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Multivariable prediction models of caries increment: a systematic review and critical appraisal



Multivariable prediction models are used in oral health care to identify individuals with an increased likelihood of caries increment. The outcomes of the models should help to manage individualized interventions and to determine the periodicity of service. The objective was to review and critically appraise studies of multivariable prediction models of caries increment.


Longitudinal studies that developed or validated prediction models of caries and expressed caries increment as a function of at least three predictors were included. PubMed, Cochrane Library, and Web of Science supplemented with reference lists of included studies were searched. Two reviewers independently extracted data using CHARMS (Critical Appraisal and Data Extraction for Systematic Reviews of Prediction Modelling Studies) and assessed risk of bias and concern regarding applicability using PROBAST (Prediction model Risk Of Bias ASessment Tool). Predictors were analysed and model performance was recalculated as estimated positive (LR +) and negative likelihood ratios (LR −) based on sensitivity and specificity presented in the studies included.


Among the 765 reports identified, 21 studies providing 66 prediction models fulfilled the inclusion criteria. Over 150 candidate predictors were considered, and 31 predictors remained in studies of final developmental models: caries experience, mutans streptococci in saliva, fluoride supplements, and visible dental plaque being the most common predictors. Predictive performances varied, providing LR + and LR − ranges of 0.78–10.3 and 0.0–1.1, respectively. Only four models of coronal caries and one root caries model scored LR + values of at least 5. All studies were assessed as having high risk of bias, generally due to insufficient number of outcomes in relation to candidate predictors and considerable uncertainty regarding predictor thresholds and measurements. Concern regarding applicability was low overall.


The review calls attention to several methodological deficiencies and the significant heterogeneity observed across the studies ruled out meta-analyses. Flawed or distorted study estimates lead to uncertainty about the prediction, which limits the models’ usefulness in clinical decision-making. The modest performance of most models implies that alternative predictors should be considered, such as bacteria with acid tolerant properties.

Trial registration

PROSPERO CRD#152,467 April 28, 2020

Peer Review reports


Prediction models are used to estimate the probability of the presence of a particular disease (diagnosis) or to estimate the probability of developing a particular outcome in the future (prognosis) [1]. Estimates of probabilities of developing an outcome are rarely based on a single predictor and care providers naturally integrate several variables [1].

Dental caries, defined as bacteria-triggered localised demineralization of dental tissues, is estimated to have a global prevalence of 35% and is associated with high societal costs [2]. A prediction model of caries involves an assessment of the probability that a number of new lesions will occur over time. The model output will help to realize individualized preventive interventions and to determine the periodicity of service. Since many clinicians apply prediction models of caries daily, critical appraisal of models is crucial. Recent evidence suggests that there is a need to improve the methodological standards, and predictive analytic methods with alternative predictors are called for [3]. Still, it is important to update facts about predictors presented in current scientific literature, and not to squander information from previous studies.

The purpose of systematic reviews (SRs) is to compile, analyse and interpret all available data to make reliable conclusions, and to identify knowledge gaps. The CHecklist for critical Appraisal and data extraction for systematic Reviews of prediction Modelling Studies (CHARMS) was designed to guide the framing of review questions of SRs and the extraction of relevant items of prediction model studies [4]. For the assessment of risk of bias and applicability, which are essential steps in any SR, the Prediction model Risk Of Bias ASsessment Tool (PROBAST) was developed [5, 6]. The objective of this study was to systematically review and critically appraise studies of development and validation of multivariable predictive models for assessment of caries increment i.e., caries onset or caries progression with the aid of CHARMS and PROBAST. In particular, we aimed to focus on the predictors, risk of bias, and the predictive performance.



We followed the PRISMA 2020 checklist [7] (Additional file 1). Prior to the formal start of the study, the review protocol was registered with the University of York Centre for Reviews and Dissemination International prospective register of systematic reviews (PROSPERO) (submitted October 3, 2019; registration April 28, 2020, Registration #152,467), and later supplemented (November 30, 2020) with a checklist based on CHARMS.

Eligibility criteria

Inclusion criteria were based on PICOTS (Participants, Intervention, Comparator, Outcome, Timing, Setting). Studies were included if they met the following criteria:

  • Study design: longitudinal prospective or retrospective study.

