A systematic review of decision analytic modeling techniques for the economic evaluation of dental caries interventions

Objectives Dental caries occur through a multifactorial process that may influence all tooth surfaces throughout an individual’s life. The application of decision analytical modeling (DAM) has gained an increasing level of attention in long-term outcome assessment and economic evaluation of interventions on caries in recent years. The objective of this study was to systematically review the application of DAM and assess their methodological quality in the context of dental caries. Methods A systematic review of the literature published to 31st December 2018 was conducted in Medline, EMBASE, NHSEED, and Web of Science electronic databases. The main information and model characteristics of studies was extracted with the methodological quality of included studies reviewed and assessed using the Philips’ checklist. Results Twenty five studies from different settings were included. Modeling techniques mainly comprised main type of modeling including Markov models (n = 12), Markov/microsimulation mixed model (n = 7), systematic dynamic models (n = 3), microsimulation models (n = 2) and decision tree (n = 1). The mean number of criteria fulfilled was 25.1 out of 60 items, which varied between year of study and research groups. The percentage of criteria fulfilled for data dimension was lower than for the structure and consistency dimension. Critical issues were data quality, incorporation of utility values, and uncertainty analysis in modeling. Conclusion The current review revealed that the methodological quality of DAM in dental caries economic evaluations is unsatisfied. Future modeling studies should adhere more closely to good practice guidelines, especially with respect to data quality evaluation, utility values incorporation, and uncertainty analysis in DAM based studies.


Introduction
Dental caries is a multifactorial process that may influence all tooth surfaces throughout an individual's life [1]. As one of the most prevalent chronic diseases [2][3][4], untreated dental caries affects 2.5 billion people worldwide with an all-age group combined prevalence of 34% [5]. Furthermore, caries are not only painful and give rise to discomfort but infection and systematic effects (i.e. sepsis) can occur when severe caries involve the pulp through dissemination of causative pathogens. Eventually, if untreated, permanent tooth decay and loss can result in disability. The World Health Organization (WHO) has estimated that caries accounted for almost 1.9 million disability adjusted life years (DALYs) globally in 2015, which is even more than the number caused by natural disasters [6]. Therefore, dental caries presents a considerable public health problem in both developed and developing countries.
Timely treatments have been shown to be cost-effective while prevention approaches such as fluoride toothpaste and water fluoridation are also of benefit. The caries intervention and prevention programs at both individual and population levels were launched many years ago, and the achievements of these programs on oral health are remarkable [7,8]. However, due to the long-term characteristics of caries that may exert influence throughout the life course, long-term outcome assessment and economic evaluation are necessary for decision-making when a number of interventions are available. Currently, health economic evaluations of all the interventions including non-pharmaceutical interventions require a long-term perspective in order to comprehensively assess their effects in comparison to real-life scenarios. Studies of long-term healthcare outcomes and cost-effectiveness exceeding a one-year follow-up period are seldom conducted when compared to clinical trials and short-term observational studies in this context.
Decision analytical modeling (DAM) is gaining increased attention in this field due to its capability in analyzing costs and consequences [9]. DAM comprises a series of approaches widely used in healthcare economics and outcome research, which can provide quantitative results to inform decision makers. Furthermore, DAM is a framework to permit synthesis of evidence from different sources and extends the time horizon beyond the follow-up period. DAM has been increasingly used in many healthcare systems and considered an indispensable approach for economic assessment of technology [10].
Mahl and colleagues [11] overviewed the use of Markov models in dental research in 2012, and several of the included studies focused on caries. However, the quality of the model and application of modeling techniques other than Markov models remains unknown even though a number of good practice DAM guidelines have been published [12][13][14]. High quality DAM is not only a scientific goal per se but should be consistent with the requirements of guidelines and support subsequent decision-making policies concerning the adoption of new technologies. Therefore, the objective of this study was to systematically review the DAM and assess the methodological quality of these in the context of dental caries. We aimed to offer insight into the utility of DAM while providing useful information, areas for quality improvement and recommendations for researchers. This would help to precipitate the outcomes from modeling more clearly and could be more attractive to decision-makers in this field.

Methods
In accordance with the principles of the Cochrane Economics Methods Group (CCEMG) [15], we developed a review protocol and conducted a systematic review of the literature in the field of dental research.

