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Journal of Stomatology
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vol. 74
Original paper

Forensic age estimation using new models of mathematical regression formula constructed with molar indexes: dental age assessment

Cristiana Palmela Pereira
1, 2, 3
Ana Rodrigues
1, 2
Diana Augusto
1, 2
Adriana Santos
1, 2
Francisco Salvado
Rui Santos
2, 5
Roberto Cameriere

FORENSEMED research group from UICOB, Faculty of Dental Medicine, University of Lisbon, Portugal
CEAUL – Centre of Statistics and its Applications, University of Lisbon , Portugal
Faculty of Dental Medicine, University of Lisbon, Lisboa, Portugal
Stomatology Department, Santa Maria Hospital, Faculty of Medicine, University of Lisbon, Portugal
School of Technology and Management, Polytechnic Institute of Leiria, Portugal
AgEstimation Project, FOR.MED.LAB, University of Macerata, Italy
J Stoma 2021; 74, 2: 95-100
Online publish date: 2021/06/14
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In forensic science, age estimation for human identification of living and deceased individuals is truly remarkable [1]. It is important for humanitarian reasons in both civil and criminal cases involving young people, in the discovery of valid identification documents, for crime agents who refuse to provide their real age, and in questions related to illegal and irregular immigration as well as asylum application for foreign countries [2, 3]. Therefore, age estimation plays a significant role in the judicial system and in law enforcement worldwide [4]. Cameriere et al. developed a regressive formula, in which the ratio given by the sum of distances from the inner sides of the open apices and the height of the developing second and third molars (second molar maturity index – I2M and third molar maturity index – I3M), is a reliable method to categorize, regardless of geographic origin and socio-economic status [5, 6]. However, as third molars are often absent or extracted, they are not always available as an age indicator, and even when present, third molars cannot always be used to estimate age in children and adolescents, due to position or shape anomalies [7]. As an alternative, the development of second molar occurs earlier and in a predictable way, being a reliable tooth for age estimation [8]. Previously, Demirjian et al. developed a method based on several mineralization stages of a tooth formation (from A to H), which can be applied to all teeth except third molars [9].


The aim of the present study was to contribute to the process of forensic age estimation using dental age assessment with the mineralization stages of Demirjian method, and maturity indexes for permanent mandibular second and third molar teeth, in a Portuguese popu­lation.

Material and methods

Ethical approval and compliance with ethical standards This study was performed in accordance with ethical standards specified by health ethics committee of the Faculty of Dental Medicine, University of Lisbon, and approved with 911105 and 911106 numbers.

Informed consent

All procedures performed in studies involving human participants are in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards. Since this was a retrospective study based on anonymized clinical records, no informed consent was obtained.


To estimate age from I2M, 591 panoramic radiographs (253 from females and 338 from males; age range, 7-15 years) were selected, and to estimate age from I3M, we selected 350 panoramic radiographs (181 from females and 169 from males; age range, 12-23 years). The sample distribution is shown in Table 1. Samples were taken randomly from an X-ray database of stomatology department, Hospital Santa Maria, targeting patients from the Lisbon North University Hospital Center. Selection criteria included healthy subjects of Portuguese origin, presence of the second and third molars in all lower quadrants, absence of congenital dental anomalies in shape or/and position, such as root canal treatment, caries, or restorations in the left mandibular permanent teeth. Heavily rotated, impacted, and unclear panoramic radiographs were excluded from the analysis. Moreover, individual’s gender, date of birth, and the date of panoramic radiograph were recorded. Chronological age (CA) for each subject was computed by subtracting the date of the X-rays from the date of birth.


As proposed by Cameriere et al. [6], the maturity index was assessed as follows: a ratio between the sum of the inner side’s width of the open apices (A1 and A2) in the left and right lower second or third molars and the tooth’s length (L), when more than one root were presented, or a ratio between the width of the open apex (A) and the tooth’s length (L), when a single root was present. X-ray images in JPG format were analyzed by ImageJ® software program. The radiographs were scaled at 400%, and the measurement was changed from pixels to millimeters. Mineralization of permanent teeth on the lower left mandible were also assessed according to Demirjian [9] classification for later comparison with a molar maturity index.