  • Participants: individuals of all ages, sex, and ethnicity. Caries should be defined at baseline and follow-up regarding prevalence and severity on an individual basis. Alternatively, caries progression should be possible to calculate from data presented in the included study or in studies referred to.

  • Intervention: a prediction model that expresses caries increment as a function of at least 3 variables as predictors. Predictors described in sufficient detail to allow calculation of model performance. When predictors were not described in detail but referred to, the referenced study was retrieved to recover key data.

  • Comparator: additional prediction model(s) included in the study.

Outcome to be predicted: development either (i) from sound tooth/tooth surface to detectable lesion in enamel or dentin: i.e., from health to disease onset, or (ii) from initial to more extensive lesion: i.e., individual caries progression, described with thresholds to allow calculation of model performance. When not described but referred to, the referenced study was retrieved to recover key data. The outcome may be phrased as caries, caries experience, caries increment, or caries progression. In the following text, the term caries increment is defined as the number of new lesions, teeth or surfaces occurring in an individual within a stated period of time [8].

  • Timing: follow-up time ≥ 1 year.

  • Setting: oral health care without restriction to geographical location.

  • Model performance: calibration, discrimination (e.g., AUC, area under receiver operating curve, equivalent to c-statistics) and classification measures (e.g., sensitivity, specificity, positive and negative predictive values, positive (LR +) and negative (LR −) likelihood ratios [4]. Measure values should be correctly calculated and presented based on data described in the study and with data allowing recalculation of model performance with confidence interval. C-statistics assessing discrimination was not accepted as the only performance measure [4].

  • Language: English.

Exclusion criteria were as follows:

  • multivariable prediction model(s) of caries increment were not presented

  • was not original research (e.g., non-systematic reviews, letters, editorials)

  • included ≤ 2 variables in final prediction model(s)

  • model performance or only AUC were not presented

  • narrative reviews, case report or case series.

Information sources and search strategy

Three databases were searched (MEDLINE via PubMed, Web of Science, and the Cochrane Library in Cochrane Database of Systematic Reviews) from 1966 up to April 23, 2021. Reference lists of included publications and 4 systematic reviews of prediction models of caries increment [9,10,11,12] were screened to identify additional studies of potential interest. We also searched the PROSPERO database on October 3, 2019, to identify any upcoming reviews.

The search plan was managed with the aid of university librarians. The MEDLINE search is presented in Additional file 2. The Web of Science search was performed in all citation databases. PubMed and Web of Science searches were screened for duplicate publications by manual search.

Selection process

The selection of studies was completed in 2 phases. In phase one, all retrieved records were independently assessed according to title and/or abstract by 2 review authors and selected according to the eligibility criteria. Records selected by at least one reviewer were retrieved in full text for further selection. In phase 2, two review authors independently included or excluded full text publications using a piloted protocol. The protocols were compared and discussed. Disagreements were resolved by involving a third review author.

Data collection process

A data extraction form based on CHARMS, tailored according to the review objective was developed. The form was piloted using five publications among four review authors, who filled out the form independently. The results of the extraction were discussed between the review authors and the extraction form was adjusted after discussion. Subsequently, two teams of two review authors independently extracted key characteristics of the included studies using the extraction form.

Data items

Information on each study, as presented in Table 1 and Additional file 4 was collected [13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33]. The event count per candidate predictor was calculated from the study information. Results of data extraction of each publication were discussed among two reviewers and disagreements were resolved by involving a third review author, and a common protocol for the reviewers was established. Thence, information of predictors and predictive model performances in particular were reviewed once more by four review authors. In case of inconsistencies, attempts were made to contact the corresponding authors for clarification. When no reply was received, the data were presented narratively or not at all. Regarding the model development, the number of candidate predictors and methods used to select predictors in final models were collected. For each model, predictors included in the final model and model performance were extracted (Table 2) [13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35].

Table 1 Main characteristics of included studies of multivariable prediction models of caries increment. A detailed description of included studies is presented in Additional file 4
Table 2 Included predictors and model performance of final multivariable prediction models of caries increment

Risk of bias and concern regarding applicability

Pairs of review authors independently assessed risk of bias (ROB) and concern regarding applicability using PROBAST [5, 6] with 20 signalling questions in 4 domains for ROB (participants, predictors, outcome, analysis) and 3 domains for applicability (participants, predictors, outcome). Each signalling question is answered by yes, probably yes, no, probably no, or no information [36]. Based on the ratings, the global ROB and applicability concerns are judged as low, high, or unclear [6]. Disagreements were resolved by discussion between 4 review authors.

