# Testing the quality of nonadult Bayesian dental age assessment methods to juvenile skeletal remains: The Lisbon collection children and secular trend effects

Yann Heuzé, Hugo F.V. Cardoso

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Yann Heuzé, Hugo F.V. Cardoso. Testing the quality of nonadult Bayesian dental age assessment methods to juvenile skeletal remains: The Lisbon collection children and secular trend effects. American Journal of Physical Anthropology, 2008, 135 (3), pp.275-283. 10.1002/ajpa.20741. hal-02322897

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Testing the quality of non-adult Bayesian dental age assessment methods to juvenile
skeletal remains: the Lisbon collection children and secular trend effects.

Yann Heuzé¹* and Hugo F.V. Cardoso²

1 Radiologie II, Medizinische Universität, 6020 Innsbruck, Austria

2 Departamento de Antropologia, Universidade de Coimbra, Portugal

Number of text pages: 25

Number of figures: 2

Number of tables: 2

Abbreviated title: Secular trends in dental age

KEY WORDS dental development; age estimation; probabilistic methods; reference collection; socioeconomic status

*Yann Heuzé, Radiologie II, Medizinische Universität, Anichstraße 35, 6020 Innsbruck,
Austria / Tel: + 43 (0) 50 504 – 24492 / Fax: + 43 (0) 50 504 – 24419 / e-mail: heuze@cict.fr

Grant Sponsor: Yann Heuzé was funded by the Foundation Fyssen. Hugo FV Cardoso was
funded by Fundação para a Ciência e Tecnologia, Portugal (grant# SFRH/BD/4917/2001 and
SFRH/BPD/22142/2005).
Testing the quality of non-adult Bayesian dental age assessment methods to juvenile
skeletal remains: the Lisbon collection children and secular trend effects.

Yann Heuzé¹* and Hugo F.V. Cardoso²

1 Radiologie II, Medizinische Universität, 6020 Innsbruck, Austria

2 Departamento de Antropologia, Universidade de Coimbra, Portugal

Number of text pages: 25

Number of figures: 2

Number of tables: 2

Abbreviated title: Secular trends in dental age

KEY WORDS dental development; age estimation; probabilistic methods; reference collection; socioeconomic status

*Yann Heuzé, Radiologie II, Medizinische Universität, Anichstraße 35, 6020 Innsbruck,
Austria / Tel: + 43 (0) 50 504 – 24492 / Fax: + 43 (0) 50 504 – 24419 / e-mail: heuze@cict.fr

Grant Sponsor: Yann Heuzé was funded by the Foundation Fyssen. Hugo FV Cardoso was
funded by Fundação para a Ciência e Tecnologia, Portugal (grant# SFRH/BD/4917/2001 and
SFRH/BPD/22142/2005).
**ABSTRACT** Age estimation of non-adult skeletons from archaeological or forensic contexts has relied heavily on modern schedules of dental formation developed on samples of children of affluent populations. Although genetic factors have been considered to have had the greatest influence on population differences in dental development, increased interest has been placed on the role of environmental influences, such as differences in socioeconomic status and secular trends. This study evaluates the quality (i.e. accuracy and reliability) of two Bayesian dental age estimation methods to a sample of identified child skeletons from the Lisbon collection (20th century Portugal). The two Bayesian methods are developed on a reference sample of modern children from France, Ivory Coast, Iran and Morocco. The test sample from Lisbon, compared to the reference sample, is separated by over 50 years of secular trends and comprises a lower socioeconomic segment. The two Bayesian methods show that the Lisbon children are consistently one-year behind in dental age compared to the modern children of the reference sample. Environmental factors largely explain the differences between dental and chronological age in historic samples of non-adults.
**ABSTRACT** Age estimation of non-adult skeletons from archaeological or forensic contexts has relied heavily on modern schedules of dental formation developed on samples of children of affluent populations. Although genetic factors have been considered to have had the greatest influence on population differences in dental development, increased interest has been placed on the role of environmental influences, such as differences in socioeconomic status and secular trends. This study evaluates the quality (i.e. accuracy and reliability) of two Bayesian dental age estimation methods to a sample of identified child skeletons from the Lisbon collection (20th century Portugal). The two Bayesian methods are developed on a reference sample of modern children from France, Ivory Coast, Iran and Morocco. The test sample from Lisbon, compared to the reference sample, is separated by over 50 years of secular trends and comprises a lower socioeconomic segment. The two Bayesian methods show that the Lisbon children are consistently one-year behind in dental age compared to the modern children of the reference sample. Environmental factors largely explain the differences between dental and chronological age in historic samples of non-adults.
Several methods for non-adult age estimation based on stages of tooth formation are available in the literature (e.g. Nolla, 1960; Moorrees et al., 1963a,b; Demirjian et al., 1973; Gustafson and Koch, 1974; Haavikko, 1974; Anderson et al., 1976). However, the accuracy and reliability of most methods has seldom been examined on juvenile skeletal material.

Some exceptions are the studies carried out by Saunders et al. (1993) and Liversidge (1994, 1999). One of the main difficulties in testing dental age estimation techniques comprehensively is that collections of identified juvenile skeletons are extremely rare. In addition, because some problems exist with radiographs of living children, particularly the very young and infants, these collections are particularly important for testing the quality of dental age assessment methods, although they too present some problems, namely in terms of sample size. Despite the fact that dental development is widely considered the single best indicator of chronological age at death in non-adult skeletal remains, it is very important to assess the accuracy of the methods in order for the researcher to decide the most reliable technique according to the material available and required level of accuracy. In addition, the testing of age estimation methods through utilization of diverse samples is fundamental to address the problem of uncertainty when a method is applied to an individual originating from a population that differs from the one that contributed to the development of the method.