Statistical analysis

The intra-class correlation coefficient (ICC) was applied to quantify intra- and inter-observer agreement in I3M, and intra-agreement in I2M. For this purpose, 10% of the study sample was randomly selected 3 months following the initial scoring process to determine percentage of agreement, for both intra- and inter-observer agreement analyses. Pearson correlation coefficients were used to evaluate the correlation between the maturity indexes and chronological age. Linear and cubic regression models were investigated, in which only variables with significant coefficients (p-value lower than 0.05) in t-test were included. Estimation errors were computed. T-test to paired samples was applied in order to test the existence of significant differences between chronological age and dental age estimated by the application of indexes.


The results of ICC for intra- and inter-observer vali­dation varied between 0.608 and 0.999 for the second and third molars. Therefore, the obtained values denoted, for the most part, excellent results both in precision and in reproducibility. The only values below 0.75 were observed in the maximum length of monoradicular teeth in the second molar. Pearson correlation coefficient between each maturity index and chronological age were calculated. All the values were similar, –0.781 for the tooth 37, –0.792 for the tooth 47, –0.775 for the tooth 38, and –0.751 for the tooth 48. All maturity indexes were significantly negatively correlated with chronological age (decrease when age increases, Figure 1). Furthermore, Spearman correlation coefficients were computed in order to measure monotone association with chronological age (and not only linear association), and also to compare maturity index results with the ones obtained by Demirjian stages. These coefficients were even more significant than Pearson correlation coefficients. Therefore, between the maturity index and chronological age, Spearman correlation was –0.856 for the tooth 37, –0.870 for the tooth 47, –0.862 for the tooth 38, and –0.850 for the tooth 48. Moreover, between Demirjian stages and chronological age, the coefficient was equal to 0.839 for the tooth 37 and to 0.862 for the tooth 47. Therefore, Demirjian stages were also strongly correlated with chronological age (Figure 2). Hence, all these variables were strongly correlated with chronological age. Despite genders being almost equally distributed in each age range for both I2M and I3M, normality was clearly rejected for the maturity index (almost null p-values) and non-parametric tests had to be applied. Thus, Mann- Whitney test revealed statistically significant differences in the I2M between genders (p-values equal to 0.002 in both teeth), but not in the I3M (p-values 0.293 and 0.639 on teeth 38 and 48, respectively).
The age estimation was obtained by using linear regression models. Each model was estimated with all the observations and then removing the observations, in which I2M = 0, because from the moment I2M = 0, there was no more evolution of the index value with age. Hence, the first model to estimate chronological age (model 1) considered I2M from the teeth 37 (I2M_37) and 47 (I2M_37), and gender (G; 0 for male and 1 for female) as explanatory variables. For model 2, Demirjian stadiums were included using artificial binary variables EC, ED, EE, EF, and EG, which were equal to one, whether the patient belonged to the corresponding stadium (equal to zero otherwise). Lastly, cubic models were also investigated (model 3). The same three models were estimated without the 101 observations, in which I2M = 0, using a total of 490 panoramic radiographs.
The same methodology was applied for I3M, first with all the observations and then without the 91 patients with I3M = 0 (remaining 258 panoramic radiographs). Hence, the fourth model considered I3M from the teeth 38 (I3M_38) and 48 (I3M_38), and gender (G) as explanatory variables (model 4). For model 5, Demirjian stages were included in model 4, using artificial binary variables. Nevertheless, the explanatory variables I3M_48 and G were removed from the model since they were not significant. The obtained cubic model was classified as model 6. All the results from the six models are summarized in Table 2. The adjusted R2 was always higher using all observations than the same model without the cases, in which the index was null. Nevertheless, the standard error of estimate (SEE) and mean absolute error (MAE) were constantly lower without patients with null index. This difference appeared from comparing the estimates in different groups. Table 2 shows the results of both methods in the age estimation of patients with maturity index not null.
Models with greater explanatory power were the ones, which included Demirjian stages (model 2 for I2M and model 5 for I3M), revealing higher determination coefficients as well as lower SEE and MAE. Moreover, models 1, 3, 4, and 6 showed some bias whenever the model was estimated using the entire sample, although SEE and MAE were almost similar. In addition, age estimation errors tended to significantly increase when the models were applied to patients with null maturity index.