Analysis of predictors and model performance

Candidate predictors in developmental model that expressed similar characteristics were grouped in categories, and allocated to different levels of a model for a caries process. The performance of each model was re-calculated as estimated LRs based on the sensitivity and specificity presented in included studies: LR + equals sensitivity divided by (1—specificity) and LR − equals (1—sensitivity) divided by specificity. We considered the analysed models to be useful for prediction of caries increment when LRs + were ≥ 5.0 and conversely, ruling out caries increment when LRs − were ≤ 0.20 [37]. Confidence intervals for LRs were calculated using the method described by Koopman [38]. We intended to perform meta-analyses by pooling estimates of the LRs whenever 3 or more studies were based on similar prediction model, participant age group and definition of caries increment, but due to variation across studies, this was waived.


Study selection

Figure 1 shows the flow of records identified through the searches and study selection. Out of 140 full-text publications, 21 were included. Excluded full-text publications with reasons for exclusion are provided in Additional file 3.

Fig. 1
figure 1

PRISMA flow chart for study selection

Study characteristics

The main characteristics of the studies included are presented in Table 1 and Additional file 4. References to publications describing methodology for candidate predictors are listed in Additional file 5. In 11 studies [13,14,15,16,17,18,19,20,21,22,23], model development was emphasized (8 studies with 23 models of coronal caries, 2 studies with 6 models of root caries, one study with a model of coronal and root caries). Ten studies [19, 24,25,26,27,28,29,30,31,32,33] focused on model validation (9 studies with 31 models of coronal caries and one study with 5 models of root caries). Most validation studies were not performed according to the study describing the model development. We did not find original studies presenting model development of CAMBRA (Caries Management by Risk Assessment) or CAT (Caries-risk Assessment Tool) with model performance measures according to CHARMS. All studies were cohort studies except for two studies, which were described as case–control and cluster sample studies, respectively.

There was high inter-study variability in predictors, outcome definitions and timing of outcome measurements. Five studies used bite-wing radiography (Table 1) and enamel caries was included in the outcome in only 2 studies. Regarding participants, they were generally children or adolescents (aged 2–19) in studies of coronal caries, and adults (aged 52–80) in studies of root caries. Sample sizes ranged from 21 to 1576 participants. In studies of model development, the number of events (outcomes) in relation to the number of variables, i.e., candidate predictors (events per variable = EPV) varied between 0.72 and 114.8, being ≥ 20 in 1 study, ≥ 10 in 2 studies, and < 10 in the remaining studies (Table 1). In half of the model validation studies, the number of events and non-events was in excess of 100 (Table 1). Logistic regression analysis was the most prevalent modelling technique, using univariate analyses to filter potential predictors for the final model. Algorithm-based modelling was used in 2 studies and a machine learning approach in 1 study.

Reported model performances are presented in Table 2. Sensitivity and specificity were reported in all studies, AUC was reported in 6 studies of model development and 12 studies of model validation, and LRs were reported in 3 studies of model validation. One study presented calibration. Confidence intervals were reported in 4 studies.

Risk of bias (ROB) and concern regarding applicability

The distribution of ROB and applicability for each domain and overall is presented in Fig. 2. Overall, ROB was high; in the Analysis domain all but one study and in the Outcome domain one third of the studies showed high ROB, while in the Participant and Predictor domains the ROB was low. Concern regarding applicability was rated low in 86% of the studies.

Fig. 2
figure 2

Distribution of risk of bias and concern regarding applicability for each domain and overall

ROB and concern regarding applicability of each study are presented in Table 3 and detailed information on signalling question responses is found in Additional file 6. The Participant domain was assessed at high or unclear ROB in 5 studies since inclusion or exclusion criteria were missing or unclear. Although the Predictor domain was assessed at low ROB in most studies, there was considerable uncertainty regarding the thresholds and measurements. For the Outcome domain, half of the studies showed high or unclear ROB. No estimates of measurement error of the method determining the outcome were presented. Only 1 study described that the outcome was determined without knowledge of predictor information. In the Analysis domain, high ROB was usually assigned due to insufficient number of EPV in model development studies or number of events in model validation studies. Other frequent reasons were inappropriate handling (or no information) of continuous and categorical predictors, and selection of predictors based on univariate analysis in model development studies. Regarding applicability, concern was low for all but 3 studies; 1 study was rated as unclear regarding the domain Participants and 2 regarding the domain Predictors (Table 3).

