A dental public health approach based on computational mathematics: Monte Carlo simulation of childhood dental decay

Abstract

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 simulated 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 dental decay was built, tested and validated.

INTRODUCTION

National data on childhood decay is often difficult to obtain except on occasional childhood dental surveys1., 2.. This is particularly the case in countries with extremely distributed populations or in those still developing a large-scale public dental service. Often surveys focus on measuring the oral health of subsets of the children and leave the reader to extrapolate the results to the wider community. However, this approach faces many difficulties, including (in countries with population fluoride programmes) the problem of a small cohort of disease spread in a large population, or more importantly, where economics prevents large-scale survey research. A parallel problem was faced nearly half a century ago in particle physics. In their case, put simply, the probability for various population level outcomes for neutron movement was known but the specific data on the penetration of individual neutrons remained unknown. The solution came with the development of a computational mathematical approach called Monte Carlo simulations3., 4.. This is where general population probabilities are applied to simulate every occurrence in a population. The results of all the individual applications of the population probabilities are accumulated to provide the specific data for testing.

Over the last 30 years the prevalence of dental decay in children in Australia has reduced significantly. Currently, 60–70% of all 12-year-olds suffer no decay and only about 10% of children have more than two decayed teeth¹. This quite exceptional outcome has resulted fundamentally from the near-universal population-level coverage of fluoride exposure (be it water or toothpaste)². Notwithstanding this outstanding achievement, a small but persistent level of decay still exists within Australian children, causing them significant pain and suffering. The challenge in dental public health now is to find a way to target these children with additional preventive strategies. Historically, school-based dental services with universal coverage have been the norm in Australia. However, it is clear that the massive resources required to continue such services, against a population background of only a small number of cases of childhood dental decay, is brought into question. Ways to find and target services at those who need care is vital to the future health of Australian children.

The present study took a Monte Carlo simulation approach and, for the first time, applied it to an entire population’s dental health. Although we used Australia as a model, the development of the approach was targeted at facilitating dental public health research and analysis in areas where robust data are not so readily available. The hypothesis tested was that the Monte Carlo method can be successfully applied to dental health and can provide opportunities to examine population-wide childhood decay variables that are, in many cases, not attainable by survey.

METHODS

All data was from open sources and therefore no ethics was required for the study5., 6., 7., 8.. In addition, all data collected and reported is for 12-year-olds unless otherwise stated. Based on previous studies it is accepted that dental decay in Australia children is strongly linked to socioeconomic strata, with poorer children suffering greater levels of decay. In addition, it has been previously clearly identified by us (and others) that Indigenous children suffer greater levels of decay than other children9., 10., 11., 12., 13., 14.. Against this backdrop these two factors (socio-economics and Indigenous status) were chosen as the drivers of the Monte Carlo simulations. Gender does not play a large role in variation in the distribution of decay in 12 year-olds and was not used as a driver of the model. However, the opportunity exists for others to replace/add more variables in the future. At this stage this approach was chosen as fundamentally a proof of outcome.

Socioeconomic strata

The nationally agreed stratification of socioeconomic disadvantage (IRSD – Index of Relative Socio-economic Disadvantage) designed and maintained by the Australian Bureau of Statistics (ABS) was used thoughtout this study⁵. The ABS presents the IRSD data in decile clusters, each 10% of the total Australian population in each decile. The deciles were clustered into pairs to provide five levels (0–4) with 0 being the poorest 20% of the population, and 4 being the wealthiest. This was applied to each statistical local area (SLA) as defined by the ABS. This approach meant that local variation in populations was accounted for at a level that was more specific that that nation- or state-wide. It is also noted that socio-economics has a linkage to the type of location where children live, with greater proportions of rural- and remote-dwelling children suffering poverty. Therefore, the usage of socio-economics as a driver in part accommodates variation in population by location of residence. Despite this, further additions to the model are possible. This study aimed to show that the methodology was appropriate and that other variables can be added in the future. Statistical local areas are a geographic clusterings of people and used a basis of census data reporting. Australia is divided into just over 1300 SLAs with no gaps and no overlaps. Clearly, within any geographic region variables can be heterogeneous, but for modelling purposes the socio-economic variable for the geographic region (in this case SLA) was applied equally to all. This is a reasonable assumption for higher-level models. At more granular levels higher resolution of all variables would need to be applied.

Population data

The numbers of children and the proportion of Indigenous children was collected from the census that most closely matched the most recently available data for childhood oral health (the 2006 census) from the ABS website⁶. The total number was 275,000 with 5% being of Indigenous heritage. It is noted that 5% is higher than the wider population average but Indigenous people, as a population, are younger than the rest of the population. Adjustments for the level of poverty that Indigenous children suffer compared with their non-Indigenous counterparts were made⁷. Although this specific figure was not publicly available it was assumed, based on various sources of available data (and extrapolations), that 25% would not be unreasonable⁷. Importantly, a series of five smaller pilot Monte Carlo simulations using only 3000 children were run in Excel and this established that within the range 20–30% there was little difference in the outcome for this assumption.

Probabilistic data

The prevalence of decay for each socioeconomic stratum, the incidence of decay and the difference in incidence for Indigenous and non-Indigenous children was obtained from previously published works contemporaneous to the population data1., 7., 8..