Three difficulties are usually associated with the cross-population applicability of dental age methods: 1) biological differences between populations of specific geographic regions, due to different gene pools; 2) differences in living conditions and socioeconomic status between contemporaneous populations or positive secular changes in living conditions responsible for advancement in dental development in extemporaneous populations; 3) methodological issues. Several decades of research have identified population and regional differences in the timing of dental development (Fanning and Moorrees, 1969; Owsley and Jantz, 1983; Nyström et al., 1986; Harris and McKee, 1990; Mappes et al., 1992; Tompkins,
Several methods for non-adult age estimation based on stages of tooth formation are available in the literature (e.g. Nolla, 1960; Moorrees et al., 1963a,b; Demirjian et al., 1973; Gustafson and Koch, 1974; Haavikko, 1974; Anderson et al., 1976). However, the accuracy and reliability of most methods has seldom been examined on juvenile skeletal material.

Some exceptions are the studies carried out by Saunders et al. (1993) and Liversidge (1994, 1999). One of the main difficulties in testing dental age estimation techniques comprehensively is that collections of identified juvenile skeletons are extremely rare. In addition, because some problems exist with radiographs of living children, particularly the very young and infants, these collections are particularly important for testing the quality of dental age assessment methods, although they too present some problems, namely in terms of sample size. Despite the fact that dental development is widely considered the single best indicator of chronological age at death in non-adult skeletal remains, it is very important to assess the accuracy of the methods in order for the researcher to decide the most reliable technique according to the material available and required level of accuracy. In addition, the testing of age estimation methods through utilization of diverse samples is fundamental to address the problem of uncertainty when a method is applied to an individual originating from a population that differs from the one that contributed to the development of the method.

Three difficulties are usually associated with the cross-population applicability of dental age methods: 1) biological differences between populations of specific geographic regions, due to different gene pools; 2) differences in living conditions and socioeconomic status between contemporaneous populations or positive secular changes in living conditions responsible for advancement in dental development in extemporaneous populations; 3) methodological issues. Several decades of research have identified population and regional differences in the timing of dental development (Fanning and Moorrees, 1969; Owsley and Jantz, 1983; Nyström et al., 1986; Harris and McKee, 1990; Mappes et al., 1992; Tompkins,
1996), thus providing support for population or geographic-specific methods, but recent research has shown that the quality of dental age assessment does not seem to depend predominantly on the use of geographic-specific standards (Liversidge and Speechly, 2001; Liversidge, 2003; Heuzé, 2004; Braga et al., 2005; Maber et al., 2006; Liversidge et al., 2006). In fact, there seems to be a marked degree of normal variation in the timing of dental development among different populations, and probably only a very small amount of it can be explained by genetic influences. Methodological factors have been identified as one potential source of variation in the detection of population and regional differences in the timing of dental development (Harris and McKee, 1990; Simpson and Kunos, 1998). However, unwarranted claims of resistance or insensitivity of dental development to environmental constraints due to high heritability (Larsen, 1997) have disregarded nutrition, disease, living conditions or secular trends as major influences in dental age estimates (Holtgrave et al., 1997; Nadler, 1998; Cardoso, 2005, 2007) and, consequently, as important explanatory factors of population differences in dental development.

The purpose of this paper is to test the quality of two Bayesian methods of dental age estimation based on non-geographic-specific standards of the permanent dentition on a sample of 20th century non-adult documented skeletons from Portugal. A large sample of children from multiple geographic origins is used to develop the two Bayesian methods, which are subsequently applied to the identified series of non-adult skeletons. Our specific goals were to examine how a non-geographic-specific method would perform on a sample of non-adult skeletal remains and, given the results, what factors would better explain variation in dental age estimates, considering that the methods were developed on a contemporaneous sample of living children and the test case derives from an historic period, albeit recent, that differs in socioeconomic background.
1996), thus providing support for population or geographic-specific methods, but recent research has shown that the quality of dental age assessment does not seem to depend predominantly on the use of geographic-specific standards (Liversidge and Speechly, 2001; Liversidge, 2003; Heuzé, 2004; Braga et al., 2005; Maber et al., 2006; Liversidge et al., 2006). In fact, there seems to be a marked degree of normal variation in the timing of dental development among different populations, and probably only a very small amount of it can be explained by genetic influences. Methodological factors have been identified as one potential source of variation in the detection of population and regional differences in the timing of dental development (Harris and McKee, 1990; Simpson and Kunos, 1998). However, unwarranted claims of resistance or insensitivity of dental development to environmental constraints due to high heritability (Larsen, 1997) have disregarded nutrition, disease, living conditions or secular trends as major influences in dental age estimates (Holtgrave et al., 1997; Nadler, 1998; Cardoso, 2005, 2007) and, consequently, as important explanatory factors of population differences in dental development.

The purpose of this paper is to test the quality of two Bayesian methods of dental age estimation based on non-geographic-specific standards of the permanent dentition on a sample of 20th century non-adult documented skeletons from Portugal. A large sample of children from multiple geographic origins is used to develop the two Bayesian methods, which are subsequently applied to the identified series of non-adult skeletons. Our specific goals were to examine how a non-geographic-specific method would perform on a sample of non-adult skeletal remains and, given the results, what factors would better explain variation in dental age estimates, considering that the methods were developed on a contemporaneous sample of living children and the test case derives from an historic period, albeit recent, that differs in socioeconomic background.
# MATERIALS AND METHODS

## Reference sample

The reference sample consists of dental panoramic radiographs which were collected between 2001 and 2004, from 2,386 healthy children aged 1.9 to 16.0 years (1,346 girls and 1,040 boys) (Table 1). The sample has a broad age range and adequate sample sizes for all one-year age groups, except between the ages of 1.9 and 3.9 and older than 15.0, where only 62 and 65 children, respectively, are included in the sample. All children in the reference sample lived in the areas of Abidjan (Ivory Coast), Shiraz (Iran), Marrakech (Morocco) or in France (Bordeaux, Montpellier, Toulouse). The panoramic X-rays had been taken for diagnostic proposes and none of the children had undergone orthodontic treatment before taking the selected radiograph. No pathologic cases (i.e. for which a surgical operation was necessary) were selected. Only children who were free of anomalies in tooth numbers were selected. The children lived in environments where they experienced normal levels of infectious diseases and were not protected from environmental insults, corresponding to the definition of a reference sample (Cameron, 2004), often called a training sample. The socioeconomic background of children living in France is mixed due to 1) the different places where the study was developed (i.e. hospitals and private clinics, representing a majority of lower and higher socioeconomic classes, respectively); 2) the fact that orthodontic treatments are free (repayment) in France thanks to social insurance (for more details on socioeconomic background of the sample from France see Heuzé, 2004 and Heuzé et al., 2005). Regarding the Ivorian, Iranian and Moroccan children, they largely represent the middle to high social class of their respective countries, mainly because orthodontic treatments are not free.

