International Dental Journal 2013; 63: 39–42    ORIGINAL ARTICLE                                                          ...
Tennant and Krugersmall number of cases of childhood dental decay, is        remote-dwelling children suffering poverty. T...
Remote area dental servicesfor the modelling. At each socioeconomic stratum              The output is 275,000 individual ...
Tennant and Krugerbeen clustered and allocated a score of 6. Also, the                    research series no. 54. Cat. no....
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A dental public health approach based on computational mathematics monte carlo simulation of childhood dental decayid j12003

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A dental public health approach based on computational mathematics monte carlo simulation of childhood dental decayid j12003

  1. 1. International Dental Journal 2013; 63: 39–42 ORIGINAL ARTICLE doi: 10.1111/idj.12003A dental public health approach based on computationalmathematics: Monte Carlo simulation of childhood dentaldecayMarc Tennant and Estie KrugerCentre 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 CarloNational data on childhood decay is often difficult to late every occurrence in a population. The results of allobtain 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 forextremely 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 dentalfocus 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 decayto the wider community. However, this approach faces and only about 10% of children have more than twomany difficulties, including (in countries with popula- decayed teeth1. This quite exceptional outcome hastion 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 waterimportantly, where economics prevents large-scale or toothpaste)2. Notwithstanding this outstandingsurvey research. A parallel problem was faced nearly achievement, a small but persistent level of decay stillhalf 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 publicoutcomes for neutron movement was known but the health now is to find a way to target these childrenspecific 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 coverageopment of a computational mathematical approach have been the norm in Australia. However, it is clearcalled Monte Carlo simulations3,4. This is where that the massive resources required to continue suchgeneral population probabilities are applied to simu- services, against a population background of only a© 2013 FDI World Dental Federation 39
  2. 2. Tennant and Krugersmall 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 partat those who need care is vital to the future health of accommodates variation in population by location ofAustralian 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 canpopulation’s dental health. Although we used Austra- be added in the future. Statistical local areas are alia as a model, the development of the approach was geographic clusterings of people and used a basis oftargeted at facilitating dental public health research census data reporting. Australia is divided into justand 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 beMonte 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 thisine 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.METHODSAll data was from open sources and therefore no Population dataethics was required for the study5–8. In addition, alldata 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 thataccepted that dental decay in Australia children is most closely matched the most recently available datastrongly linked to socioeconomic strata, with poorer for childhood oral health (the 2006 census) from thechildren suffering greater levels of decay. In addition, ABS website6. The total number was 275,000 withit 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 thedrop these two factors (socio-economics and Indige- rest of the population. Adjustments for the level ofnous status) were chosen as the drivers of the poverty that Indigenous children suffer compared withMonte 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 available12 year-olds and was not used as a driver of the it was assumed, based on various sources of availablemodel. However, the opportunity exists for others to data (and extrapolations), that 25% would not bereplace/add more variables in the future. At this stage unreasonable7. Importantly, a series of five smallerthis 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 strataThe nationally agreed stratification of socioeconomic Probabilistic datadisadvantage (IRSD – Index of Relative Socio-eco-nomic Disadvantage) designed and maintained by the The prevalence of decay for each socioeconomicAustralian Bureau of Statistics (ABS) was used stratum, the incidence of decay and the differencethoughtout 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 workslian 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 0being the poorest 20% of the population, and 4 being Preliminary calculationsthe wealthiest. This was applied to each statisticallocal area (SLA) as defined by the ABS. This approach The decay prevalence data for each socioeconomicmeant that local variation in populations was stratum was fitted to a line, based on the mid-pointaccounted for at a level that was more specific that IRSD strata and the low-point. This fitted line functionthat nation- or state-wide. It is also noted that socio- simplified further calculations in the Monte Carloeconomics has a linkage to the type of location where simulation. This allowed the translation of the quartilechildren live, with greater proportions of rural- and (previously reported data) into quintiles appropriate40 © 2013 FDI World Dental Federation