Table 3 Risk of bias and concern regarding applicability for studies of multivariable prediction models of caries increment

Analysis of predictors and model performance

Based on a caries process model (Fig. 3), we allocated the predictors to the following levels: (i) societal structural, (ii) physiological, (iii) tooth, (iv) life-style situational, (v) oral biological, (vi) caries experience and other types of predictors. In the following text, variables considered in the model development are labelled candidate predictors and variables included in the final models, predictors in accordance with CHARMS.

Fig. 3
figure 3

A caries process model with 6 levels. Each level holds a set of variables used as predictors in included studies. The horizontal line CAUSALITY LOST indicates that the 3 top levels do not commute with the other levels. Protons in dental plaque (H+) are the driving force in the caries process in development of dysbiosis as well as demineralisation of dental tissues. Acid tolerant bacteria in dental plaque are proposed as novel candidate predictors

Predictors in studies of model development

Sampling methods, measurement methods, and thresholds varied across studies. For example, caries experience and caries increment were assessed using different criteria (e.g., according to WHO, Radike, ICDAS [34, 35, 39,40,41,42,43]) and caries was defined as dentinal caries or cavity in all but 2 studies that included enamel lesions. Predictors at the Societal structural Level were collected using unvalidated questionnaires. One example of methods not clearly reported was for the predictor mutans streptococci: information on detection limits in saliva was not given, no criteria for colony forming units on Mitis-Salivarius Bacitracin (MSB) agar was offered, and biochemical testing were not used to confirm mutans streptococci.

Altogether, more than 150 candidate predictors were identified, and the number included in each model ranged between 3 and 46 (Additional file 7). Many of these were similar in nature but their names varied across studies, e.g., food intake frequency was described with 21 different names. In studies of coronal caries, candidate predictors from 2 to 6 levels were represented, with 5 of them being the most prevalent (Fig. 4A). Final models of coronal caries included 31 predictors with between 3 and 23 predictors in each model and models of root caries included 16 predictors with between 6 and 13 predictors in each model. Three studies of coronal caries included ≥ 2 models and for those studies the information about predictors was merged in Fig. 4A. Caries experience was utilized as predictor in all studies; other commonly included predictors were visible dental plaque, mutans streptococci in saliva, and fluoride supplements (Fig. 4A). Predictor combinations (occurring in ≥ 2 studies) are illustrated as a network in Fig. 4B. The most prevalent set of 4 predictors was caries experience, use of fluoride supplements, mutans streptococci in saliva, and visible dental plaque (Fig. 4B), identified in 4 studies.

Fig. 4
figure 4

Predictors in developmental models of coronal caries increment. A Candidate predictor [□] and predictor remaining [] in at least one final model of actual study. B Predictor networks in final models with coloured lines showing predictors included in 2–5 studies. The pink area indicates a set of 4 predictors identified in 4 studies

Performance of development and validation models

Owing to the heterogeneity of the studies and the high overall ROB, model performances are reported without meta-analyses, thus avoiding apparent estimates at odds with the underlying data. Table 2 presents model performances expressed as LRs. LR + ranged between 0.78 and 10.3 and LR − between 0.0 and 1.1. Models based on many predictors performed no better than models based on fewer predictors. For example, LR + was 3.5 and LR − 0.49 for the model with the highest number of predictors (n = 23), while a model with 6 predictors yielded LR + 10.3 and LR − 0.18. As shown in Fig. 5, LR +  ≥ 5 was achieved in 5 models, 4 of coronal caries in children [17, 26, 29], and 1 of root caries in the elderly [23]. LR −  ≤ 0.20 was expressed in 3 of these 5 models [17, 26, 29] and in 5 additional models [14, 21, 29]. Two models of children aged 3–6 differed in that 1 model included 12 predictors and the other model only 6 [17]. The model with 6 predictors achieved a somewhat higher LR + (10.3 vs. 9.0) but did not include the predictors fluorides and caries experience. The distribution of LRs related to age groups was scattered, further indicating heterogeneity (Fig. 5). For children aged 2–6 and adolescents aged 12–19, most LRs were scattered, whilst the LRs for schoolchildren aged 7–11 were more coherent.