Therefore, the reference sample represents not only an ample spectrum of socioeconomic backgrounds from France, but also the affluent of the Ivorian, Iranian and Moroccan populations, which may not necessarily be at the same level of the French high socioeconomic
## Reference sample

The reference sample consists of dental panoramic radiographs which were collected between 2001 and 2004, from 2,386 healthy children aged 1.9 to 16.0 years (1,346 girls and 1,040 boys) (Table 1). The sample has a broad age range and adequate sample sizes for all one-year age groups, except between the ages of 1.9 and 3.9 and older than 15.0, where only 62 and 65 children, respectively, are included in the sample. All children in the reference sample lived in the areas of Abidjan (Ivory Coast), Shiraz (Iran), Marrakech (Morocco) or in France (Bordeaux, Montpellier, Toulouse). The panoramic X-rays had been taken for diagnostic proposes and none of the children had undergone orthodontic treatment before taking the selected radiograph. No pathologic cases (i.e. for which a surgical operation was necessary) were selected. Only children who were free of anomalies in tooth numbers were selected. The children lived in environments where they experienced normal levels of infectious diseases and were not protected from environmental insults, corresponding to the definition of a reference sample (Cameron, 2004), often called a training sample. The socioeconomic background of children living in France is mixed due to 1) the different places where the study was developed (i.e. hospitals and private clinics, representing a majority of lower and higher socioeconomic classes, respectively); 2) the fact that orthodontic treatments are free (repayment) in France thanks to social insurance (for more details on socioeconomic background of the sample from France see Heuzé, 2004 and Heuzé et al., 2005). Regarding the Ivorian, Iranian and Moroccan children, they largely represent the middle to high social class of their respective countries, mainly because orthodontic treatments are not free.

Therefore, the reference sample represents not only an ample spectrum of socioeconomic backgrounds from France, but also the affluent of the Ivorian, Iranian and Moroccan populations, which may not necessarily be at the same level of the French high socioeconomic
segment, due to overall country-level differences in living conditions and socioeconomic
development. Before the study was initiated it was ethically approved by a French
institutional board (Commission Nationale de l'Informatique et des Libertés) and no
regulations exist in Morocco, Iran or the Ivory Coast.

Test sample

The test sample is a 20th century cemetery sample and is derived from the Lisbon
documented skeletal collection (Cardoso, 2006). Because both the dependent and independent
Bayesian methods tested here were deemed unreliable under the age of 4 and over the age of
15, due to small sample sizes in these age groups of the reference sample, only children
between 4 and 15 years old were selected in the test sample. Consequently, the material from
the Lisbon collection consists of the skeletal remains of 40 children between the ages of 4 and
15, of which 20 are females and 20 are males (Table 1). For all children age at death was
calculated from the death and birth date, obtained from death and birth civil records. Children
who showed inconsistencies between reported age at death in death records and age at death
calculated by subtracting the date of death to the date of birth were also not selected. All
children in the test sample were Portuguese-born and were buried in Lisbon between 1913
and 1972, but most (65%) died in the 1940s and 1950s. Most of the children represent the
middle to low social class of the city of Lisbon, as inferred from the origin of the remains
(temporary graves) and from the father's occupations, which include a large proportion of
menial jobs (Cardoso, 2005, 2007). In addition, these children represent a population who was
going through tremendous social and economic difficulties during Salazar's dictatorial regime
between 1926 and 1974. Compared to the reference sample, the test sample is representative
of a lower socioeconomic level, which is not only separated temporally from the other
samples by several decades, but also by the improvements in living conditions that they entail.

Dental stage assessment method
segment, due to overall country-level differences in living conditions and socioeconomic
development. Before the study was initiated it was ethically approved by a French
institutional board (Commission Nationale de l'Informatique et des Libertés) and no
regulations exist in Morocco, Iran or the Ivory Coast.

Test sample

The test sample is a 20th century cemetery sample and is derived from the Lisbon
documented skeletal collection (Cardoso, 2006). Because both the dependent and independent
Bayesian methods tested here were deemed unreliable under the age of 4 and over the age of
15, due to small sample sizes in these age groups of the reference sample, only children
between 4 and 15 years old were selected in the test sample. Consequently, the material from
the Lisbon collection consists of the skeletal remains of 40 children between the ages of 4 and
15, of which 20 are females and 20 are males (Table 1). For all children age at death was
calculated from the death and birth date, obtained from death and birth civil records. Children
who showed inconsistencies between reported age at death in death records and age at death
calculated by subtracting the date of death to the date of birth were also not selected. All
children in the test sample were Portuguese-born and were buried in Lisbon between 1913
and 1972, but most (65%) died in the 1940s and 1950s. Most of the children represent the
middle to low social class of the city of Lisbon, as inferred from the origin of the remains
(temporary graves) and from the father's occupations, which include a large proportion of
menial jobs (Cardoso, 2005, 2007). In addition, these children represent a population who was
going through tremendous social and economic difficulties during Salazar's dictatorial regime
between 1926 and 1974. Compared to the reference sample, the test sample is representative
of a lower socioeconomic level, which is not only separated temporally from the other
samples by several decades, but also by the improvements in living conditions that they entail.

