, the risks with this approach are that it
results are very close to previously published data1. rests on the original population-level probabilities.
The overall DMFT is within 2% of that reported for However, the approach can be adjusted and devel-
2005 and the SiC10 is within 4% of the same oped as further refined data becomes available.
reported statistic. These values do not differ greatly However, notwithstanding this risk, the simulation
from the contemporaneously reported statistical data1. can be tested against available population data out-
This level of congruity provides strong assurance that comes (in this case average DMFT and Sic10) to test
the Monte Carlo simulation approach to population its integrity.
oral health is a viable approach. Further enhancements to this particular simulation
The data set that derives from the simulation results would be expected to include the addition of a ran-
in a child-by-child simulation of caries data in Australia. dom seed factor to adjust for where DMFT 6+ has
© 2013 FDI World Dental Federation 41

4. Tennant and Kruger
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In this study a Monte Carlo simulation approach to
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Acknowledgments lian Institute of Health and Welfare, 2005.
None. Correspondence to:
Estie Kruger,
Conflicts of interest Centre for Rural and Remote Oral Health,
The University of Western Australia,
None. Nedlands, WA 6009,
Australia.
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42 © 2013 FDI World Dental Federation