Fig. 5
figure 5

Positive (LR +) and negative likelihood ratio (LR −) of final models of caries increment for various age-groups

Model validation of the Cariogram

Six studies of model validation (5 regarding coronal caries and 1 root caries) referred to the Cariogram. However, the studies did not validate the original Cariogram model [18] per se, but presented modifications of which. As shown in Fig. 6, models provided modest LR + (range 1.1–3.8) and LR − (range 0.5–0.61), with the exception of 1 model. LRs were not substantially influenced by the exclusion of the predictor mutans streptococci in saliva. In a study of root caries, LR + increased and LR − remained unchanged when the predictor mutans streptococci in saliva was omitted. Similarly, model performance was unaffected by removal of the predictors saliva secretion and saliva buffer.

Fig. 6
figure 6

Predictors and positive (LR +) and negative likelihood ratio (LR −) in studies of model validation of Cariogram. lbc = lactobacilli; ms = mutans streptococci


Main findings

In this SR of multivariable models of caries increment, we identified and critically appraised 11 studies of model development [13,14,15,16,17,18,19,20,21,22,23], and 10 of model validation [19, 24,25,26,27,28,29,30,31,32,33]. Model performance expressed as LR + of at least 5, a commonly used arbitrary definition for moderate increase in the probability of a condition after model implementation [44], was achieved for few models. All studies were appraised to have high ROB, in particular in the domain Analysis. Heterogeneity across the studies ruled out meta-analyses and thereby any conclusion about evidence for the applicability of caries prediction models included.

Strengths and limitations

To the best of our knowledge, this is among the first systematic reviews of studies of model development and model validation of prediction of caries increment that applied CHARMS together with PROBAST. The strength of CHARMS is the thorough description of domains and key items relevant to extract with rationales, enabling reviewers and readers to understand the reasons for the items extracted. Even so, relevant data were sometimes difficult to identify since different terms for participants, predictors, outcomes, model development, and performance were used, and not always reported. While CHARMS was relied on to organize and identify relevant items, PROBAST was applied to identify potential sources of bias and concern regarding applicability. For the reporting of studies developing or validating prediction models, the TRIPOD Statement (Transparent Reporting of a multivariable prediction model for Individual Prognosis Or Diagnosis) [45] provides helpful.

As emphasized in a recent systematic review of oral health prediction models [46], there is a need to employ the same rigour to prediction models in dental as well as medical research.

Another strength of this review is the rigorous process by which 2 teams of 2 review authors independently screened records and selected full-text publications using protocols. Multiple rounds of piloting were used to refine the CHARMS and PROBAST protocols and we profited from being experts in different fields. As emphasized by Lasserson et al. [47], research teams with different expertise may identify different sources of evidence and reach different judgements. Additionally, the review authors were calibrated how to use the CHARMS and PROBAST tools.

Although the findings of this review are valuable and substantially add to the current literature, the study has limitations. We did not perform a search of grey literature, which could make the search more comprehensive. Another potential limitation is failing to assess publication bias.

Critical appraisal using PROBAST

All studies were found to have high ROB, indicating that all models’ ability to predict caries increment is potentially flawed. In particular, concerns about the methods and inherent measurement errors were identified in the domains Predictors and Outcomes. Risk of bias is higher for predictors and outcomes that involve subjective judgment, such as the visual-tactile examination of caries used in the majority of included studies. Furthermore, the sensitivity is rather modest for visual examination to identify dental cavities and ranges from 0.12 to 0.50 depending on the raters [48]. This affects estimates of the predictor as well as the outcome (and thereby the predictive performance) but this limitation was not discussed in any study. Rater reliability for assessment of caries experience was sometimes reported, but this measure does not encompass the total measurement error.

High ROB was mainly found in the domain Analysis. In studies of model development, the EPV number was low and was not reported, but had to be calculated from other study information. EPV is generally poorly reported in prediction model studies [4]. To minimize overfitting, an EPV of at least 10 in model development studies has been widely recommended, but higher EPV (≥ 20) has also been suggested [6]. Only 1 study [17] in the current review was based on EPV > 20, and another 2 on EPV ≥ 10 [14, 18].