Dental stage assessment method
The degree of formation of the crowns and roots for the seven permanent teeth of the mandible ($I_1$ to $M_2$) were assessed according to the stages defined by Demirjian et al. (1973). Demirjian and co-workers defined eight stages of fractional development of the crown and root, assigned the letters A to H, which were converted to the numbers 1 to 8, respectively, in order to generate a dental mineralization sequence (DMS) for each individual. The DMS is the macrostructural event sequence observed on an individual's developing teeth at a precise moment of his life, i.e. it represents a formula with seven numbers that corresponds to the stages of development of each permanent tooth of that individual. For example, the DMS is equal to 88 8 87 87 if $I_1$, $I_2$, C, $P_3$, $P_4$, $M_1$ and $M_2$ are assessed as stages 8, 8, 8, 8, 7, 8, 7 respectively (or H, H, H, H, G, H, G in the original Demirjian's stages).

Assessment of tooth formation stages in the test sample was assessed by HC directly on loose teeth and on periapical radiographs and YH assessed tooth formation in the reference sample using panoramic X-rays. Intra- and inter-observer agreement was estimated in a random sample of 20 X-rays from the Lisbon collection, representing a total of 160 teeth. Intra-observer agreement was always greater than 90% and inter-observer agreement was 74% (i.e. 118 out of 160 teeth were assessed with the same dental stage). In both intra- and inter-observer tests, when a difference existed, it was never greater than one stage. A signed Wilcoxon test also showed that the inter-observer difference in scores was equally likely to be positive or negative (T=59.5, p=0.6603), thus indicating that one observer is not systematically underscoring or overscoring relative to the other observer.

When dealing with human non-adult skeletal remains recovered from archaeological and forensic contexts, one is faced with the inability to accurately determine the sex of the individuals, due to the lack of reliable macroscopic methods for sex determination as most of the sex-specific traits are only developed during adolescence. Therefore, although this is an important limitation to anthropological studies, because sex-specific methods based on tooth
The degree of formation of the crowns and roots for the seven permanent teeth of the mandible ($I_1$ to $M_2$) were assessed according to the stages defined by Demirjian et al. (1973). Demirjian and co-workers defined eight stages of fractional development of the crown and root, assigned the letters A to H, which were converted to the numbers 1 to 8, respectively, in order to generate a dental mineralization sequence (DMS) for each individual. The DMS is the macrostructural event sequence observed on an individual's developing teeth at a precise moment of his life, i.e. it represents a formula with seven numbers that corresponds to the stages of development of each permanent tooth of that individual. For example, the DMS is equal to 88 8 87 87 if $I_1$, $I_2$, C, $P_3$, $P_4$, $M_1$ and $M_2$ are assessed as stages 8, 8, 8, 8, 7, 8, 7 respectively (or H, H, H, H, G, H, G in the original Demirjian's stages).

Assessment of tooth formation stages in the test sample was assessed by HC directly on loose teeth and on periapical radiographs and YH assessed tooth formation in the reference sample using panoramic X-rays. Intra- and inter-observer agreement was estimated in a random sample of 20 X-rays from the Lisbon collection, representing a total of 160 teeth. Intra-observer agreement was always greater than 90% and inter-observer agreement was 74% (i.e. 118 out of 160 teeth were assessed with the same dental stage). In both intra- and inter-observer tests, when a difference existed, it was never greater than one stage. A signed Wilcoxon test also showed that the inter-observer difference in scores was equally likely to be positive or negative ($T=59.5, p=0.6603$), thus indicating that one observer is not systematically underscoring or overscoring relative to the other observer.

When dealing with human non-adult skeletal remains recovered from archaeological and forensic contexts, one is faced with the inability to accurately determine the sex of the individuals, due to the lack of reliable macroscopic methods for sex determination as most of the sex-specific traits are only developed during adolescence. Therefore, although this is an important limitation to anthropological studies, because sex-specific methods based on tooth
formation can increase accuracy of age estimates, it is preferable to test the quality of the Bayesian method by pooling the sexes. In this way the test sample is treated as an archaeological or forensic sample of documented age and unknown sex, and non-sex specific standards were used for both dependent and independent Bayesian methods employed in this study.

**Dependent Bayesian Method (DBM)**

The principle of a Bayesian dental age assessment method (dependent or independent) is to produce for each individual, according to his/her dental formation status, a distribution of posterior probability of belonging to a particular age group. The age group with the highest posterior probability is the “dental age group” of the individual. In this study, one-year age intervals (12 months) were used to determine dental age groups, because they are closer to the required level of accuracy in archaeological samples. After having assessed stages of tooth formation, the dependent Bayesian method (DBM) using uniform priors (Braga et al., 2005) was applied to each individual to estimate age by means of the DMS, since for each DMS there is a posterior probability distribution to be observed at different age groups. The particularity of DBM is that, by using the DMS, it considers the seven permanent mandibular teeth as dependent attributes. In fact, the DMS is the result of a dynamic pattern corresponding to sequenced, interrelated mechanisms and processes between developing teeth. A limited variability (but not necessary a low variability) in DMS is observed because teeth are topographically, developmentally and functionally associated to each other, and essentially grow as a unit (Heuzé, 2004; Braga et al., 2005). The inconvenience of DBM concerns the age assessment of children who have a DMS not represented in the reference sample. Because of mathematical specificities of DBM, the dental age of these children cannot be assessed (for more details see Braga et al., 2005). It is important to note, however, that DBM is able to assess dental age of incomplete (i.e. by examining just 1, 2, 3, 4, 5 or 6
formation can increase accuracy of age estimates, it is preferable to test the quality of the Bayesian method by pooling the sexes. In this way the test sample is treated as an archaeological or forensic sample of documented age and unknown sex, and non-sex specific standards were used for both dependent and independent Bayesian methods employed in this study.