Over the years, age estimation methods involving the development of second and third molars have been used. For the same reason, several studies have been conducted to improve the precision of this technique. The obtained results for ICC showed excellent results both on precision and reproducibility, so much for I2M as for I3M, which was confirmed in literature [6, 10-14]. Regarding Pearson correlation of I2M, it was possible to verify that IM of the 47 tooth revealed a slightly more significant correlation with chronological age than IM of the 37 tooth. In fact, the use of I2M makes this study relevant because there were quite few studies in literature regarding the application of I2M in age estimation. Mann-Whitney test revealed statistically significant differences between genders in I2M, which was experienced in some published literature, since girls usually tend to have a faster development of second molars than boys [15]. For I3M, it was evaluated both 38 and 48 teeth, contrasting with most studies using the same method [5, 10-12, 14, 16, 17], including only the lower left third molar (38th tooth). This was a significant evaluation since we concluded that the information of both teeth did not allow to improve the estimates since the information of the index of one of the teeth was considered irrelevant, when the index of the other was already in a model.
Regarding gender, the obtained results revealed that there were no statistically significant differences, which was sustained with most of the published studies [5, 10, 12]. However, there are some studies with opposite evidence. According to Balla et al. [16], the correlation between I3M and real age shows better results in girls, while Kelmendi et al. [18] proved that boys presented better results. The association between Demirjian stages and chronological age for both methods revealed no statistically signi­ficant differences between the two genders, which was also in accordance with the existing literature [6, 19].
To the best of our knowledge, there are no other studies regarding age estimation by regression models with I2M as an explanatory variable. This highlights the results of this investigation, which are quite satisfactory, although future confirmation of the application of different samples is necessary. We can confirm that the best models included Demirjian stages and maturity index. Hence, the use of both methods simultaneously provides a more accurate age estimate. Regarding the inclusion of I2M = 0 (as it is typical in this kind of studies), despite the improved determination coefficient, the estimation errors increased, and the estimates were less accurate. Thus, we cannot advise the use of I2M = 0. In case of the I3M, the same occurs. Thus, the inclusion of Demirjian stage classification improves the model, achieving more accurate estimates. Additionally, with the inclusion of all observations, the SEE was much higher than the one obtained in the original study [6]. In relation to the cubic regression model, it has an explanatory power, which is clearly superior to the linear regression model as a function of the I3M of tooth 38, but lower than the regression including Demirjian stages as explanatory variables. The R2 values were similar to those obtained by Balla et al. [20] in a sample with 1,283 OPG, age range, 7-22 years (0.72 for girls and 0.74 for boys) as well as the mean absolute error (18.36 meses for girls and 19.08 for boys).
Therefore, we advise the use of maturity index and Demirjian stages simultaneously in a regression model, restricted to non-zero indexes. Moreover, until I2M equals zero, the age estimate based on the second molar is more accurate. Then, when I2M = 0, the third molar shall be applied. However, it should only be applied until I3M = 0, since from there, the age estimation errors significantly increase.


Based on the obtained results, it is possible to state that the application of the maturity index based on the second molar is reproducible in a Portuguese popu­lation (age range, 7-15 years) for medical-legal application as the corresponding maturity index is positive. Subsequently, the third molar must be only used as long as its maturity index is positive. Moreover, the inclusion of Demirjian staging in both models significantly increases the accuracy of the estimates. Hence, the provided estimates have the required precision to be used in medico-legal applications.


Age estimation based on the second molar maturity index I2M is accurate in a Portuguese population aged 7 to 15 years, only when this maturity index is positive. Age estimation based on the third molar maturity index I3M is accurate in a Portuguese population aged 12 to 23 years, only when this maturity index is positive. The use of maturity index and Demirjian stages simul­taneously with a regression model is more accurate.


This research was supported by the Centro de Esta­tística e Aplicações da Universidade de Lisboa, CEAUL, FCT – Fundação para a Ciência e a Tecnologia Project reference UIDB/00006/2020.


The authors declare no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.


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