Literature search
The search strategy was developed by epidemiologists (ZQ and CK) and dental specialists (SZ and XL). A systematic review of the literature published to 31 st December 2018 was conducted in several electronic databases including Medline, EMBASE, National Health Service Economic Evaluation Database (NHS EED), and Web of Science (detailed search strategies are provided in S1 Table). The term "model" is based on the definition by the International Society For Pharmacoeconomics and Outcomes Research (ISPOR) Task Force on Good Research Practices-Modeling Studies: "an analytic methodology that accounts for events over time and across populations, that is based on data drawn from primary and/or secondary sources, and whose purpose is to estimate the effects of an intervention on valued health consequences and costs" [16].

Eligibility criteria
This review included economic evaluation studies applying DAM techniques to assess dental caries interventions. Meanwhile, the included studies had to fulfill: • Population: general population and selected sub-population having undergone caries interventions • Intervention: healthcare intervention for prevention and treatment in the context of caries • Comparator: no intervention or all alternative interventions • Outcome: healthcare outcome using quality adjusted life years (QALYs) or quality adjusted tooth years (QATYs). Economic outcome including cost or benefit, incremental cost-effectiveness ratio (ICER) • Study design: evaluation of long-term results and cost-effectiveness analysis The language was restricted to English and no time restriction for when articles were published. We excluded descriptive studies and studies using models for illustration of the disease process or treatment options but without long-term benefits or cost measurements and noneconomic studies in this field. Studies published as abstracts but without full information of the model were also excluded. We also performed manual examination of reference lists and citations of articles, and publications from other sources as a supplementary to the results.

Review and data extraction
After combination and de-duplication of search results from databases, title and abstract screening were carried out on the basis of previously set inclusion and exclusion criteria. We then performed full text review to further exclude the ineligible studies. All included study information was systematically extracted into the pre-defined table. Literature review and data extraction were critically and independently performed by two authors (ZQ and SZ). Inconsistent judgments and data extraction results were collected and discussed with another author (XL) in order to reach consensus. When required information was missing or unclear, the authors were contacted to clarify the study details.

Model assessment
As methods of DAM vary significantly and different approaches are needed for different problems requiring decisions, a complete standardization of models is difficult to infer. However, there are still well accepted guidelines worthy of referring to for good modeling practices. Philips and colleagues [17] have developed a framework for DAM quality assessment, which has already been widely applied in many health technology assessments for medical interventions. The Philips' framework generally assesses the quality of DAM and its consistency with good practice guideline with respect to the three main dimensions: model structure, data, and consistency. Within each of the three dimensions, there are detailed criteria for checking whether the related information in the model was reported as fulfilled, not fulfilled, or not applicable. The detailed assessment of included models was initially performed by one author (ZQ) and reviewed by another author (SZ). We deliberately visualized the performance of the DAM in accordance with the good practice guideline, therefore we present the assessment results of included models with a bar chart on the basis of this checklist. The criteria for assessment are based on the example and explanation in Philips' publication, and the ISPOR guideline for good practice [12].

Search results
The database search identified 601 references and five additional ones were identified through hand search. After exclusion of 137 duplicates, 469 were further screened by title and abstract, 397 references were subsequently excluded as these were not related to dental caries. In further full text screening of remaining 72 references, studies were further excluded for the following reasons: non DAM based research (n = 22), literature review or systematic review (n = 7), focused on other outcome of interest rather than caries (n = 6), non-economic evaluation studies (n = 5), model structures were not presented (n = 4), used the same model of previous publication (n = 1). In addition, studies without available full text (n = 2) were excluded (S2 Table). After exclusion of 47 studies in total, 25 studies were finally included in the review . The details of study selection are presented in Fig 1.

Quality assessment
The results of the methodological quality assessment of included studies are shown in Fig 2. The mean number of fulfilled criteria were 25.1 out of 60 (median 26, range 12-35). Altogether, the percentage of criteria fulfilled varied between year of study and research groups. Furthermore, the percentage of criteria fulfilled for data section was lower than the structure and consistency section. Critical issues were data quality, incorporation of utility values, and uncertainty analysis in models. More detailed information for quality assessment is available in the supporting information (S3 Table).