**Dependent Bayesian Method (DBM)**

The principle of a Bayesian dental age assessment method (dependent or independent) is to produce for each individual, according to his/her dental formation status, a distribution of posterior probability of belonging to a particular age group. The age group with the highest posterior probability is the “dental age group” of the individual. In this study, one-year age intervals (12 months) were used to determine dental age groups, because they are closer to the required level of accuracy in archaeological samples. After having assessed stages of tooth formation, the dependent Bayesian method (DBM) using uniform priors (Braga et al., 2005) was applied to each individual to estimate age by means of the DMS, since for each DMS there is a posterior probability distribution to be observed at different age groups. The particularity of DBM is that, by using the DMS, it considers the seven permanent mandibular teeth as dependent attributes. In fact, the DMS is the result of a dynamic pattern corresponding to sequenced, interrelated mechanisms and processes between developing teeth. A limited variability (but not necessary a low variability) in DMS is observed because teeth are topographically, developmentally and functionally associated to each other, and essentially grow as a unit (Heuzé, 2004; Braga et al., 2005). The inconvenience of DBM concerns the age assessment of children who have a DMS not represented in the reference sample. Because of mathematical specificities of DBM, the dental age of these children cannot be assessed (for more details see Braga et al., 2005). It is important to note, however, that DBM is able to assess dental age of incomplete (i.e. by examining just 1, 2, 3, 4, 5 or 6
permanent mandibular teeth) and of complete dentitions (i.e. all 7 permanent mandibular teeth).

**Independent Bayesian Method (IBM)**

Developing teeth can also be studied as independent attributes. Although this does not correspond to the biological reality of the development process, some researchers have developed an independent Bayesian method (IBM) for dental age assessment associated with either non-uniform priors (Lucy et al., 1996; Chaillet, 2003; Foti et al., 2003) or with uniform priors (Heuzé, 2004). Only the uniform priors approach is used in this paper. Compared to DBM, IBM offers the possibility to generate dental age estimations for more children than DBM, because calculations are made “tooth by tooth” and not “DMS by DMS”, as illustrated by the following example. Using a hypothetic sample of three children A, B, and C with “$I_1$ and $I_2$” at stage “8 and 7”, “8 and 8”, and “7 and 6”, respectively, the probability to present “$I_1$ and $I_2$” at stage “8 and 7” is computed as “$2/3 \times 1/3$” with IBM, because stage “8” is represented by two children and stage “7” by one child. The probability to present “$I_1$ and $I_2$” at stage “8 and 7” is computed as “$1/3$” with DBM, because there is only one child with “$I_1$ and $I_2$” at stage “8 and 7”; the individual A. Because the probability of finding the same tooth at the same stage of dental development in both the reference and test sample is always greater or equal to the probability of finding the same DMS in both the reference and test sample (for more details on calculations see Lucy et al., 1996; Braga et al., 2005), the ability to assess the age of an individual is increased by using IBM rather than using DBM. On the other hand, dental age cannot be assessed on an individual whose stages of development of the seven teeth are not represented in at least one age group of the reference sample. Contrary to DBM, the dental stages of the test individual can be represented by different individuals in the same age group of the reference sample. In our hypothetic sample, assume A, B, and C represent three individuals of the reference sample in the same age group; IBM will be able to
permanent mandibular teeth) and of complete dentitions (i.e. all 7 permanent mandibular teeth).

**Independent Bayesian Method (IBM)**

Developing teeth can also be studied as independent attributes. Although this does not correspond to the biological reality of the development process, some researchers have developed an independent Bayesian method (IBM) for dental age assessment associated with either non-uniform priors (Lucy et al., 1996; Chaillet, 2003; Foti et al., 2003) or with uniform priors (Heuzé, 2004). Only the uniform priors approach is used in this paper. Compared to DBM, IBM offers the possibility to generate dental age estimations for more children than DBM, because calculations are made “tooth by tooth” and not “DMS by DMS”, as illustrated by the following example. Using a hypothetic sample of three children A, B, and C with “$I_1$ and $I_2$” at stage “8 and 7”, “8 and 8”, and “7 and 6”, respectively, the probability to present “$I_1$ and $I_2$” at stage “8 and 7” is computed as “$2/3 \times 1/3$” with IBM, because stage “8” is represented by two children and stage “7” by one child. The probability to present “$I_1$ and $I_2$” at stage “8 and 7” is computed as “$1/3$” with DBM, because there is only one child with “$I_1$ and $I_2$” at stage “8 and 7”; the individual A. Because the probability of finding the same tooth at the same stage of dental development in both the reference and test sample is always greater or equal to the probability of finding the same DMS in both the reference and test sample (for more details on calculations see Lucy et al., 1996; Braga et al., 2005), the ability to assess the age of an individual is increased by using IBM rather than using DBM. On the other hand, dental age cannot be assessed on an individual whose stages of development of the seven teeth are not represented in at least one age group of the reference sample. Contrary to DBM, the dental stages of the test individual can be represented by different individuals in the same age group of the reference sample. In our hypothetic sample, assume A, B, and C represent three individuals of the reference sample in the same age group; IBM will be able to
produce a dental age for a test individual with “I₁ and I₂” at stage “8 and 6”, but DBM will not
because the DMS “8 and 6” is not represented in the hypothetic reference sample. Like DBM,
IBM is able to assess dental age in incomplete dentitions according to only 1, 2, 3, 4, 5, or 6
permanent mandibular teeth and also in complete dentitions (i.e. all 7 permanent mandibular
teeth).

Assessing the quality of dental age assessments

Each child was assigned to one-chronological-year age group (e.g. if the child is 6.4
years old, the chronological age group is [6-7]). For each individual assessed, the dental age
group (the age interval with the highest posterior probability) was compared to the
chronological age group and subsequently given a rank (dental age group minus chronological
age group). If the child's dental age group overlaps the chronological age group, he or she
was given a rank 0. If the rank value is positive, dental age is advanced relative to
chronological age, and if it is negative, dental age is delayed. The absolute value of the rank
indicates how many age groups the dental age differs from chronological age. For example, if
dental age is three one-year groups behind true chronological age then the child is assigned a
rank of -3.

