ORIG INAL ART ICLE

A dental public health approach based on computationalmathematics: Monte Carlo simulation of childhood dentaldecay

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 decayusing Australian children as a test environment. Monte Carlo simulation has been used for a half a century in particlephysics (and elsewhere); put simply, it is the probability for various population-level outcomes seeded randomly to drivethe production of individual level data. A total of five runs of the simulation model for all 275,000 12-year-olds inAustralia were completed based on 2005–2006 data. Measured on average decayed/missing/filled teeth (DMFT) andDMFT of highest 10% of sample (Sic10) the runs did not differ from each other by more than 2% and the outcome waswithin 5% of the reported sampled population data. The simulations rested on the population probabilities that areknown 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 casesonly was 1.9 (n = 13,749). In the simulation population the Sic25 was 3.3 (n = 68,750). Monte Carlo simulations werecreated in particle physics as a computational mathematical approach to unknown individual-level effects by resting asimulation 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 toobtain except on occasional childhood dental sur-veys1,2. This is particularly the case in countries withextremely distributed populations or in those still devel-oping a large-scale public dental service. Often surveysfocus on measuring the oral health of subsets of thechildren and leave the reader to extrapolate the resultsto the wider community. However, this approach facesmany difficulties, including (in countries with popula-tion fluoride programmes) the problem of a smallcohort of disease spread in a large population, or moreimportantly, where economics prevents large-scalesurvey research. A parallel problem was faced nearlyhalf a century ago in particle physics. In their case, putsimply, the probability for various population leveloutcomes for neutron movement was known but thespecific data on the penetration of individual neutronsremained unknown. The solution came with the devel-opment of a computational mathematical approachcalled Monte Carlo simulations3,4. This is wheregeneral population probabilities are applied to simu-

late every occurrence in a population. The results of allthe individual applications of the population probabili-ties are accumulated to provide the specific data fortesting.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 decayand only about 10% of children have more than twodecayed teeth1. This quite exceptional outcome hasresulted fundamentally from the near-universal popu-lation-level coverage of fluoride exposure (be it wateror toothpaste)2. Notwithstanding this outstandingachievement, a small but persistent level of decay stillexists within Australian children, causing them signifi-cant pain and suffering. The challenge in dental publichealth now is to find a way to target these childrenwith additional preventive strategies. Historically,school-based dental services with universal coveragehave been the norm in Australia. However, it is clearthat the massive resources required to continue suchservices, against a population background of only a

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International Dental Journal 2013; 63: 39–42

doi: 10.1111/idj.12003

small number of cases of childhood dental decay, isbrought into question. Ways to find and target servicesat those who need care is vital to the future health ofAustralian children.The present study took a Monte Carlo simulation

approach and, for the first time, applied it to an entirepopulation’s dental health. Although we used Austra-lia as a model, the development of the approach wastargeted at facilitating dental public health researchand analysis in areas where robust data are not soreadily available. The hypothesis tested was that theMonte Carlo method can be successfully applied todental health and can provide opportunities to exam-ine population-wide childhood decay variables thatare, in many cases, not attainable by survey.

METHODS

All data was from open sources and therefore noethics was required for the study5–8. In addition, alldata collected and reported is for 12-year-olds unlessotherwise stated. Based on previous studies it isaccepted that dental decay in Australia children isstrongly linked to socioeconomic strata, with poorerchildren suffering greater levels of decay. In addition,it has been previously clearly identified by us (andothers) that Indigenous children suffer greater levelsof decay than other children9–14. Against this back-drop these two factors (socio-economics and Indige-nous status) were chosen as the drivers of theMonte Carlo simulations. Gender does not play alarge role in variation in the distribution of decay in12 year-olds and was not used as a driver of themodel. However, the opportunity exists for others toreplace/add more variables in the future. At this stagethis approach was chosen as fundamentally a proof ofoutcome.

