The intention of the present study was to generate reference data for mandibular third molar eruption in PAN in a German population for forensic age assessment procedures. There are two applications for using the resulting reference data in practice.

First, the reference data can be used to estimate the most probable age of the person being examined. The distribution of age within each stage is known to be skewed. Therefore, information about the shape and distribution of age within each stage is best informed by quantiles, for which the median and lower and upper quartiles are useful summary statistics and the commonly presented for asymmetric distributions. To increase the accuracy of the prediction of the most probable age, different feature systems need to be combined [20]. However, issues of imprecision in determining the most probable age will remain due to biological variability and the spread of age-related features.

Second, the so-called “minimum age principle” can be used [8]: if exceeding legally relevant age limits is to be assessed with the highest level of certainty, the forensic minimum age of the person under examination is found by comparing the stage of the age-related feature to the reference data and deriving the age from the minimum age of the stage for the given age-related trait.

In practice, more than one feature system is used for age assessment [20]; in this case the highest minimum age found across the different features is considered to be the minimum age for the individual examined.

Due to this context and the importance of this principle, the minimum ages in the stages are critical. Since in practice the question of the age of majority of the examined subject often has to be clarified, it is necessary to determine whether the minimum age in a stage is above the age of 18 years. This was not the case, not even for the highest stage, D. Thus, the assessment of the eruption of mandibular third molars according to the minimum age principle is not suitable for proving information on majority (seen here as 18 years or older) based on our results.

As the accuracy of age assessment is heavily dependent on the quality of the underlying reference studies [22,23,24], guidelines for reference studies have been proposed [20]. The requirements formulated by Schmeling et al. in 2008 served as the basis for the current study [20]. Overall, we were able to meet these requirements. In particular, the distribution of age in our sample was approximately uniform [22]. Minor deviations between age groups in our population can be attributed to the practical conditions of the study such as the absence of a specific pre-selection of the X-ray images before the actual evaluation. In addition, we examined the biological sexes separately, as required, and provided critical information on the population studied.

Another requirement is for an adequate sample size [20]. This is particularly important with regard to the representation of the minimum age for a stage. For this purpose, a sufficient number of individuals with an age around the potential minimum age of a feature expression should be included. In a recent study from 2023, Sgheiza and Liversidge were able to demonstrate that sample size is the decisive aspect for the quality of reference studies in age assessment [24]. The study explicitly addressed dental age assessment [24]. Sheiza and Liversidge even gave specific numbers for filling the individual age groups. They stated a minimum population of 20–40 individuals per age group as a requirement [24]. Specifically, sample sizes of n < 20 per age group led to poorer age prediction results [24]. In this regard, it can be stated that our study meets this requirement for each age group within each sex.

The size of the reference sample also raises the question of the process of acquiring the data. This is commonly a challenge for studies on forensic age assessment, as previously deliberated by Roberts and Lucas in 2021, since assembling prospectively randomly selected population-based study populations is not feasible due to ethical constraints associated with X-ray examinations and radiation exposure [25]. Consequently, studies on forensic age assessment typically rely on X-ray images acquired for medical purposes, a practice that was also adhered to in our study [25]. It is assumed that samples consisting of orthodontic patients and young adults with wisdom tooth issues generally exhibit normal developmental patterns relevant to the research question [25]. However, it is noteworthy that Roberts and Lucas in 2021 underscore the necessity of excluding individuals displaying clinical and/or pathological irregularities from the examinations [25]. Our study adopted the principles proposed by Roberts and Lucas, leading to stringent exclusion criteria.