The quality of the dental age assessments were obtained by calculating four
parameters: 1) percentage of response; 2) 95% credible interval; 3) performance; and 4)
symmetry to rank 0. Percentage of response corresponds to the number of children in the
sample who could be assigned a dental age. When using the DBM, the percentage of response
indicates the number of children who could be assigned a dental age by comparing his/her
DMS with those of the reference sample. In contrast, when using the IBM, the percentage of
response corresponds to the number of children who could be assigned a dental age by
comparing each individual's tooth stage with those of the reference sample. The Bayesian
95% credible interval is a posterior probability interval and provides a measure of reliability
produce a dental age for a test individual with “I₁ and I₂” at stage “8 and 6”, but DBM will not
because the DMS “8 and 6” is not represented in the hypothetic reference sample. Like DBM,
IBM is able to assess dental age in incomplete dentitions according to only 1, 2, 3, 4, 5, or 6
permanent mandibular teeth and also in complete dentitions (i.e. all 7 permanent mandibular
teeth).

Assessing the quality of dental age assessments

Each child was assigned to one-chronological-year age group (e.g. if the child is 6.4
years old, the chronological age group is [6-7]). For each individual assessed, the dental age
group (the age interval with the highest posterior probability) was compared to the
chronological age group and subsequently given a rank (dental age group minus chronological
age group). If the child's dental age group overlaps the chronological age group, he or she
was given a rank 0. If the rank value is positive, dental age is advanced relative to
chronological age, and if it is negative, dental age is delayed. The absolute value of the rank
indicates how many age groups the dental age differs from chronological age. For example, if
dental age is three one-year groups behind true chronological age then the child is assigned a
rank of -3.

The quality of the dental age assessments were obtained by calculating four
parameters: 1) percentage of response; 2) 95% credible interval; 3) performance; and 4)
symmetry to rank 0. Percentage of response corresponds to the number of children in the
sample who could be assigned a dental age. When using the DBM, the percentage of response
indicates the number of children who could be assigned a dental age by comparing his/her
DMS with those of the reference sample. In contrast, when using the IBM, the percentage of
response corresponds to the number of children who could be assigned a dental age by
comparing each individual's tooth stage with those of the reference sample. The Bayesian
95% credible interval is a posterior probability interval and provides a measure of reliability
(in months) of the dental method. It is determined by choosing the interval of ranks (number of one-year intervals), centered on rank 0 and containing 95% of the individuals in the test sample. The Bayesian 95% credible interval is analogous to the more common 95% confidence interval used in frequentist statistics. For example, if to include 95% of the individuals in the test sample we establish a rank interval from -3 to +3, the credible interval of the method will be 7×12 months=84 months, with 7 being the number of ranks in the interval (3 ranks below zero + 1 rank zero + 3 ranks above zero) and 12 months the one-year interval of each rank. Thus, the posterior probability that any individual lies in the interval from -3 to +3 is 0.95. Performance corresponds to the percentage of children classified in rank 0, i.e. the percentage of children whose age was estimated with the best accuracy (±6 months). The symmetry to rank 0 allowed the authors to study the relative proportions of both positive and negative ranks and, thus, provides a measure of relative advancement or delay in dental ages, respectively. A statistically significant majority of negative ranks is represented by a minus sign (-), and a statistically significant majority of positive ranks by a plus sign (+).

These four quality parameters (percentage of response, 95% credible interval, performance, and rank distribution symmetry to rank 0) were calculated for each method (DBM and IBM) and for each sample, the reference and the Lisbon (test) samples.

Crossvalidation (Tukey, 1977) was the method used to obtain the quality parameters of the reference sample using both DBM and IBM. The results for each method and sample were then contrasted and compared. The reference sample results comprise the model of “optimal quality” against which the quality of the test sample is compared. Chi-square tests were used to test whether the rank distributions differed between the reference and test samples.

Distribution of ranks in the test sample were considered the observed frequencies and distribution of ranks in the reference sample were used as the expected frequencies. Although there are no specific recommendations for how small a sample can be to be suitable for a chi-
(in months) of the dental method. It is determined by choosing the interval of ranks (number of one-year intervals), centered on rank 0 and containing 95% of the individuals in the test sample. The Bayesian 95% credible interval is analogous to the more common 95% confidence interval used in frequentist statistics. For example, if to include 95% of the individuals in the test sample we establish a rank interval from -3 to +3, the credible interval of the method will be 7×12 months=84 months, with 7 being the number of ranks in the interval (3 ranks below zero + 1 rank zero + 3 ranks above zero) and 12 months the one-year interval of each rank. Thus, the posterior probability that any individual lies in the interval from -3 to +3 is 0.95. Performance corresponds to the percentage of children classified in rank 0, i.e. the percentage of children whose age was estimated with the best accuracy (±6 months). The symmetry to rank 0 allowed the authors to study the relative proportions of both positive and negative ranks and, thus, provides a measure of relative advancement or delay in dental ages, respectively. A statistically significant majority of negative ranks is represented by a minus sign (-), and a statistically significant majority of positive ranks by a plus sign (+).

These four quality parameters (percentage of response, 95% credible interval, performance, and rank distribution symmetry to rank 0) were calculated for each method (DBM and IBM) and for each sample, the reference and the Lisbon (test) samples.

Crossvalidation (Tukey, 1977) was the method used to obtain the quality parameters of the reference sample using both DBM and IBM. The results for each method and sample were then contrasted and compared. The reference sample results comprise the model of “optimal quality” against which the quality of the test sample is compared. Chi-square tests were used to test whether the rank distributions differed between the reference and test samples.

