According to the Transparent Reporting of a prediction model for Individual Prognosis or Diagnosis (TRIPOD), this manuscript has been prepared for reporting prediction model proposal/development focused on the short-term progression of caries lesions.
Examiner training
Two examiners were involved in this study: one responsible for the baseline examinations (MMB) and the other for the follow-up (IF). This last examiner (IF) was introduced to the ICDAS by an experienced examiner (MMB), who is engaged in previous clinical studies in caries diagnosis. This experienced examiner was considered as a reference examiner for this study. Firstly, the original index description was studied [16]. The trained examiner then individually evaluated projections of clinical photographs of caries lesions. Finally, 36 occlusal surfaces of extracted primary molars were assessed for both separately. Among these surfaces, sound surfaces and caries lesions at different levels of severity were included. After each training phase, the reference examiner discussed any divergence between the examiners and coordinated the training. The next step was started after all doubts and divergences had been solved.
For the assessment of potential predictors, the reference examiner examined this same sample of teeth twice in random orders to permit the calculation of intra-examiner calibration.
Source of data/study population/participant selection
The focus of this prospective cohort study was on children with primary molars (approximately from 3 to 12 years) who sought dental treatment at a dental clinic. These children could have preventive or therapeutic needs (caries experience or not). The clinic, located in a Dental School in São Paulo, Brazil, is a reference for Pediatric Dentistry. São Paulo presents human development index equal to 0.805 (https://www.br.undp.org/content/brazil/pt/home/idh0/rankings/idhm-municipios-2010.html) and regularly fluoridated water at 0.7 ppm. This Brazilian region's mean dmft index among 5-year-old children is 2.1 (95%CI 1.79–2.42) [17].
This sample constituted our development cohort. At this time, we did not include a validation cohort. This cohort was formed from 2011 to 2013 and then was followed up for one year. Children from this cohort were referred to dental care in the same dental school clinics where the research was being conducted. However, neither the researchers were not responsible for their treatment, nor specific research protocol for dental treatment was adopted for these children. Protocols used for dental care providers at the institution (or where they had the dental treatment performed) were followed independently of research participation.
All children who had at least one primary molar available to be examined were eligible for enrolment. The children's assent and their parents' consent had to be obtained to guarantee participation in the study. When consent/assent was not obtained, the child was excluded from the sample. The same was done when children and their family stated that it is impossible for them to comply with the 1-year follow up.
If a child presented more than one eligible molar, one included all of them. Surfaces with restorations, hypoplastic defects, sealants, or frank cavities (ICDAS 5–6) were excluded from the study sample.
An external researcher pre-selected a site for each surface based on the highest ICDAS score found on the respective surface. Sites were recorded using a specific illustration in the participant's file to guide the following stages.
Study outcome
Caries progression was set as the primary outcome. As caries progression, we considered those surfaces that, with a 1-year follow-up, presented cavities with dentine exposure and/or teeth were restored or extracted due to caries. This examination was performed approximately one year after the baseline examination by a different examiner from the baseline assessments. On this occasion, children occlusal surfaces were examined using the ICDAS [16]. Restorations and teeth that had been extracted (because of caries) were also recorded. Changes not related to cavitation exposing the dentine (e.g., ICDAS score 1 or 2 to ICDAS 3) were registered, but they were not considered as an event for the analysis.
The children were examined in a dental unit using the halogen operating light lamp for the dental chair. Examiner used a plane dental mirror, a ball-ended probe, and a three-in-one syringe. Before the examination, teeth were gently cleaned with a rotating bristle brush and pumice/water slurry. For this evaluation, the examiner followed pre-signalled charts with the occlusal sites evaluated at the baseline.
Sample size
The required sample size was estimated based on the assessment of active caries lesions in children. Sample size calculation [18] was based on a prevalence of active lesions of 62.5%, observed in a previous study conducted on a Brazilian population [19]. We assumed that surfaces with active caries lesions would be those prone to progress for frankly cavitated lesions. For this calculation, we adopted the most conservative condition to guarantee the maximum possible sample size, as if one surface could be included per child and a confidence level of 95%. A minimum sample size of 126 surfaces was calculated, and this number was increased by 20% to compensate for parent or children's refusal to participate and for possible dropouts. Hence, a sample of 151 surfaces was required. Since more than one occlusal surface could be included in the sample, we assumed a factor of correction of 1.4 to compensate for the clustering effect. Then, we determined that at least 212 surfaces were needed for our sample.