Olze et al. examined a total of 666 PANs from 144 males and 522 females, aged 12–26 years, within a German population in 2008 [26]. The staging classification Olze et al. developed in 2008 was highly akin to the method of our study, with the exception of Stage C, which varies from the method used in our study. Concerning the complete eruption of mandibular third molars, it is notable that Olze et al. reported a minimum age of 19.5 years for males, while for females this age was 17.4 years, which were considerably higher than the corresponding values in our study. This is particularly important for males, as the minimum age from the 2008 Olze study was above the age limit of 18 years. Our results show that the eruption can be completed before the age of 18 years in males in the population studied. One possible explanation for this difference is that Olze et al. included only one individual in the male 17 years age group, and consequently Olze et al. may have missed complete eruption at this age because of the small number of individuals in this age group. In contrast, Olze et al. were able to collect 45 individuals in the 16 years old age group in females. This group was larger than in our study. Nevertheless, Olze et al. did not find a complete eruption in this age group, in contrast to our study. Similar to the results of our study, Olze et al. also found an earlier completion of the eruption in females.

In 2012, Olze et al. again studied the eruption in a German population. In this study, the staging also used in our study was applied [27]. Olze et al. examined a total of 606 PANs from 515 females and 91 males aged 12 to 25 years [27]. The minimum ages for stage D were now 20.0 (tooth 38) and 15.2 (tooth 48) years for the females. The comparable minimum ages for male teeth 38 and 48 were 20.6 and 20.6 years, respectively. Here, the minimum age of 15.2 years at tooth 48 for females is noteworthy. This value is almost exactly one year lower than the value found in our study for the minimum age of complete eruption in females. A remarkable aspect of this study is that Olze et al. in 2012 did not include a single 17 year old male. Thus, they could not find a completed eruption in this age group with their study. The male age groups at 18 and 19 years were also relatively small with only five individuals in each group. In contrast, there were more females in the 15 years old age group (n = 48) than in our study.

In 2019, Gambier et al. examined eruption in a French population comprising a total of 557 individuals (340 males, 217 females) using PAN [32]. Despite the utilization of a different staging system than the ones by Olze et al. from 2008 to 2012, the results were compared to our study given the geographical proximity and apparently comparable socio-economic status of the populations. The maximal stage of Gambier et al.’s study, which also corresponds to complete eruption, is comparable to stage D in our study. Gambier et al. identified a minimum age of 15.11 years for males and 15.28 years for females for full eruption. In the 15 years old age group, Gambier et al. included 22 females and 17 males. Gambier et al. concluded that eruption was not a suitable indicator for the 18 years age limit. The minimum ages for complete eruption found by Gambier et al. are well below the results of our study. It is striking that the result for females is comparable to the result of the 2012 study by Olze et al. [27]. Gambier et al. stated that primary retained teeth were excluded from their study. They did not provide more detailed information on the criteria of retention or angulation of the teeth.

Future studies should validate the completion of mandibular third molar eruption by age 15 in relevant populations, as our study did not contribute to the validation of this aspect.

In the past, the question of the extent to which eruption is linked to ethnicity has been raised repeatedly [33,34,35,36,37,38,39,40,41,42]. Specifically, it was discussed that specific ethnic groups could pass through the individual stages of eruption earlier than others [43]. In instances marked by substantial interethnic disparities, the utilization of a standard reference would result in inaccurate and potentially spurious estimations. Existing results suggest that individuals of African descent exhibit an accelerated eruption [42], while Asians, in comparison to Europeans, demonstrate delayed eruption [43]. The basis for these investigations were populations that did not entirely meet the requirements for reference populations [43]. It remains pending whether the results can be substantiated in further, high-quality reference studies. Therefore, high-quality studies in different ethnic groups, following the requirements for reference studies and conducted with a comparable method, are urgently needed.

Our results demonstrate that eruption in a German population may be fully completed by the age of 16 or 17 years. The practical usefulness of the method for the proof of majority is thus limited. However, it is important to note that our results indicate that the development of mandibular third molars may not be complete, even if the teeth are fully erupted (Fig. 2). This finding is in accordance with the existing literature [21, 44]. Because mandibular third molars may not be fully developed after eruption, the assessment of mandibular third molar mineralisation may yet offer an alternative means for DAE.

Nevertheless, our reference data may offer a means of estimating the most probable age of a person based on mandibular third molar eruption, ideally in combination with other age-related traits. Therefore, determination of eruption should continue to be an important component of forensic age assessment.