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. 2026 Sep 9;26:1885. doi: 10.1186/s12903-026-09819-w

Development of a nomogram for prediction of occlusal dentin caries in Norwegian children at risk: a 36-month follow-up study

Lina Stangvaltaite-Mouhat 1,✉, Ibrahimu Mdala 1, Ingrid Volden Klepaker 1, Tove Irene Wigen 1,2, Marte-Mari Uhlen-Strand 1, Rasa Skudutyte-Rysstad 1,2
PMCID: PMC13628957  PMID: 42823705

Abstract

Background

The aim of this study was to develop and internally validate a nomogram predictive model for occlusal dentin caries development on first permanent molars (FPMs) over 36 months in children at risk in Norway.

Methods

For a practice-based split-mouth randomized trial (ClinicalTrials.gov ID: NCT03315312, retrospectively registered in October 2017) comparing effectiveness of caries control methods (fissure sealants versus fluoride varnish), children aged 6 to 10 years considered at high caries risk (D3MFT/d3mft > 0) were recruited by calibrated dentists and dental hygienists during routine examination in the public dental service and monitored for 36 months. Outcome was development of occlusal dentin caries lesion on FPMs. Data on biological predictors were collected at baseline by clinicians. Data on behavioral predictors were collected using a questionnaire for parents. Clinical predictors included clinic’s county, whether the participant was followed up by the same clinician and caries control method. The least absolute shrinkage and selection operator (Lasso) logistic regression model was used to select relevant predictors and develop a nomogram for predicting dentin caries development.

Results

Of 330 participants, 174 (51.7) were boys. The Lasso logistic regression selected four predictors, d3mft at age 5 years, occlusal surface baseline status, caries control method, and use of fluoride toothpaste, which were used to construct a nomogram. The Area Under the Receiver Operating Characteristic Curve was 0.69 (95% CI 0.62–0.77), and Concordance Index was 0.68 (95% CI 0.60–0.76) in the training set and 0.67 (95% CI 0.59–0.74) in the validation set. The calibration belt indicated good calibration of the model (p > 0.05).

Conclusion

In this study, based on 36-month follow-up data in children at risk, we have developed and internally validated a nomogram to predict dentin caries on occlusal surfaces of FPMs. The findings suggest that nomogram approach may be a useful visual aid in clinical practice to facilitate informed decision-making; however, external validation in a large cohort study, transportability and applicability to different settings are needed.

Keywords: Caries control, Caries prediction, Child, Clinical trial, Dental caries, Fluoride varnish, Fissure sealants, Nomogram, Prevention

Background

Even though dental caries is a highly preventable and controllable oral disease, the global prevalence of untreated dental caries in permanent teeth remains high [1]. The expenditures of managing dental conditions are the third highest health expenditures in the European Union [2, 3] and are estimated to increase over the coming decades [4]. Occlusal surfaces are the most susceptible to dental caries [5, 6], and in permanent molars, caries development is most likely within the first few years after eruption [7, 8]. It is now well-established that dental caries is a ‘biofilm-mediated, diet modulated, multifactorial, non-communicable, dynamic disease’ having biological, behavioral, psychosocial, and environmental risk factors [9]. Prediction of individual caries risk has potential to enhance person-centered caries control by supporting clinicians in choosing targeted preventive strategy, and it also can serve as an educational and communication tool between patients/guardians and clinicians in decision making.

Several caries risk assessment (CRA) tools, which incorporate information of different sets of caries risk and preventive factors in combination with the clinical findings, have been developed [10–16]. However, a systematic review concluded that the validity of standardized CRA tools remains limited [17]. The authors identified two types of CRA tools: ‘algorithm-driven’ and ‘reasoning-based’ [17].