Distribution of ranks in the test sample were considered the observed frequencies and distribution of ranks in the reference sample were used as the expected frequencies. Although there are no specific recommendations for how small a sample can be to be suitable for a chi-
square test, the general rule of thumb is that the smallest expected frequency should be five or
more (Sokal and Rohlf, 1995). Therefore, whenever rank classes with expected frequencies of
less than five occurred, expected and observed frequencies for those classes were pooled with
an adjacent class to obtain a joint class with an expected frequency greater than five. In order
to be sure that the age structure of the reference sample and of the test sample is not
influencing the results due to older children tending to be more delayed than younger children
(they may accumulate more growth deficit over the years), the two were also compared using
a chi-square test. All comparisons were guided by a 5% significance level. All Bayesian
calculations were performed using a Microsoft Excel 2000® Visual Basic macro created by
Dr. Houët (from UMR 5199 PACEA, University of Bordeaux 1, France). This Microsoft
Excel 2000® Visual Basic macro has been used in previous studies (Heuzé, 2004; Braga et
al., 2005) and is available upon request to YH.

RESULTS

The age distributions of both the reference and test samples are shown in Table 1 and
do not show any significant differences (χ²=0.42, p>0.99, df=10). Quality parameters of age
estimation in both the reference and test samples are presented in Table 2. The percentage of
response for both samples and both methods are similar, although only the reference sample
shows 100% of response using IBM. With respect to the 95% credible interval, both samples
do not differ when using the two methods, showing an interval of 84 months. In other words,
the percentage of individuals with ranks comprised between -3 and +3 (84 months) allowed us
to combine at least 95% of the tested sample. The Lisbon sample shows a lower performance
in both methods compared to the reference sample, which means fewer individuals at rank 0.
This is related to the fact that whatever the method used, the Lisbon sample presents a
significant and consistent majority of negative ranks (i.e. delay in dental age) and the mode of
square test, the general rule of thumb is that the smallest expected frequency should be five or
more (Sokal and Rohlf, 1995). Therefore, whenever rank classes with expected frequencies of
less than five occurred, expected and observed frequencies for those classes were pooled with
an adjacent class to obtain a joint class with an expected frequency greater than five. In order
to be sure that the age structure of the reference sample and of the test sample is not
influencing the results due to older children tending to be more delayed than younger children
(they may accumulate more growth deficit over the years), the two were also compared using
a chi-square test. All comparisons were guided by a 5% significance level. All Bayesian
calculations were performed using a Microsoft Excel 2000® Visual Basic macro created by
Dr. Houët (from UMR 5199 PACEA, University of Bordeaux 1, France). This Microsoft
Excel 2000® Visual Basic macro has been used in previous studies (Heuzé, 2004; Braga et
al., 2005) and is available upon request to YH.

RESULTS

The age distributions of both the reference and test samples are shown in Table 1 and
do not show any significant differences (χ²=0.42, p>0.99, df=10). Quality parameters of age
estimation in both the reference and test samples are presented in Table 2. The percentage of
response for both samples and both methods are similar, although only the reference sample
shows 100% of response using IBM. With respect to the 95% credible interval, both samples
do not differ when using the two methods, showing an interval of 84 months. In other words,
the percentage of individuals with ranks comprised between -3 and +3 (84 months) allowed us
to combine at least 95% of the tested sample. The Lisbon sample shows a lower performance
in both methods compared to the reference sample, which means fewer individuals at rank 0.
This is related to the fact that whatever the method used, the Lisbon sample presents a
significant and consistent majority of negative ranks (i.e. delay in dental age) and the mode of
both rank distributions obtained with the Lisbon sample are shifted to the negative rank values. These significant asymmetries to rank 0 of the test sample contrast with the corresponding rank distribution obtained with the reference sample, where with DBM a significant majority of positive ranks is observed (i.e. advance in dental age) and with IBM no significant asymmetry exists.

When DBM is used, the distribution of ranks obtained with the test sample was compared to the distribution of ranks obtained with the reference sample and is illustrated in Figure 1. The same comparison was carried out when IBM is used and is shown in Figure 2. Statistically, the distribution of ranks obtained with the test sample always differed significantly from the distribution of ranks obtained with the reference sample in either the dependent ($\chi^2=19.71, p<0.01, df=4$) and independent Bayesian methods ($\chi^2=33.25, p<0.01, df=4$). Data in both graphs show that the Lisbon children are consistently and systematically one-year delayed relative to the reference sample children.

## DISCUSSION

Results in this study show that both dependent and independent Bayesian methods were relatively precise in determining the age of the Lisbon children, but were not accurate. This means that, in the test sample, both Bayesian methods provided consistent results in relation to each other, showing similar percentages of response (IBM slightly higher), equal 95% credible intervals and similar performances and symmetries to rank 0. However, when the test sample results are compared to the reference sample results, the Lisbon children show a one-year delay relative to the reference sample children. As a result, the test sample shows considerably lower performances and a majority of negative ranks in both dependent and independent Bayesian methods compared to the reference sample. This delay cannot be interpreted as a methodological bias, since the validation of the reference sample (using cross
both rank distributions obtained with the Lisbon sample are shifted to the negative rank values. These significant asymmetries to rank 0 of the test sample contrast with the corresponding rank distribution obtained with the reference sample, where with DBM a significant majority of positive ranks is observed (i.e. advance in dental age) and with IBM no significant asymmetry exists.

When DBM is used, the distribution of ranks obtained with the test sample was compared to the distribution of ranks obtained with the reference sample and is illustrated in Figure 1. The same comparison was carried out when IBM is used and is shown in Figure 2. Statistically, the distribution of ranks obtained with the test sample always differed significantly from the distribution of ranks obtained with the reference sample in either the dependent ($\chi^2=19.71, p<0.01, df=4$) and independent Bayesian methods ($\chi^2=33.25, p<0.01, df=4$). Data in both graphs show that the Lisbon children are consistently and systematically one-year delayed relative to the reference sample children.

