This manuscript is a health economic analysis plan following the International Society for Pharmacoeconomics and Outcomes Research (ISPOR) Good Research Practices Task Force Report recommendations  and the Consolidated Health Economic Evaluation Reporting Standards (CHEERS)  checklist.
A trial-based economic evaluation will be conducted (piggyback approach), including three cost-effectiveness analyses (CEA) - different health effects- and a cost-utility analysis (CUA). The clinical trial investigating the diagnostic strategy for restorations assessment is the third diagnostic study conducted by the CARDEC collaborative group at the School of Dentistry of the University of São Paulo (São Paulo, Brazil). The CARDEC-03 trial is a two-arm, parallel-group, patient-randomized controlled trial aiming to assess which of the two diagnostic strategies (based on FDI criteria or CARS) leads to less new interventions in restored primary teeth during two years of follow-up. Further details regarding the trial have been published in the study protocol .
The strategy based on the FDI criteria will be acknowledged as the reference strategy for assessing the restorations. However, recognize there is no robust evidence supporting this assumption. Despite this, a reference strategy for economic evaluation must be assumed. Considering that the CARS strategy is associated with a less interventionist approach, we will consider it as the new strategy. Moreover, FDI criteria were first proposed and appointed by experts as the standard criteria for restorations' assessment [16, 17].
Target population and Eligibility Criteria
Children's participation was voluntary. Our sample includes 3-to-10-year-old children seeking dental care at the Pediatric Dentistry clinic from our school, with at least one dental restoration in a primary tooth. The exclusion criteria were children whose parents did not consent to their participation; children who did notassent in participating in this study; and children with limited ability to co-operate even when behavior management was used .
Comparators - Interventions and Follow-up
Aiming to compare a more interventionist strategy to a supposedly less interventionist approach when assessing dental restorations and guiding clinical decision-making, children were allocated to one of the two diagnostic strategies for the assessment of restorations. To simplify, we will refer to them, from that point, as FDI and CARS strategies. A trained and calibrated examiner (BLPM) performed the assessments, and treatment decisions were based on the criteria. The FDI criteria  can be adapted depending on the purpose of the study. Therefore, since dental caries is the most common reported reason for reinterventions in primary teeth, we chose to evaluate related parameters as marginal staining and adaptation, besides the recurrence of caries. The CARS strategy will be used as originally proposed  (Table 1). Details regarding clinical criteria, sample size, randomization, allocation, blinding, and treatment of the restorations have been previously described in a clinical trial protocol .
Children will be followed for 24 months after the baseline interventions. Clinical assessments are being scheduled at 6-month intervals. In the baseline and at each follow-up visit, children are being instructed about diet and oral hygiene. The same examiner responsible for baseline evaluation will reassess the restorations at each appointment and propose a new treatment plan for each child, based on the respective randomized strategy.
Time horizon, study perspective and discount rate
The time horizon for the main evaluations was set as 24 months (time of study enrollment). Secondary longer-term economic evaluation with trial results will be performed to extrapolate the results over a primary tooth lifetime horizon. We will adopt the societal perspective, accounting for direct and indirect costs. A discount rate of 5% will be applied for costs and effects as the trial is being conducted in Brazil, a lower-middle-income country . Further sensitivity analyses will test the influence of this assumption by considering different discount rates (0–10%).
Costs and resources
The costs of each strategy will be estimated using a micro-costing approach. The direct and indirect costs per tooth and child will be calculated over 24 months (Supplemental Material 1). Direct costs will comprise the costs related to the dental office accommodation, dental instruments and equipment and their respective maintenance, materials used to implement the strategies and staff expenses (based on working hours and time spent on patient's care). Firstly, direct costs will be estimated per tooth included in the trial. Then, we will sum up all child's included teeth for calculating direct costs with each child.
We will calculate the accommodation costs using rental costs and municipal taxes per m2 of the area used by each dental unit. Subsequently, the accommodation costs per hour will be calculated. The same calculation will be used for dental instruments and equipment, estimating a life span of 3 years for instruments  and 5 years for equipment , with a monthly usage of 160 hours. The staff salary (dentists and dental auxiliaries) will be calculated based on the Brazilian Federal Law's monthly wage, allowing 40 hours per week (8 hours/day) for each dentist and dental nurse. For dental material, we will calculate the mean value of each item in three different dental stores and quantities used during clinical appointments.