In general, the terminology of risk assessment/prediction models is inconsistent in the literature. ‘Risk assessment tools’ are often defined more loosely and rely mainly on subjective judgment and informal or qualitative evaluations [18]. Specifically for caries risk, it has been discussed that ‘most available tools are expert-informed, with limited formal evaluation and lacking validation’ and the authors in their call-for-action article encouraged to improve the scientific basis for multivariable caries risk prediction models [19].

Caries risk prediction models refer to ‘the statistical modeling of factors related to caries development in populations or defined groups of people’ [20]. They apply ‘multiple predictors which are not necessary causal to estimate the specific outcome within a specified time frame and offer numerical probabilities based on the predictions’ [18, 21].

A recent systematic review and meta-analysis, including 11 studies on risk prediction models for dental caries in children and adolescents, concluded that all models had a high risk of bias, mainly due to inappropriate statistics and insufficient reporting [22].

Nomograms are graphical representations of statistical models used for risk prediction. Medical nomograms use biologic and clinical variables to graphically depict a statistical prognostic model that generates a probability of a clinical event for a given individual [23]. For prediction purposes, nomograms are extensively used in clinical medicine, particularly for cancer prognosis [24]. This visual tool has gained popularity because it simplifies complex predictive statistical models into a single individual numerical estimate of the probability of an event [25].

Nomogram use in the dental field is increasing. Promising results have been achieved for benchmarking [26], predicting peri-implantitis [27], screening for periodontitis [28] and in implantology [29]. Studies performed in China, using nomograms for detection of high caries risk children [30], screening children for severe caries [31], and assessment of root caries [32], evaluated their models as having a good performance.

Since data used to develop prediction models are usually context specific, i.e., different places, populations, and follow-up times, the transportability of those models to different settings might be challenging [18]. In Norway, caries prevalence among children is low, it remains skewed, with the highest proportion of caries lesions accumulating in a small subset of children [33]. The potential of nomograms for predicting caries of high risk children in a low caries population has not yet been investigated. In Norway, children receive free dental care through the Public Dental Service (PDS). In addition to recommendations on toothbrushing with fluoridated toothpaste and diet guidance, current guidelines also include the use of fluoride varnish applications or fissure sealants for occlusal caries control on newly erupted permanent molars in children at moderate and high risk [34]. It has been shown that clinicians’ preferred occlusal caries control method depended on child’s age, caries experience, and region [35]. Therefore, to support clinicians in choice of occlusal caries control method, enhance education of patients, and improve communication between patients/guardians and clinicians facilitating user involvement in the decision-making, we investigate a predictive model of nomograms in children at risk in Norway.

Methods

Aim

The aim of this study was to develop and internally validate a nomogram predictive model for occlusal dentin caries development on first permanent molars (FPMs) over 36 months in children at risk in Norway.

Study design and participants

This study is based on a secondary analysis of data from a randomized practice-based split-mouth trial to compare effectiveness of fissure sealants and a fluoride varnish application for caries control of occlusal surfaces of FPMs after 36 months [36]. The trial was conducted in nine PDS clinics in three counties in South-Eastern Norway. Trained and calibrated dentists and dental hygienists recruited participants during the routine checkup. Children aged 6 to 10 years, having previous dental caries experience (d3mft/D3MFT > 0) and fully erupted FPMs with sound occlusal surfaces or initial caries lesions (grade 1–2) where moisture control could be achieved were invited to participate. The caries assessment was based on clinical examination and supplied with information from the radiographs if available. The criteria for occlusal caries are described in Amarante et al. 1998 [37] and were as follows:

  • Grade 1: Caries characterized by white or brown discoloring without substance loss. No radiographic findings.

  • Grade 2: Little substance loss with break in the enamel surface or discoloring fissure with gray/opaque adjacent enamel and/or caries restricted to enamel in a bitewing radiograph.

  • Grade 3: Moderate substance loss and/or caries in the external 1/3 of the dentin radiographically.

  • Grade 4: Considerable substance loss and/or caries in the middle 1/3 of the dentin radiographically.