Socioeconomic strata

The nationally agreed stratification of socioeconomicdisadvantage (IRSD – Index of Relative Socio-eco-nomic Disadvantage) designed and maintained by theAustralian Bureau of Statistics (ABS) was usedthoughtout this study5. The ABS presents the IRSDdata in decile clusters, each 10% of the total Austra-lian population in each decile. The deciles were clus-tered into pairs to provide five levels (0–4) with 0being the poorest 20% of the population, and 4 beingthe wealthiest. This was applied to each statisticallocal area (SLA) as defined by the ABS. This approachmeant that local variation in populations wasaccounted for at a level that was more specific thatthat nation- or state-wide. It is also noted that socio-economics has a linkage to the type of location wherechildren live, with greater proportions of rural- and

remote-dwelling children suffering poverty. Therefore,the usage of socio-economics as a driver in partaccommodates variation in population by location ofresidence. Despite this, further additions to the modelare possible. This study aimed to show that the meth-odology was appropriate and that other variables canbe added in the future. Statistical local areas are ageographic clusterings of people and used a basis ofcensus data reporting. Australia is divided into justover 1300 SLAs with no gaps and no overlaps.Clearly, within any geographic region variables can beheterogeneous, but for modelling purposes the socio-economic variable for the geographic region (in thiscase SLA) was applied equally to all. This is a reason-able assumption for higher-level models. At moregranular levels higher resolution of all variables wouldneed to be applied.

Population data

The numbers of children and the proportion of Indig-enous children was collected from the census thatmost closely matched the most recently available datafor childhood oral health (the 2006 census) from theABS website6. The total number was 275,000 with5% being of Indigenous heritage. It is noted that 5%is higher than the wider population average but Indig-enous people, as a population, are younger than therest of the population. Adjustments for the level ofpoverty that Indigenous children suffer compared withtheir non-Indigenous counterparts were made7.Although this specific figure was not publicly availableit was assumed, based on various sources of availabledata (and extrapolations), that 25% would not beunreasonable7. Importantly, a series of five smallerpilot Monte Carlo simulations using only 3000 chil-dren were run in Excel and this established thatwithin the range 20–30% there was little difference inthe outcome for this assumption.

Probabilistic data

The prevalence of decay for each socioeconomicstratum, the incidence of decay and the differencein incidence for Indigenous and non-Indigenous chil-dren was obtained from previously published workscontemporaneous to the population data1,7,8.

Preliminary calculations

The decay prevalence data for each socioeconomicstratum was fitted to a line, based on the mid-pointIRSD strata and the low-point. This fitted line functionsimplified further calculations in the Monte Carlosimulation. This allowed the translation of the quartile(previously reported data) into quintiles appropriate

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for the modelling. At each socioeconomic stratum(0–4) the incidence ‘curves’ were calculated based onthe residual prevalence [i.e. after taking out thedecayed/missing/filled teeth (DMFT) = 0 proportion].In short, caries incidence ‘curves’ were calculated foreach socioeconomic stratum (0–4) for non-Indigenouschildren, giving a total of five separate curves. A sim-ple best-fit linear function that adjusted the incidencecurves for Indigenous status was based on the datapresented by Jamieson et al. 20077 which reported sig-nificantly higher caries in Indigenous children acrosssocio-economic strata. The highest and the lowestscore in the previously published work was used informing the best-fit linear function. Application of thisfunction to the five non-Indigenous probabilities (onefor each socio-economic quintile) produced five addi-tional probabilities specific for Indigenous children.The constraints of these probabilities (socioeconomicand Indigenous) were used to control the boundariesof the randomly generated DMFT score.

Monte Carlo simulation

Trial Monte Carlo simulations were run on Excel(Microsoft, Redmond, WA, USA) but it was foundthat it would not be possible to run large-scale (over50,000 children) simulations with Excel. Personallydeveloped software (Visual Basic 6.0; Microsoft) wasemployed to run the large-scale Monte Carlo simula-tions. All resultant data was outputted to CSV(comma separated values) format and imported intoMySQL (Community edition; Oracle, Atlanta, GA,USA) for analysis. Analysis included average overallDMFT, Significant Caries index (SiC), SiC25, DMFTof caries-affected children and DMFT of Indigenouschildren. These outputs from each SLA were cumu-lated to a total population level and compared withpreviously reported data.