Structure
All included studies clearly stated the decision aims and had a consistent objective. However, none of the studies specified the main decision-maker. Most studies clearly stated the perspective except five [19,22,25,28,32]. Therefore, it was questionable whether the input of the model was consistent with the scope of the aims of these studies. Nine of the included studies [18,19,22,23,25,28,32,37,41] introduced evidence regarding model structure but none of these considered other theories of model structure. All included studies specified the source of data except for one [19], and only in one study was it not clear what the rationale was for the type of model [22]. Over half of the included studies used a lifetime horizon [22][23][24]27,[29][30][31][34][35][36]38] (Philips, 2006). A 'yes' answer represents if a question was fulfilled, 'no' represents that is not fulfilled. 'yes/no' represents if a question was consisted of two sub-questions, one was fulfilled but one was not. 'NA' was assigned when the answer is not applicable. '?' was assigned when the answer was not clear for assessment. https://doi.org/10.1371/journal.pone.0216921.g002 Decision analytic models and economic evaluation of interventions for dental caries or "almost lifetime" horizon [27,42] but none of the remaining studies justified the use of a shorter time horizon. In five studies [24,28,32,33,38] disease states or pathway were not explicitly stated.

Data
Quality assessment of data was not performed in any of the included studies. Over half of the included studies [18,21,23,24,27,[29][30][31]35,[37][38][39]41] analyzed the data using a justifiable epidemiological technique in the pre-model analysis. Calculation of transition probabilities were not justified in six studies [18,[20][21][22]25,38]. Only one study [33] mentioned the deviation for utility index and justified the utilization. None of the studies addressed all types of uncertainties and only one of them [38] justified the omission of a particular form. One study [38] addressed the heterogeneity by running the model separately for different populations.

Consistency
Only two studies [22,28] were tested for mathematical logic before use, and three studies clearly stated that their models [22,29,32] were calibrated against independent data. No counter-intuitive results were reported thus no further explanation and justification was given.
In addition, over half of the included studies compared their results to the previous DAMs used in other studies.

Discussion
Our study systematically reviewed decision analytical models in the published literature for economic evaluations in the field of caries. This review brings all applied models together and thus provides helpful information regarding the current situation for dental healthcare givers, while also identifying aspects that could be improved in future modeling studies. To date, this is the first systematic review that depicts the characteristics of decision analytical models used in this field and quantitatively assessed the methodological quality with the widely used Philips' checklist. The methodological quality of the models is comparable with the findings from peers' studies in other areas as acute coronary syndrome [43] and lower extremity artery disease [44] but still unsatisfying. The modeling approach types in the included studies were mainly Markov models or Markov-based microsimulation models. The characteristics of Markov models could provide a framework to represent sequences of events and effects (such as the demineralization-remineralization dynamic processes in teeth surface) of treatment over time. Compared with the widely used decision-tree model in the context of other oral diseases, patients with caries may experience the disease and intervention process more frequently, thus state transition models such as Markov models could represent the condition more realistically. Besides, use of microsimulation models could provide a way of keeping track of the natural history of certain patients, which more accurately models the interaction within populations and their environment over time. Such models are more suitable when community intervention is performed e.g., water or salt fluoridation. However, there is no general classification that connects decision problems and modeling type. Different caries intervention evaluations require different modeling approaches. Markov models have also been used in clinical and service evaluation of dental diseases, such as implantology for decisionmaking [45], prosthodontic dentistry for treatment cycles [46], and dental health services [47]. Selection of the modeling method should be based on the natural history of the disease and characteristics of intervention alternatives, model appropriateness, dimensions, ease and speed of model development, and data sources [48].
As mentioned above, the quality and availability of data is another key element in modeling studies. However, assessment of the data quality was not conducted in any of the included studies within this systematic review. Choosing the right input parameters and assuring its accuracy is as important as conceptualizing an appropriate model structure when conducting analyses [49]. Data sources of included studies are mainly local retrospective studies and literature reviews. Although results derived from RCTs are more reliable in quantifying the effect of interventions, observational evidence (e.g., disease registries and administrative claim data) may be more useful in estimating the natural progression of the disease, resource use/cost, and utility data [50]. Moreover, observational data can be used to mitigate against the shortage of RCT data as it might miss interested events or combine the endpoints as outcomes [43]. Published literature is an important aggregate data source for modeling, which was adapted by most of the included studies in this review. In the current review, two thirds of all included studies performed systematic literature reviews for more accurate input parameters, which is in accordance with the recommendations in the good practice guideline. Systematic reviews and meta-analysis are useful approaches to solving disagreements in the literature, at least for important effectiveness parameters or the main clinical effects of interests. However, for many researchers, it is not feasible to perform a systematic review because of the restriction of time and other resources, thus an explanation for choice of data source should be made to assure the reliability and validity of the model [43]. Expert opinion was adapted in one study, which was used as an additional data source. Although expert opinion is the least preferred data source because of the subjectivity, it is still worth considering when clinical treatment information is not available. Under the decision analytical model framework, all available sources of information should be integrated to achieve the most appropriate model.
The perspective determines the input parameters and measurement of costs in DAM studies. The societal perspective which aims to include all type of costs is generally considered as the most appropriate point of view for decision makers [9]. However, it is worth noting that only one study in current research stated a societal perspective clearly and none of the included studies define the decision makers. Although there is no optimal choice among these different and contradicted perspectives, clarifying the decision maker before modeling analysis and choosing corresponding perspective is highly recommended on the basis of current findings.
The employment of QALYs as the measurement of outcomes allows the comparison of different interventions with clinical outcomes cross the DAM based studies from different area. Although the oral symptoms such as toothache and consequent poor nutritional intake has significantly detrimental influences on the quality of life of patients [1], some researchers believe it was not possible to measure health benefits in terms of QALYs for dental caries treatment [19], thus the cost-effectiveness measurement of utility in dentistry, which was analogous to QALYs was to calculate the year of single tooth (i.e. quality adjusted tooth years, QATYs) as proposed by Birch and colleagues [51]. Despite using QATYs may limit the comparability of results, we recommend the use of QATYs as outcome measures for DAM or other economic evaluations in the field of dentistry, especially if the decayed, missing, and filled teeth or surface (DMFT/S) is used as the outcome, in order to achieve more accurate and practical outcome measurement. To our best knowledge, there are few DAM based studies using QATYs for outcome measurement, therefore further studies should also focus on improvement of the oral health-related quality of life measurement, while also considering the school or workplace absence, and increased risk of hospitalization.
Uncertainty is the fabric of modeling and statistics [52]. Although more than one guideline recommends uncertainty analysis in methodological, structural population heterogeneity and parameter levels, most of the included studies performed sensitivity analyses only for important parameters, while none of the studies addressed other aspects of uncertainty. As accounting for uncertainty has become a standard part of decision analytic modeling, we recommend that more comprehensive uncertainty analysis should be considered in further modeling practice, in order to improve the methodological quality and accuracy. A step-by-step practical guide developed by Bilcke and colleagues [53] could be a useful reference for assessment.
In addition to the practical guide, communication and collaboration between researchers who are interested to take first steps in DAM studies and experienced researchers is crucial. One research group performed almost one third of included studies and dominated the research work in this area which demonstrates that there is a huge lack of DAM studies in this area. We hope the current research provide a comprehensive overview of and encourage more researcher to participate into the development of DAM in this area.