  • Grade 5: Great substance loss and/or caries in the internal 1/3 of the dentin radiographically.

The recruitment was performed from February 2017 to November 2019, and 36 months follow-up was completed November 2022. All participants received chairside caries control methods (fissure sealant and fluoride varnish application) on contralateral FMPs according to clinicians’ standard procedures for application and maintenance. The trial is described in detail elsewhere [36].

Caries predictors

Caries predictors were chosen based on the current caries definition referring to different level determinants and the Norwegian context [9, 34, 35]. Biological predictors selected for risk prediction model were age, sex, d3mft at age 5 years, plaque (no visible plaque/visible plaque), occlusal surface baseline status (sound/caries grade 1–2), and jaw of FPMs (upper/lower). These were recorded at baseline by a clinician from the electronic dental records or during clinical examination.

Behavioral predictors were tooth brushing frequency (twice daily/less than twice daily), use of fluoride supplements (fluoride tablets used daily/less frequently than daily), use of fluoride toothpaste (usually/not usually), if parents help brushing (sometimes or never/once daily or more), and sugar-containing diet (less frequent/more frequent) were collected via a questionnaire for parents. For statistical analyses, sugar-containing diet was calculated by adding frequency consumption scores of three sugar-containing items (sugary drinks/sweet biscuits or pastry/sweets or chocolate: ‘0’ less than once a week, ’1’ once a week, ‘2‘ several times a week, ‘3’ several times daily’) and grouped into ‘less frequent’ and ‘more frequent’ based on a median value of 3 as a cut-off point.

Clinical predictors were clinic’s county and clinician, categorized as whether the same clinician performed caries control method applications and all the follow-ups, or if the child was seen by more than one clinician during the study period (same/not same). Caries control method (fissure sealants or fluoride varnish) was recorded by clinicians. Fissure sealants were applied at baseline and maintained according to clinicians’ conventional procedures, while fluoride varnish was applied at baseline, 6- and 12-month follow-up.

Outcomes

The outcome was occlusal surface status of FPM over 36 months follow-up dichotomized into intact (sound or caries grade 1–2) and dentin caries (dentin caries lesion or restoration).

Sample size

Sample size was calculated for a randomized split-mouth clinical trial to detect a clinically significant difference of 10% between fluoride varnish and fluoride sealant. The calculations were based on the assumptions that 80% of included FPMs would not develop dentin caries and that the between-methods correlation would be 0.3. Based on 80% power and 5% significance, it was estimated that 180 participants were needed. To compensate for a potential dropout rate of 20–25% over 36 months, a total of 400 participants needed to be enrolled.

Statistical methods

Caries predictors stratified by occlusal surface status of FPM over 36 months follow-up were summarized using mean (standard deviation) for continuous variables and frequency (percentage) for categorical variables. Mean differences between the groups were assessed using the independent samples t-test whereas associations between categorical variables were assessed using the Chi-square test for expected cell counts > 5 and the Fisher’s exact test for cell counts ≤ 5. Missing values were excluded and complete-case analysis performed.

Model development

The least absolute shrinkage and selection operator (lasso) logistic regression model was used to select potential predictors of dentin caries in FPMs. The lasso selected a subset of predictors by shrinking regression estimates of the least contributing independent variables to zero. Therefore, all independent factors that were set to zero were eliminated from the prediction model. The factors that were selected using the lasso logistic regression were then used to fit a multivariable logistic regression model and subsequently, a predictive nomogram was generated. Using the R package shiny [38], we developed an online calculator (https://linas-tko2025.shinyapps.io/R_caries_project/) for predicting dental caries on occlusal surfaces on first permanent molars in children at risk. The dataset is multilevel, as teeth are nested into participants, but since mixed models cannot be used for nomogram development, we handled clustering by introducing the variance-covariance estimator (VCE) to our logistic regression models.