A second concern was that univariate analysis was used as selection method for the predictors in the final models. Significant association in univariate analysis is not recommended to merit inclusion due to risk of bias in 2 directions. Firstly, predictors may have a large but non-causal association with the outcome, and secondly, in small samples, predictors may only show association with the outcome after adjustment for other variables.

A final concern was model performance measures; in general, only the classification measures sensitivity and specificity were presented. Calibration was carried out in only 1 study [19]. In addition, most studies did not report statistical uncertainty even though post facto calculated confidence intervals for the LRs were wide for many models, i.e., a clear indication of low precision.

The high ROB identified in all studies of the current review is in accord with those reported by Du et al. [46] but differed from the results by Su et al. [49], who reported low ROB for 3 validation studies of coronal caries [26, 29, 31], which we rated as high ROB. Since no responses to the signalling questions as required by PROBAST were provided by Su et al. [49], a comparison of the conflicting results was untenable. Our results on high ROB of studies of prediction models, in particular in the domain Analysis were not exceptional. A meta-review of 50 systematic reviews that used PROBAST to appraise 2104 prediction models demonstrated unclear or high ROB, in particular of the Analysis domain [50]. The latter results were markedly stable over time, highlighting the urgent need to consider ROB in prediction studies. Generally, systematic reviews of prediction models in other dental fields, such as for orthodontic treatment outcomes [51], for periodontitis [52], and for tooth loss and oral cancers [46] conclude that there is a lack of transparent reporting and identification of bias across included studies. As a consequence, predictive performance of the models is not possible to be fully assessed or compared quantitatively.

Implications of the results for future practice and research

In this review, predictive performance was re-calculated and presented as LRs. In comparison with the commonly used sensitivity and specificity, LRs are considered to be more clinically meaningful [53, 54] as LRs have the advantage of incorporating all four cells of the 2 × 2 table, in contrast to sensitivity and specificity which makes use of only two cells. LRs +  ≥ 5.0 was selected as the threshold for prediction of caries increment, and this was achieved for only 5 models [17, 23, 26, 29]. To develop pertinent models, future investigations must address obvious deficiencies and avoid ROB in model design and investigation protocols. One key aspect is to verify the utility of predictors and the most useful set of predictors. In most included studies of the present review, predictors with a statistically significant association with the outcome were selected. As proposed in PROBAST, a better approach is to use non-statistical methods and select a few predictors based on existing knowledge in combination with reliability, consistency, applicability, availability, and costs of predictor measurement relevant to the targeted setting. Considering that numerous redundant predictors pose a burden in terms of availability and expenditure, it may be wise to reconsider the number of predictors included. Regarding studies in the current review, the performance of models with several predictors were inferior or equivalent to those of models based on fewer predictors, as demonstrated by Gao et al. [17].

The most prevalent predictor was caries experience, expressed as a cavity, dentinal caries or filling in all but two studies. In adolescents, a considerable proportion of caries occurs as enamel lesions or as progression of enamel caries into dentinal caries [55, 56]. If the purpose of future prediction models is to take a preventive approach as regards the progression of lesions, it can be argued that the impact of prediction models will be limited if enamel lesions are not considered. Inclusion of enamel caries is also critical when evaluating and comparing results of interventions based on prediction models. Therefore, we recommend an implementation of a common language with criteria for dental caries also comprising enamel lesions, as described by ICDAS [34].

Another prevalent predictor was mutans streptococci in saliva included in all but 6 studies and in several networks with other predictors. The consistent inclusion of mutans streptococci can be attributed to that the studies of model development performed between 1992 and 2010 probably were influenced by the “Specific Plaque Hypothesis”, with mutans streptococci considered as the major etiological agent for caries [57]. By focusing on mutans streptococci, identified by growth on the selective MSB medium, the possibility to recognize other bacteria that exhibited an equally strong association with caries was disregarded in huge numbers of clinical studies. In a study using 16SDNA sequencing [58], it was demonstrated that more than 20 different colony forming units resembling the morphology of mutans streptococci colonies on MSB agar were in fact not mutans streptococci but identified as, e.g., Streptococcus sanguinis or Streptococcus anginosus. Caries does occur in the absence of mutans streptococci, and several other acid-producing and acid tolerant microbial species might contribute to caries development [59]. In other words, mutans streptococci in saliva might have been overestimated as a predictor, while the impact of other microbiota has been underestimated.