Limitations
It is noteworthy that a major limitation of the current research is that our review on model structure and evaluation of model quality is based on published literature and appendices, while technical reports of the studies included were not publicly available. Although the guideline for model construction and good practice were published decades ago, due to the space constraint of academic journals, authors cannot fully describe the details and extensive consideration of their models, and how these fulfill the guideline. Our communication with authors did not make all items in the checklist clear; this was limited by the approach and style of communication itself, which may lead to an overestimation of the methodological quality. This may affect the results of the model evaluation, thus we recommend that the technical reports of modeling studies could be published as an appendix or be open to the researchers who are interested in secondary study, which would permit transparency of communication into practice. Another limitation is the publication bias. Though manual searches were conducted to further enhance the electronic database search, the included publications in the current review were published in peer-reviewed journals only, and some relevant reports in the grey literature may have been missed. It could be eliminated when all economic studies were registered before the start as clinical trial. Currently, publication bias cannot be ruled out.

Conclusion
Based on the current systematic review of decision analytic models for prevention and treatment of caries, we conclude that in most studies, Markov models were applied to simulate the progress of disease and effectiveness of interventions. Although the qualities of models are acceptable according to the Philips checklist, the percentage of criteria that were fulfilled varied between studies.
We recommend that decision analytical modeling in the context of economic evaluation of interventions for caries considers an assessment of the data quality and appropriately incorporate utility values. Furthermore, special emphasis should be given to uncertainty analysis, which is important for the transparency and communication of modeling. Practical guidelines are worth referring to when performing uncertainty analysis. Appropriate model structure and systematic evaluation of data together with adherence to good practice guidelines will inform the healthcare provider in allocating resources when novel interventions emerge in the future.
Supporting information S1