Model’s predictive performance and internal validation

The predictive performance of our nomogram was evaluated by a measure of calibration, i.e., Calibration belt, and measures of discrimination: (i) Area Under the Receiver Operating Characteristic Curve (AUC-ROC), which quantify the model’s ability to distinguish FPMs with occlusal dentin caries after 36 months follow-up from those without, and (ii) Concordance Index (C-index), which measures the probability that a randomly selected FPM with occlusal dentin caries has a higher predicted risk than a non-caries FPM. We used 1000 bootstrap re-sampling to internally validate our model.

All analyses were performed in Stata/SE 18.0, statistical significance was set at p < 0.05.

The nomogram development process followed a step-by-step guide [39] and TRIPOD guidelines were used for reporting results [40].

Results

Out of 409 recruited participants, 4% [16] were lost during the follow-up and occlusal surface status of FPM for a further 24 children were not known at 36 months follow-up. Only participants who received both caries control methods at baseline and three FV applications as described in the protocol (i.e., baseline, 6 and 12 months) were included. Therefore, the analyses included data from 330 participants, of which 174 (52.7%) were boys. In total, 51 FPMs had an outcome, i.e., developed dentin caries lesions or were restored. A higher proportion of FPMs developed caries lesions over 36 months follow-up if a participant had higher d3mft at age 5 years and initial caries lesion at baseline (Table 1).

Table 1.

Caries predictors (individual and tooth level) at baseline stratified by occlusal surface status over 36 months follow-up

Caries predictors Occlusal surface status over 36 months follow-up P-value
Intact Dentine caries lesion
 Total number of teeth (tooth level: n = 660) 609 (92.3) 51 (7.7) < 0.01
Biological
 Age in years (Mean ± SD) 7.77 ± 1.06 7.60 ± 1.00 0.27
 Sex (patient level: n = 330) 0.30
  Girl 131 (84.0) 25 (16.0)
  Boy 153 (87.9) 21 (12.1)
 d3mft at age 5 years (Mean ± SD) 2.23 ± 2.98 3.35 ± 3.60 0.01
 Plaque at baseline (tooth level: n = 632) 0.24
  No plaque 253 (92.3) 17 (6.3)
  Plaque present 330 (91.2) 32 (8.8)
 Occlusal surface baseline status (tooth level: n = 660) 0.02
  Sound 508 (93.4) 36 (6.6)
  Caries grade 1–2 101 (87.1) 15 (12.9)
 Jaw of first permanent molar (tooth level: n = 660) 0.83
  Upper jaw 349 (92.1) 30 (7.9)
  Lower jaw 260 (92.5) 21 (7.5)
Behavioral (at patient level: n = 330)
 Brushing frequency (patient level: n = 326) 0.63
  Twice daily 239 (86.3) 38 (13.0)
  Less than twice daily 41 (83.7) 8 (16.3)
 Fluoride supplements (patient level: n = 323) 0.36
  Daily 119 (88.1) 16 (11.9)
  Less frequently than daily 159 (84.6) 29 (15.4)
 Fluoride toothpaste (patient level: n = 325) 0.49
  Usually 265 (86.0) 43 (14.0)
  Not usually 16 (94.1) 1 85.9)
 Parents help brushing (patient level: n = 325) 0.76
  Once daily or more 151 (85.3) 26 (14.7)
  Sometimes or never 128 (86.5) 20 (13.5)
 Sugar-containing diet (patient level: n = 316) 0.58
  Less frequently 136 (85.0) 24 (15.0)
  More frequently 136 (87.2) 20 (12.8)
Clinical
 County (patient level: n = 330) 0.39
  Hedmark 69 (89.6) 8 (10.4)
  Østfold 66 (88.0) 9 (12.0)
  Oppland 149 (83.7) 29 (16.3)
 Clinician (patient level: n = 329) 0.99
  Not same clinician 178 (86.0) 29 (14.0)
  Same clinician 105 (86.1) 17 (13.9)
 Caries control method (tooth level: n = 660) 0.013
  Fissure sealant 313 (94.9) 17 (5.2)
  Fluoride varnish 296 (89.7) 34 (10.3)