Possible predictor variables
We identified possible predictor variables based on previously published literature review [2] describing possible clinical parameters associated with active caries [5]. These parameters have been combined in different systems for caries activity assessment [7, 20] and were described in details in a previous publication [5] (Fig. 1). In the present study, we decided to investigate these parameters' ability in predicting short-term caries progression (1 year). For that, we tested their prediction solely or in combination with one or more parameters under investigation.
An experienced examiner in caries diagnostic research (MMB), different from that of the follow-up examination, assessed eligible occlusal surfaces in the baseline and classified the selected sites by independently considering the possible predictor variables: colour, lustre, surface integrity, depth, and texture (Fig. 1). The examiner did not use any specific system but classified the sites as described. The clinical examination was performed at the same clinical conditions (light, air-drying, and the use of specific probe) mentioned above for outcome assessment.
Model proposal/derivation
For model development, we opted for a complete-case analysis, excluding those cases in which there is the absence of information related to the prediction variables assessment and/or follow-up assessment for outcome evaluation. Firstly, each of the clinical features related to caries lesions' activity status (colour, lustre, surface integrity, texture, and lesion depth) was tested as independent variables (Models 1–7). Univariate multilevel Poisson models were fitted to test each of the independent variables (clinical features) as predictors of short-term caries progression. These variables were chosen based on information criteria [21], and plausible models were tested. Since there is a previously established theory supporting the studied construct, we opted to perform a multimodel inference based on the Akaike Information Criteria (AIC) [21, 22]. The unit of analysis was the tooth. The levels for these analyses were: the tooth and the child. This option permits the adjustment of analyzing more than one tooth per child, if necessary.
Afterwards, we tested the plausible interactions among some variables to evaluate the possible benefit of combining these variables when assessing caries lesion activity, as proposed for some available systems. The conceptual and statistical framework of these potential interactions is illustrated in Fig. 2. We tested the interactions between two variables using the interaction terms (product variables) created as dummy variables in the respective models (Additional file 1). Firstly, these “product terms” were used to represent the interaction between variables based on a priori meaning defined in the conceptual framework (Fig. 2). Moreover, variables resulting in lower AICs in univariate models were first selected to be tested in conjunction with the others (statistical framework—Fig. 2) since a reasonable construct was available. All possible combinations were tested, but only the most relevant will be described in the results.
The dummy variables created were used as independent variables in the regression equation of multilevel models and tested as a meaningful predictor (Additional file 2). Hence, it is used to investigate the potential benefit of combining two variables when predicting the outcome of interest. A multiple regression model was not used including more than one characteristic as independent variables because of the likelihood of multicollinearity among them. Indeed, one variable could cancel out the effect of another related variable in the multiple model if they are strongly associated with each other, even being equally crucial individually in explaining the outcome.
Finally, to simulate the use of systems that combine these characteristics, we created specific dummy variables representing the number of active lesions' characteristics. First, we assumed an initial or established active lesion would be ideally whitish/yellowish with no lustre and rough enamel. In one of the models, we tested if occlusal surfaces, presenting at least two of these positive factors, may predict caries progression after one year. For the other one, we tested if the presence of any one of the positive factors above could predict the same outcome (Additional file 3).
Subgroup analyses were also performed by considering only the non-cavitated lesions at the baseline. We adopted the same strategies mentioned earlier for model derivation for these analyses, but the interpretation of results was made carefully due to the limitations inherent to this approach.
Prediction model performance
The relative risk (RR) for the clinical features predicting the outcome (alone or combined with one or more other clinical features) was calculated with a 95% confidence interval (95% CI). Two-sided p values < 0.05 were considered to be statistically significant.
The overall goodness-of-fit of the models was compared in the development cohort based on AIC. To evaluate model discrimination, we used the C statistic [12]. As we had a dichotomous outcome, we calculated the area under Receiver Operator Characteristic (ROC) curves to obtain the C-statistics [12].
We used bootstrap resampling for internal validation to adjust for the overfitting and optimistic performance of the model. One thousand bootstrap samples were drawn with replacement, and the performance was also evaluated in the bootstrap sample. The uniform shrinkage factor was computed using this bootstrap procedure [23], and regression slopes were recalculated based on that.
Statistical analyses were performed in Stata Software (version 13.1), StataCorp, Texas, USA.