  3. 3. Remote area dental servicesfor 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 simulatedthe 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). TheIn short, caries incidence ‘curves’ were calculated for first random seed generates to IRSD score. The secondeach 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 selectionple best-fit linear function that adjusted the incidence of one of the 10 curves calculated from the populationcurves for Indigenous status was based on the data level statistics. The data presented by the simulationpresented by Jamieson et al. 20077 which reported sig- can then be treated in a similar form as populationnificantly higher caries in Indigenous children across data to test its validity and to test other publicsocio-economic strata. The highest and the lowest health measures. For example, DMFT of all childrenscore in the previously published work was used in with caries was 2.3 (n = 128,609) and DMFT forforming 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 literaturefor each socio-economic quintile) produced five addi- is the SiC25 and from this simulation was determinedtional 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 wereand 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 overallMonte Carlo simulation DMFT or SiC10, and therefore no further runs to testTrial 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 availablethat 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 averagedeveloped 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 thosetions. 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 assumptionMySQL (Community edition; Oracle, Atlanta, GA, data cut-off being 6) was 4.13 (n = 42,088).USA) for analysis. Analysis included average overallDMFT, Significant Caries index (SiC), SiC25, DMFT DISCUSSIONof caries-affected children and DMFT of Indigenouschildren. These outputs from each SLA were cumu- The application of Monte Carlo simulations to publiclated to a total population level and compared with dental health can provide a new and innovativepreviously reported data. approach to looking at oral health where sampling at population levels is available. This approach rests on the previously reported population-level probabilitiesRESULTS but then extends these to construct a theoretical fullA Monte Carlo simulation model for 275,000 chil- population data set. The full population dataset (indren (with 5% being Indigenous) was undertaken. this example all Australian children aged 12 years oldFrom the full run of the simulation it was found that in 2005) provides a real opportunity to interrogatethe 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 itresults 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 simulationfrom 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 testthe 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. 4. Tennant and Krugerbeen clustered and allocated a score of 6. Also, the research series no. 54. Cat. no. DEN 213. Canberra: AIHW; 2011.use of geographic factors to isolate areas of high riskof caries based on the simulated population. 2. Armfield JM, Roberts-Thomson KF, Spencer AJ. The Child Dental Health Survey, Australia 1998. AIHW Cat. No. DEN Dental decay in Australian children is no longer a 88. Adelaide: Adelaide University (AIHW Dental Statistics andsimple problem to address. Limited resources can no Research Series No. 24); 2001.longer be used across entire populations when the 3. Chen Z, Roy K, Gotway CA. Evaluation of variance estimatorsmajority have no disease and there is little risk associ- for the concentration and health achievement indices: a Monte Carlo simulation. Health Econ 2011 21: 1375–1381.ated with the disease. This systematic approach to 4. Fishman G. S. Monte Carlo: Concepts, Algorithms, and Appli-the development of population-wide simulations cations. New York: Springer; 1995. ISBN 038794527Xallows the testing of modern targeted approaches to 5. Available from: http://www.abs.gov.au/websitedbs/D3310114.service planning. In many States of Australia historical nsf/home/Seifa_entry_page. Accessed 5 January 2012.universal service models are still being applied. 6. Available from: http://www.abs.gov.au/cdataonline. Accessed 5 Simulation data for all children also provides the January 2012.opportunity for research and analysis groups outside 7. Jamieson LM, Armfield JM, Roberts-Thomson KF. Indigenous and non-indigenous child oral health in three Australian statesthose who hold population-level sample data to look and territories. Ethn Health 2007 12: 89–107.for innovative solutions. The use of Monte Carlo 8. Available from: www.aihw.gov.au/WorkArea/DownloadAsset.simulations gives many more researchers the opportu- aspx?id=10737419619. Accessed 5 January 2012.nity to take their experimental outcomes and test 9. Kruger E, Smith K, Atkinson D et al. The oral health status andthese at population levels: for example, examining the treatment needs of Indigenous adults in the Kimberley region ofeffect on Australian children of a new intervention Western Australia. Aust J Rural Health 2008 6: 283–289.that decreases the prevalence of decay by 5% in an 10. Steering Committee for the Review of Government Service Pro- vision. Overcoming Indigenous Disadvantage: Key Indicatorsexperimental population. 2011. Canberra, Productivity Commission; 2011. 11. Smith K, Kruger E, Dyson K et al. Oral health in rural and remote Western Australian Aboriginal communities: a two-yearCONCLUSION retrospective analysis of 999 people. Int Dent J 2007 57: 93– 99.In this study a Monte Carlo simulation approach to 12. Australian Bureau of Statistics Australian Institute of Healthchildhood dental decay in Australia was built and tested. and Welfare. The Health and Welfare of Australia’s AboriginalThe simulation provided data that was within 5% of and Torres Strait Islander Peoples. Canberra: Australian Bureauthe known and was stable over a number of runs. The of Statistics Australian Institute of Health and Welfare. 2005.methodology has clear advantages for communities 13. AIHW Dental Statistics and Research Unit. Oral health and access to dental care – rural and remote dwellers. DSRUwhere only fragmented sampled decay rates are known. research report no. 20. Cat. no. DEN 144. Canberra: AIHW.The simulation of a population from these samples can 2005. Available from: http://www.aihw.gov.au/publication-detail/provide significant opportunities for communities to ?id=6442467750. Accessed 6 January 2012.develop plans targeted at reducing decay. 14. Australian Bureau of Statistics Australian Institute of Health and Welfare. National Aboriginal and Torres Strait Islander Social Survey. Canberra: Australian Bureau of Statistics Austra-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.REFERENCES Email: ekruger@crroh.uwa.edu.au1. Ha DH, Roberts-Thomson KF, Armfield JM. The Child Dental Health Surveys Australia, 2005 and 2006. Dental statistics and42 © 2013 FDI World Dental Federation

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