The lasso logistic regression selected four predictors: d3mft at age 5 years, occlusal surface baseline status, caries control method, and use of fluoride toothpaste (Table 2). The predictive nomogram and online calculator generated from an adjusted logistic regression model using the four predictors is given in Fig. 1. VCE of the logistic regression model had impact mainly on the standard errors, hence the model output and nomogram remained unchanged (data not shown). How to use the nomogram in predicting dentin caries development on occlusal surface of FPMs is shown in Textbox 1.

Table 2.

Predictors of dental caries obtained from the Lasso logistic regression model, odds ratios (ORs) and 95% confidence intervals

Predictors OR (95% CI) P-value
d3mft at age 5 years 1.09 (1.01, 1.17) 0.028
Caries control method (ref: Fissure sealant)
 Fluoride varnish 2.33 (1.25, 4.35) 0.008
Occlusal surface baseline status (ref: Sound)
 Caries grade 1–2 2.22 (1.16, 4.26) 0.016
Fluoride toothpaste (ref: Usually)
 Not usually 1.44 (0.35, 5.94) 0.612

Fig. 1.

Fig. 1

Predictive nomogram and online calculator generated from an adjusted logistic regression model using the four predictors: dentine caries experience at age 5 (0–20), baseline status of occlusal surfaces of first permanent molars (health/caries grade 1–2), caries control method (fissure sealant/fluoride varnish) and use of fluoride toothpaste (usually/not usually)

Textbox 1. Demonstrating how to use the nomogram to predict occlusal dentin caries lesion development on first permanent molar (FPM) in children
Consider a hypothetical FPM of a 6-year-old girl. Caries experience, d3mft, at age 5 years was 5. Initial caries lesion (caries grade 1 – 2) was diagnosed on occlusal surface of this tooth. Fluoride varnish was applied as caries control method. The child does not usually use fluoride toothpaste. Her approximate total score is given as follows:
Predictor Value/ category Risk score (approximate)
d3mft at age 5 years 5 2.5
Occlusal surface baseline status Caries grade 1 - 2 4.5
Caries control method Fluoride varnish 4.25
Fluoride toothpaste Not usually 2.0
Total score 13.25
Estimated probability 0.22
From the total score line, the estimated probability for the occlusal surface of this FPM developing dentin caries in 36 months is approximately 0.22, i.e., there is approximately a 22% likelihood of developing dentin caries

The nomogram’s ability to discriminate FPM’s risk of developing occlusal dentin caries over 36 months was evaluated as AUC-ROC, which was 0.69 (95% CI 0.62 - 0.77) (Fig. 2). In the training set, the C-index estimate was 0.68 (95% CI 0.60 - 0.76), while in the validation set, the estimate was 0.67 (95% CI 0.59 - 0.74). The calibration belts in the training and the validation sets showed that the model fit was good (p>0.05) (Fig. 3). This suggests that the prediction of the model does not deviate from the observed rate significantly.

Fig. 2.

Fig. 2

Receiver operating characteristic curve illustrating the predictive performance of the nomogram for dentine caries lesion development. The area under the curve is 0.694, showing moderate ability to distinguish between first permanent molars developing lesions and those not.

Fig. 3.

Fig. 3

Calibration belt comparing predicted probability of dentine caries lesions on occlusal surfaces of first permanent molars and the observed probability, (A) training set and (B) validation/test set. The light blue shaded area represents the 95% confidence interval, and the red dashed line is the reference line (bisector) representing an ideal nomograph. The blue line is a smoother, which indicates whether there are systematic deviations from perfect calibration. For example, if the smoother was consistently above the bisector, this would mean that the model is overestimating the probability of dental caries. In the test set, the 95% calibration belt encompasses the bisector over the range of predicted probability of < 0.3 and there is no systematic deviation from the bisector in those ranges

Discussion

The present study developed and internally validated a nomogram for predicting development of occlusal dentin caries on FPMs in 6–10-year-old children over 36 months receiving regular dental care. Higher d3mft at age 5 years, initial caries lesion, fluoride varnish as caries control method, and not usually use of fluoride toothpaste were the selected predictors.