Preliminary calculations

The decay prevalence data for each socioeconomic stratum was fitted to a line, based on the mid-point IRSD strata and the low-point. This fitted line function simplified further calculations in the Monte Carlo simulation. This allowed the translation of the quartile (previously reported data) into quintiles appropriate for the modelling. At each socioeconomic stratum (0–4) the incidence ‘curves’ were calculated based on the residual prevalence [i.e. after taking out the decayed/missing/filled teeth (DMFT) = 0 proportion]. In short, caries incidence ‘curves’ were calculated for each socioeconomic stratum (0–4) for non-Indigenous children, giving a total of five separate curves. A simple best-fit linear function that adjusted the incidence curves for Indigenous status was based on the data presented by Jamieson et al. ⁷ which reported significantly higher caries in Indigenous children across socio-economic strata. The highest and the lowest score in the previously published work was used in forming the best-fit linear function. Application of this function to the five non-Indigenous probabilities (one for each socio-economic quintile) produced five additional probabilities specific for Indigenous children. The constraints of these probabilities (socioeconomic and Indigenous) were used to control the boundaries of the randomly generated DMFT score.

Monte Carlo simulation

Trial Monte Carlo simulations were run on Excel (Microsoft, Redmond, WA, USA) but it was found that it would not be possible to run large-scale (over 50,000 children) simulations with Excel. Personally developed software (Visual Basic 6.0; Microsoft) was employed to run the large-scale Monte Carlo simulations. All resultant data was outputted to CSV (comma separated values) format and imported into MySQL (Community edition; Oracle, Atlanta, GA, USA) for analysis. Analysis included average overall DMFT, Significant Caries index (SiC), SiC25, DMFT of caries-affected children and DMFT of Indigenous children. These outputs from each SLA were cumulated to a total population level and compared with previously reported data.

RESULTS

A Monte Carlo simulation model for 275,000 children (with 5% being Indigenous) was undertaken. From the full run of the simulation it was found that the overall DMFT was 1.08 while the DMFT of highest 10% of sample (Sic10) was 4.76. Both these results are very close to previously published data¹. The overall DMFT is within 2% of that reported for 2005 and the SiC10 is within 4% of the same reported statistic. These values do not differ greatly from the contemporaneously reported statistical data¹. This level of congruity provides strong assurance that the Monte Carlo simulation approach to population oral health is a viable approach.

The data set that derives from the simulation results in a child-by-child simulation of caries data in Australia. The output is 275,000 individual records of data that can then be analysed. Each child’s data is simulated from two randomly seeded calculations (that are constrained by known population-level constraints). The first random seed generates to IRSD score. The second seed is used to generate the incidence of caries depending on the relevant distribution, based on the selection of one of the 10 curves calculated from the population level statistics. The data presented by the simulation can then be treated in a similar form as population data to test its validity and to test other public health measures. For example, DMFT of all children with caries was 2.3 (n = 128,609) and DMFT for Indigenous children only was 1.9 (n = 13,749). Another commonly reported statistic in the literature is the SiC25 and from this simulation was determined to be 3.3 (n = 68,750).

An additional four runs of the simulation were completed to test the sensitivity of the model to random 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 DMFT or SiC10, and therefore no further runs to test this effect were carried out.

Once a full simulation of a population is available an alternative statistical analysis can be completed. For example, this simulation found that the average DMFT for those with a DMFT of greater than 3 (noting that 6 was given as a nominal score for all those with scores of 6 and above as the capacity to calculate exact scores above 6 was limited by the assumption data cut-off being 6) was 4.13 (n = 42,088).

DISCUSSION

The application of Monte Carlo simulations to public dental health can provide a new and innovative approach to looking at oral health where sampling at population levels is available. This approach rests on the previously reported population-level probabilities but then extends these to construct a theoretical full population data set. The full population dataset (in this example all Australian children aged 12 years old in 2005) provides a real opportunity to interrogate the dataset in interesting ways.

Clearly, the risks with this approach are that it rests on the original population-level probabilities. However, the approach can be adjusted and developed as further refined data becomes available. However, notwithstanding this risk, the simulation can be tested against available population data outcomes (in this case average DMFT and Sic10) to test its integrity.

Further enhancements to this particular simulation would be expected to include the addition of a random seed factor to adjust for where DMFT 6+ has been clustered and allocated a score of 6. Also, the use of geographic factors to isolate areas of high risk of caries based on the simulated population.

Dental decay in Australian children is no longer a simple problem to address. Limited resources can no longer be used across entire populations when the majority have no disease and there is little risk associated with the disease. This systematic approach to the development of population-wide simulations allows the testing of modern targeted approaches to service planning. In many States of Australia historical universal service models are still being applied.

Simulation data for all children also provides the opportunity for research and analysis groups outside those who hold population-level sample data to look for innovative solutions. The use of Monte Carlo simulations gives many more researchers the opportunity to take their experimental outcomes and test these at population levels: for example, examining the effect on Australian children of a new intervention that decreases the prevalence of decay by 5% in an experimental population.

CONCLUSION

In this study a Monte Carlo simulation approach to childhood dental decay in Australia was built and tested. The simulation provided data that was within 5% of the known and was stable over a number of runs. The methodology has clear advantages for communities where only fragmented sampled decay rates are known. The simulation of a population from these samples can provide significant opportunities for communities to develop plans targeted at reducing decay.

Acknowledgments

None.

Conflicts of interest

None.