Indirect costs will include the out-of-pocket expenditures, such as transportation (public or private), any opportunity costs of accompanying a person's absence from the workplace, and the patient's time accessing care. These costs will be estimated per child, considering the time spent during appointments and waiting or travelling to/from the dental clinic. For indirect costs per tooth, time spent when performing procedures related to each specific tooth will be first considered. For child's general appointments (e.g. instructions, fluoride applications) and child's and accompanying person's waiting/travelling, the time spent will be fully considered for each tooth, as if only one tooth had been included per child.
Possible dental interventions received externally to the research, but related to the included teeth, will also be considered indirect costs. Transportation will be calculated using the municipality’s fares for public transportation. For private transportation, we will consider the distance from the family's house to the University and an average price for fuel obtained from the Brazilian National Agency, considering an 8 km per litre efficiency. The patient's and accompanying person's time will be valued, respectively, based on the Brazilian minimum wage and mean Brazilian salary. If the accompanying person reports any earning loss due to being present at child's appointments, an additional cost of a working day will be added for each received appointment.
The accompanying person's working absence time will also be calculated based on the mean Brazilian salary. In this case, the working days and hours will be considered to calculate this person's value per working hour. When treatments have been performed externally to the research, the same strategy used for missing data will be used for cost estimation. To estimate the costs, we have registered in a specific form the number of appointments, the time spent at each one and materials used during patient care (Supplemental Material 2). This form has also been used to collect information about transportation and absence from work. Details about the cost estimation of each of the resources mentioned above can be found in Supplemental Material 1.
Costs will be calculated in Brazilian Real (BRL) considering the base year for the analysis and converted to international dollars using Purchasing Power Parities (PPP) measured for the same period (or the most recent indicator available at the time of the analyzes).
Three health effects will be considered for different CEAs. They are the percentage of children who did not need new operative interventions, the number of new operative interventions after the baseline assessment using FDI or CARS on the baseline, and the Oral Health-Related Quality of Life (OHRQoL) scores (Table 2).
For the two first health outcomes (related to new operative interventions), we will assess the included restored teeth with a 6-month interval, and the cumulative result will be accumulated for 24 months. The restorations will be evaluated by another examiner (TKT), blinded to the diagnostic strategy. At this assessment, surfaces were scored according to the restoration integrity and occurrence of caries, determining the need (or not) of repair, replacement or other possible new interventions [22–23] (Table 2). At this stage, the idea was using an external assessor using a different approach (from those under comparison) not to bias the outcome assessment. Based on this assessment, new interventions will be considered when any need for restoration repair or replacement is identified, any presence of secondary caries lesion exposing dentin is detected, any need for extension of the existing restoration or endodontic treatment is required (due to caries or tooth fracture) and/or any episode of pain is reported (Table 2).
The OHRQoL will be assessed using the Brazilian version of the Early Childhood Health Impact Scale (B-ECOHIS) . This questionnaire is answered by parents as a proxy of the child’s OHRQoL and is a valid measure for children . Although the ECOHIS has been proposed for pre-school children , it was chosen to measure effectiveness in the entire sample, comprising children from 3-to-9 years-old. The questionnaire was answered in the baseline and will be answered at 24-month follow-up completion. The difference between the ECOHIS final and baseline scores will be calculated.
For CUA, the effect will be the gain in Quality Adjusted Life Years (QALYs). To estimate QALYs, we will use the Standard Gamble (SG) approach to calculate weights (utility scores) based on patients' parent's preferences regarding health states related to dental caries. The parent preference will be used as a proxy measure for the child’s preference regarding different health status. More details about the Standard Gamble experiment may be found in the next section.
We will conduct an SG experiment to measure different oral health states' preferences related to dental caries in primary teeth. As parents’ answers will be considered a proxy measurement, a representative sample of those parents seeking dental treatment in a reference center will be selected. A minimum sample size of 50 parents was calculated to permit an absolute difference of 0.05 units and to guarantee the power of 80% and a significance level of 5%. To compensate for possible non-normal distribution and possible non-response or lost participants, we added up, respectively, 10% and 20% to this calculated sample, totalizing 63 participants to be recruited.
To also guarantee the representativeness, the recruited sample will be stratified by the child’ caries experience and opportunity for dental treatment (children firstly seeking the treatment vs those already enrolled in treatment). Part of this sample will be selected among' 'children's parents from the main clinical trial (CARDEC-3). The other will be recruited among parents from a sample of children seeking treatment in the school's dental clinics. Adults will be asked about their preference between two courses of action resulting in different outcomes regarding his/her child’s oral condition.