For this nomogram model, AUC-ROC was estimated to be 0.69 (95% CI 0.62–0.77). A combined predictive model incorporating six caries predictors achieved an AUC of 0.79 (95% CI: 0.73 to 0.84) according to the systematic review and meta-analysis including 11 studies of caries prediction in children and adolescents [22]. A systematic review and critical appraisal of multivariable prediction models of caries increment concluded that the ‘modest performance of most models implies that alternative predictors should be considered’, and suggested that the attention should be directed toward bacterial phenotypes, specifically acid-tolerant bacteria, as one of the most common predictors [41]. This and other potential predictors, such as salivary secretion rate, were not collected in the present study. It has been discussed that other predictors for example human genetic variation, microbiota composition and microbial genome may enhance the predictive value of models [19], however, the collection of this type of information in a routinely clinical practice setting would require additional skills and equipment from clinicians and might be costly and challenging to implement.

In this nomogram, the use of fluoride toothpaste was the only behavioral thus modifiable predictor depicted, which was also identified in a systematic review and meta-analysis [22]. Based on the results of our nomogram, clinicians should have more emphasis on daily toothbrushing using fluoride toothpaste for children with unfavorable biological risk factors.

Although children in Norway are considered as a low-caries population, the prevalence is skewed. Therefore, in this study, we included children at risk defined as those with dental caries experience at the time of enrollment. In our study, higher previous caries experience was identified as the most significant predictor. This result aligns with another nomogram study performed in a high-caries population, where previous caries experience was the strongest predictor [30], and with several prospective studies demonstrating that previous caries experience is associated with the development of dentin caries lesions on occlusal surface [42–44]. A recent systematic review of multivariable prediction models of caries increment identified caries experience being among the most common predictors though included studies were assessed as having high risk of bias [41]. An older systematic review also investigated single predictors; although multivariable models had better accuracy, caries experience as a single predictor was evaluated as having from good to limited accuracy in caries prediction in children and adolescents [45].

Occlusal surface baseline status was identified as a predictor in our nomogram: initial caries lesion increased risk for dentin caries lesion development, despite fluoride varnish or fissure sealant use. Pits and fissures on the occlusal surface serve as ideal niches for bacterial accumulation, as they are difficult to clean effectively. In the case of initial lesions, there is, first, a greater bacterial load, and second, deeper penetration into the tooth tissues compared to sound occlusal surfaces. This leads to prolonged exposure to a lower pH, accelerating the demineralization process. In addition, the probability that the individual risk factors for caries disease were not successfully managed cannot be ruled out.

Fluoride varnish as caries control measure (versus fissure sealant) was identified as a predictor in our nomogram. In Norway, the choice of caries control measure mainly depends on the practitioners’ preferences as national guidelines recommend using both [34]. Newest evidence suggests that both fissure sealants and fluoride varnish are effective for occlusal caries control [46], but a Cochrane systematic review could not conclude which one was more effective [47]. Given the pragmatic nature of the study and the involvement of many clinicians, it can be speculated that the threshold for operative treatment of questionable occlusal lesions might be lower for surfaces with fluoride varnish compared to fissure sealants. Although this was a practice-based study in which clinicians were instructed to use fissure sealants and fluoride varnishes available in their clinics, resulting in the use of several different commercial brands, all clinicians applied resin-based fissure sealants and fluoride varnishes, containing 5% sodium fluoride formulations delivered in film-forming systems based on either rosin-derived resins or synthetic polymer resins.