As suggested by Fontana et al. [3], new predictors, such as microbiota composition and metabolomics of dental plaque or saliva, should be considered in the future. As illustrated in a model of the caries process (Fig. 3), predictors at the societal structural, tooth, and physiological levels at the top of the model do not command causal associations with events close to demineralization of dental tissues. Unless predictors from the top levels carry over to predictors at the lower levels, such predictors will not improve the predictive performance. The necessary condition for demineralization is prolonged periods of low pH in dental plaque (below pH 5.5) (Fig. 3). The former will only occur if most of the dental plaque microbiota is acid tolerant. Therefore, we propose that attention should be given to a specific phenotype of bacteria (i.e., acid tolerant) as predictor instead of a specific genotype (e.g., mutans streptococci) as an additional predictor to caries experience. Our proposal is in line with the Ecological Plaque Hypothesis” for caries [60, 61]. Frequent intake of fermentable carbohydrates resulting in lactic acid production is the driving force to create low pH conditions in dental plaque, provoking acid adaptation of bacteria that result in further enhanced acid production (Fig. 3). If the acidic conditions persist, the most adept acid tolerant bacteria will be selected and the mineral balance that accelerates demineralisation will be disturbed further. In this way, protons (H+) induced by saccharolytic bacteria in dental plaque, are responsible for both demineralization of dental tissues and acid adaptation of plaque bacteria. Future studies should be encouraged to verify the utility of biomarker predictors and the most useful predictor combinations, in line with the proposed caries process model.


The results of model performance should be interpreted with caution due to shortcomings in the design, execution, and reporting of the included studies. The modest performance of most models leads us to question the inclusion of a wide range of predictors and to underline the importance of selecting a few predictors based on their applicability, availability, and costs. Hence, in an effort to identify non-redundant predictors, based on existing knowledge of the caries process, attention should be given to acid tolerant bacteria in the dental plaque. Our critical appraisal of the studies of caries prediction models highlighted methodological deficiencies and inadequate reporting. Shortcomings in study design, conduct and analysis can affect the predictive ability of the models. Flawed or distorted estimates will lead to uncertainty about the prediction. Nevertheless, the models are presented continuously in the dental scientific literature, utilized in dental education and applied in clinical decision-making.

Availability of data and materials

In addition to data in Supplementary information presented in Additional files “Protocol for inclusion and exclusion of full text studies” and “Protocol for data extraction according to CHARMS” are available from the corresponding author in reasonable request.



Area under receiver operating curve


Caries Management by Risk Assessment


Caries-risk Assessment Tool


The CHecklist for critical Appraisal and data extraction for systematic Reviews of prediction Modelling Studies


Number of events in relation to number of variables; ICDAS: International Caries Detection and Assessment System

LR + :

Positive likelihood ratio

LR − :

Negative likelihood ratio


Mitis-Salivarius Bacitracin medium


The Prediction model Risk Of Bias ASsessment Tool


Risk of bias


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The authors thank Zoltan Blum for providing valuable suggestions for improvement of the manuscript.

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Open access funding provided by Malmö University. Research Program Foresight at Malmö University, Futurum at The Academy for Healthcare at County Council of Jönköping.

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Authors and Affiliations




MR and GS contributed to the conception. All authors contributed to the design of the work, acquisition, analysis, and interpretation of data. KH and PEI contributed to the creation of new software. KH, MR, and GS drafted the work and substantively revised the work. All authors read, provided critical suggestions, and approved the submitted version.

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Correspondence to Kristian Havsed.

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Supplementary Information

Additional file 1.

PRISMA 2020 Checklist.

Additional file 2.

MEDLINE search for study selection.

Additional file 3.

Excluded full-text studies with reasons for exclusion.

Additional file 4.

Detailed description of included studies as supplementary information to Table 1.

Additional file 5.

Reference list of publications describing methodology for predictors presented in Additional file 4.

Additional file 6.

Responses to signalling questions of PROBAST [6].

Additional file 7.

Distribution of predictors by Level and category in multivariable developmental models of coronal caries increment. Predictors included in final models highlighted in red.

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Havsed, K., Hänsel Petersson, G., Isberg, PE. et al. Multivariable prediction models of caries increment: a systematic review and critical appraisal. Syst Rev 12, 202 (2023).

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