The health states will be illustrated on cards, and the SG will be conducted using a chance board. The health states considered are: 1) a primary molar with dentin caries lesion; 2) a restored primary molar; 3) a restored primary molar needing repair/replacement. Children's parents will choose between alternatives A and B. Alternative A offers a probability “p” of achieving the best possible health state, which is a sound tooth that will last like that until it exfoliates. Then, a probability “1 – p” of having the worst possible condition assumed (early tooth loss) (Fig. 1). Alternative B will be a certain health state of a restored primary molar. The probability “p” will be changed in the chance board until the parent is indifferent to the two options . This probability will be considered the parent’ weigh given for his/her child’s health state (utility value). We will then calculate the QALYs, also considering the time for which the child presented such a state. The same experiment with the other health states will be conducted, as demonstrated in Fig. 1.
The economic evaluations will be considered intention-to-treat analyses using data collected after two years, as previously described. In the case of missing data, we will investigate their nature and choose the most appropriate method to handle the missing data, e.g. multiple imputations. Imputations will consider health and economic outcomes and the possible relationship between them and other pertinent covariates.
Cox regression model with shared frailty will be used to compare the need for a new intervention. Some of the health effects listed above (number of new interventions and will be compared between groups using the most appropriate statistical test (McNemar or Student´s test) depending on data distribution. Given the usual right-skewed distribution of cost data, we will use the bootstrapping quantile regression to compare the total costs of the diagnostic strategies . Bootstrapping replications will be set at 1,000, and a fixed seed will be determined. To compare the effects, we will choose an appropriate statistical strategy according to data distribution. We will use the software Stata13 (StataCorp LP, Texas, USA) and set a 5% significance level for these analyses.
We will work with the difference between the strategies both regarding the inputs (∆costs: \(CARS costs-FDI costs\)) and outputs (∆effects: \(CARS effects-FDI effects\)) since the focus of this series of economic evaluations is the economic impact of using the minimally invasive strategy (based on CARS) instead of the conventional strategy (based on FDI criteria) for managing dental restorations. Bootstrap confidence intervals will be calculated for each parameter considering the costs, effects, incremental costs and incremental effects.
Deterministic one-way sensitivity analysis will be conducted for CEAs and CUA to assess the quantitative relationship among estimates in parameters that could perform differently in a distinct scenario, such as costs, discount rate, and effects. In these analyses, we will also test the influence of different baseline conditions as covariates associated with the effects and costs , checking the possibility of extrapolating data from this single trial to a broader population. The results will be demonstrated in a tornado diagram.
Additionally, a Bayesian approach will be used to explore uncertainties on the same parameters. By adopting this approach, we will describe the probabilities around the actual values obtained in this study [31–33]. The data distribution of costs and effects will be checked using XLSTAT 2017 (Addinsoft, Paris, France), and, based on that distribution, Monte-Carlo simulations (10,000) will be generated to be plotted in a cost-effectiveness plane (CE plane). The proportion of points in each quadrant of the CE plane will be calculated, and the location of points will also be assessed visually. We will calculate the incremental net benefit using the following equation:
\(Incremental Net Benefit=Incremental Effect \times Ceiling Ratio -Incremental Cost\) , being value 1 for a positive coefficient and 0 for a negative coefficient value. Thus, for the interpretation, if the difference is higher than zero (the value 1), it means that for one additional unit of effectiveness, the incremental cost is below the Ceiling Ratio (the maximum value that decision-makers are willing to pay). If the difference is less than zero (the value 0), then, for one additional unit of effectiveness the incremental cost is above the Ceiling Ratio . Finally, acceptability curves will be plotted for each effect using incremental net benefit framework and assuming different ceiling ratios to check the uncertainties around threshold points.
Subgroup analyses considering age (3 to 6 vs 7 to 10 years) and patients' caries experience (≤ 3 vs > 3 restorations) will also be conducted.
Modelling for primary tooth lifetime horizon
As a secondary aim, we will construct a decision analytic modelling framework to extrapolate the results for a primary molar lifetime horizon. As the base case, we will consider a child as those enrolled in the trial. Then, based on the mean age of children enrolled on the main trial, we will establish the number of cycles of the Markov model.
Probabilities and costs will be extracted from the main trial. If necessary, any additional reference value will be identified from the literature. The SG experiment will generate utility values. We will assume that probabilities will maintain the same at each cycle until such horizon. The half-cycle correction will be used to account for the fact that events and transitions can occur at any point during the cycle, not necessarily at the start or end of each cycle.
The same strategies of the 2-year time analyses will be used for deterministic and probabilistic analyses using the model framework. The final interpretation of uncertainties will be considered for this longer time horizon. Data will be modelled and analyzed using a Markov simulation model. Tree Age Pro 2017 (TreeAge Software, Williamstown, MA, USA).