We constructed and internally validated a nomogram for predicting occlusal dentin caries among children at risk receiving regular dental care. The model provides risk estimates based on real-life data and time frame of 36 months rather than traditional subjective judgment risk. Children in our study were identified as at risk, i.e., having dental caries experience at the time of enrollment, even though receiving regular dental care by salaried clinicians (no financial incentives for possible overtreatment involved), and chairside occlusal caries management, but still developing dentin caries.

Several predictors identified by our nomogram were in line with the most common predictors found in other multivariable prediction models. However, our results should be interpreted with caution, as transportability and applicability of this nomogram to different contexts will require external validation, i.e., validation of the model in new datasets [18]. The model should also undergo testing in a clinical trial before it can be recommended for clinical use, as the extent to which its utilization improves outcomes and reduces costs is unknown. Main limitations of this study were a relatively limited number of behavioral predictors, small sample size and potentially insufficient number of outcomes per predictor [41]. This could have resulted in a ceiling effect regarding the upper end of predicted risk, limiting the ability to discriminate between individuals with high scores. Additionally, the data about fissure sealant maintenance was not included, and therefore it is unknown which impact reapplications may have had on the prediction. There were no actions taken to blind assessment of the predictors or outcome, however, 63% of children were followed up by different clinicians. Also, only occlusal surfaces were included in the study. On the other hand, occlusal surfaces are the most susceptible to caries and most challenging to manage. It might be anticipated that the nomogram being visual tool may facilitate more patient centered, informative and motivational communication with children and their parents and contribute to informed decision-making for children at caries risk.

Conclusions

In this study, based on 36-month follow-up data in children at caries risk, we have developed and internally validated a nomogram to predict dentin caries on occlusal surfaces of FPMs. The findings suggest that nomogram approach may be a useful visual aid in clinical practice to facilitate informed decision-making; however, external validation in a large cohort study, transportability and applicability to different settings are needed.

Acknowledgements

We would like to acknowledge the participants of this study, and the clinical dental personnel at Fredrikstad, Gjøvik, Halden, Kongsvinger, Lena, Lillehammer, Raufoss, Valdres public dental service clinics for their contribution to data collection in the study.

Clinical trial number

ClinicalTrials.gov ID: NCT03315312, retrospectively registered in October 2017.

Abbreviations

AUC

ROC–Area Under the Receiver Operating Characteristic Curve

CI

Confidence interval

C

Index–Concordance Index

CRA

Caries risk assessment

FPMs

First permanent molars

Lasso

Least absolute shrinkage and selection operator

VCS

Variance–covariance estimator

WHO

The World Health Organization

Authors’ contributions

MMUS, IVK, and RSR made substantial contributions to the conception of the main study. IM, LSM, and RSR contributed to the design of this work. IM performed statistical analyses and together with LSM, RSR and MMUS interpreted them. LSM, IM, and RSR drafted the manuscript, MMUS, TIW and IVK revised the manuscript.All authors approved the final version of the manuscript and agreed to be personally accountable for their contribution and to ensure that questions related to the accuracy or integrity of any part of the work, even parts in which the authors were not personally involved, are appropriately investigated, resolved, and the resolution documented in the literature.

Funding

None.

Data availability

The data that support the findings of this study are not publicly available due to containing information that could compromise the privacy of research participants but are available from the last author (RSR) upon reasonable request.

Declarations

Ethics approval and consent to participate

This study was performed in compliance with Good Clinical Practice and the Declaration of Helsinki. Approval was obtained from the Regional Committee for Medical Research Ethics South East Norway (2016/2002/REK sør-øst) and registered at ClinicalTrials.gov (ID: NCT03315312). Participation was voluntary and based on a parental signed written informed consent form.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.

Footnotes

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Data Availability Statement

The data that support the findings of this study are not publicly available due to containing information that could compromise the privacy of research participants but are available from the last author (RSR) upon reasonable request.


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