RESULTS

A Monte Carlo simulation model for 275,000 chil-dren (with 5% being Indigenous) was undertaken.From the full run of the simulation it was found thatthe overall DMFT was 1.08 while the DMFT ofhighest 10% of sample (Sic10) was 4.76. Both theseresults are very close to previously published data1.The overall DMFT is within 2% of that reported for2005 and the SiC10 is within 4% of the samereported statistic. These values do not differ greatlyfrom the contemporaneously reported statistical data1.This level of congruity provides strong assurance thatthe Monte Carlo simulation approach to populationoral 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 thatcan then be analysed. Each child’s data is simulatedfrom two randomly seeded calculations (that are con-strained by known population-level constraints). Thefirst random seed generates to IRSD score. The secondseed is used to generate the incidence of caries depend-ing on the relevant distribution, based on the selectionof one of the 10 curves calculated from the populationlevel statistics. The data presented by the simulationcan then be treated in a similar form as populationdata to test its validity and to test other publichealth measures. For example, DMFT of all childrenwith caries was 2.3 (n = 128,609) and DMFT forIndigenous children only was 1.9 (n = 13,749).Another commonly reported statistic in the literatureis the SiC25 and from this simulation was determinedto be 3.3 (n = 68,750).An additional four runs of the simulation were

completed to test the sensitivity of the model to ran-dom seed change, each time with new random seedsapplied. The data from all five runs did not differ bymore than 2%, as measured by change in overallDMFT or SiC10, and therefore no further runs to testthis 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 averageDMFT for those with a DMFT of greater than 3 (not-ing that 6 was given as a nominal score for all thosewith scores of 6 and above as the capacity to calculateexact scores above 6 was limited by the assumptiondata cut-off being 6) was 4.13 (n = 42,088).

DISCUSSION

The application of Monte Carlo simulations to publicdental health can provide a new and innovativeapproach to looking at oral health where sampling atpopulation levels is available. This approach rests onthe previously reported population-level probabilitiesbut then extends these to construct a theoretical fullpopulation data set. The full population dataset (inthis example all Australian children aged 12 years oldin 2005) provides a real opportunity to interrogatethe 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 devel-oped as further refined data becomes available.However, notwithstanding this risk, the simulationcan be tested against available population data out-comes (in this case average DMFT and Sic10) to testits integrity.Further enhancements to this particular simulation

would be expected to include the addition of a ran-dom seed factor to adjust for where DMFT 6+ has

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Remote area dental services

been clustered and allocated a score of 6. Also, theuse of geographic factors to isolate areas of high riskof caries based on the simulated population.Dental decay in Australian children is no longer a

simple problem to address. Limited resources can nolonger be used across entire populations when themajority have no disease and there is little risk associ-ated with the disease. This systematic approach tothe development of population-wide simulationsallows the testing of modern targeted approaches toservice planning. In many States of Australia historicaluniversal service models are still being applied.Simulation data for all children also provides the

opportunity for research and analysis groups outsidethose who hold population-level sample data to lookfor innovative solutions. The use of Monte Carlosimulations gives many more researchers the opportu-nity to take their experimental outcomes and testthese at population levels: for example, examining theeffect on Australian children of a new interventionthat decreases the prevalence of decay by 5% in anexperimental population.

CONCLUSION

In this study a Monte Carlo simulation approach tochildhood dental decay in Australia was built and tested.The simulation provided data that was within 5% ofthe known and was stable over a number of runs. Themethodology has clear advantages for communitieswhere only fragmented sampled decay rates are known.The simulation of a population from these samples canprovide significant opportunities for communities todevelop plans targeted at reducing decay.

Acknowledgments

None.

Conflicts of interest

None.

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Correspondence to:Estie Kruger,

Centre for Rural and Remote Oral Health,The University of Western Australia,

Nedlands, WA 6009,Australia.

Email: ekruger@crroh.uwa.edu.au

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Tennant and Kruger