## DISCUSSION

Results in this study show that both dependent and independent Bayesian methods were relatively precise in determining the age of the Lisbon children, but were not accurate. This means that, in the test sample, both Bayesian methods provided consistent results in relation to each other, showing similar percentages of response (IBM slightly higher), equal 95% credible intervals and similar performances and symmetries to rank 0. However, when the test sample results are compared to the reference sample results, the Lisbon children show a one-year delay relative to the reference sample children. As a result, the test sample shows considerably lower performances and a majority of negative ranks in both dependent and independent Bayesian methods compared to the reference sample. This delay cannot be interpreted as a methodological bias, since the validation of the reference sample (using cross
validation) did not show any significant majority of negative ranks (i.e. delay in dental age).

On the contrary, the validation step showed either a significant majority of positive ranks with DBM (i.e. advance in dental age) or no asymmetry in ranks using IBM. In addition, the rank distributions for both test and reference samples are statistically different and are displaced by one rank (one year) thus providing further support for a consistent delay in dental development between the children in the test sample and in the reference sample. Since both reference and Lisbon samples did not present any significant difference in age distributions, this delay cannot be the consequence of differing age distributions. Although the power to find a difference in age distributions of the two samples may be considered low given the small test sample size; the chi-square statistic is a robust test (Zar, 1999) and only the power to detect very small differences is likely to be affected.

The similarity of results between DBM and IBM in the test sample was also observed in the quality parameters of the reference sample, with the exception of the symmetry to rank 0. Therefore, DBM and IBM provided basically the same results and this could mean the individual teeth provide enough accuracy and that the relationship between teeth does not add to the prediction of the dental age. However, in the reference sample, DBM results showed a majority of positive ranks (i.e. advance in dental age – see Table 2) and, given that the reference sample includes a significant majority of females, this advancement may suggest a greater sensitivity of this method to sex differences in dental development. Several studies have reported sex differences in both permanent teeth emergence (Hurme, 1949; Dahlberg and Menegaz-Bock, 1958; Garn et al., 1959 were the first – see Demirjian, 1986 for more details) and formation; females reaching most stages ahead of males (Haavikko, 1970 reported difference between 0.3 and 1.7 years). A recent study on the chronology of dental macrostructural mineralization using DBM and 6-month age groups confirmed these sex differences (Heuzé, 2004).
validation) did not show any significant majority of negative ranks (i.e. delay in dental age).

On the contrary, the validation step showed either a significant majority of positive ranks with DBM (i.e. advance in dental age) or no asymmetry in ranks using IBM. In addition, the rank distributions for both test and reference samples are statistically different and are displaced by one rank (one year) thus providing further support for a consistent delay in dental development between the children in the test sample and in the reference sample. Since both reference and Lisbon samples did not present any significant difference in age distributions, this delay cannot be the consequence of differing age distributions. Although the power to find a difference in age distributions of the two samples may be considered low given the small test sample size; the chi-square statistic is a robust test (Zar, 1999) and only the power to detect very small differences is likely to be affected.

The similarity of results between DBM and IBM in the test sample was also observed in the quality parameters of the reference sample, with the exception of the symmetry to rank 0. Therefore, DBM and IBM provided basically the same results and this could mean the individual teeth provide enough accuracy and that the relationship between teeth does not add to the prediction of the dental age. However, in the reference sample, DBM results showed a majority of positive ranks (i.e. advance in dental age – see Table 2) and, given that the reference sample includes a significant majority of females, this advancement may suggest a greater sensitivity of this method to sex differences in dental development. Several studies have reported sex differences in both permanent teeth emergence (Hurme, 1949; Dahlberg and Menegaz-Bock, 1958; Garn et al., 1959 were the first – see Demirjian, 1986 for more details) and formation; females reaching most stages ahead of males (Haavikko, 1970 reported difference between 0.3 and 1.7 years). A recent study on the chronology of dental macrostructural mineralization using DBM and 6-month age groups confirmed these sex differences (Heuzé, 2004).
The inability of dental age estimation methods, based on several teeth, to assess
relative heterochrony in dental development (i.e. patterning) is one important problem with
both Bayesian methods; they both depend exclusively on the timing information (as the
majority of subadults dental age assessment methods) of individual teeth that can be estimated
by the mean of dental stages. Because the timing information is dependent on the number of
teeth from which the mean of dental stages is calculated, it is important to quantify the
influence over the dental age estimation quality of the number of teeth available. However, in
a recent study applying both dependent and independent Bayesian methods to assess the
dental age of the Spitalfields collection children, Heuzé and Braga (2007) showed that the
quality of both Bayesian methods remains relatively stable regardless of the number of teeth
available in each individual. The authors also pointed out that the teeth that complete their
development later (i.e. mainly P₄, M₂ and secondly P₃ and C) are more “powerful” (i.e. more
useful) in age assessments than teeth that complete their development earlier.

Another problem related to patterning is the fact that dental age cannot be assessed
with DBM on an individual whose DMS is not represented in the reference sample, or with
IBM, on individuals whose stages of development of the available teeth are not represented at
least in one age group of the reference sample. In the test sample, only one child could not be
aged using IBM and DBM (specimen# 1448; DMS 55 4 31 53) and three other children could
not be aged using DBM. This caveat of the methods is important because there may be a
systematic bias in particular teeth and stages which are not being incorporated into the
Bayesian estimate. However, such bias could only explain the inability to determine the age
of just one child (specimen# 1448), since in the other three, failure to assess dental age is a
result of the relative heterochrony between the stages of mineralization of the different teeth
compared to the reference sample. For example, on the first child (specimen# 385; DMS 65 4
35 64), P₄ shows a relative advance to C and especially to P₃. The second child (specimen#
The inability of dental age estimation methods, based on several teeth, to assess relative heterochrony in dental development (i.e. patterning) is one important problem with both Bayesian methods; they both depend exclusively on the timing information (as the majority of subadults dental age assessment methods) of individual teeth that can be estimated by the mean of dental stages. Because the timing information is dependent on the number of teeth from which the mean of dental stages is calculated, it is important to quantify the influence over the dental age estimation quality of the number of teeth available. However, in a recent study applying both dependent and independent Bayesian methods to assess the dental age of the Spitalfields collection children, Heuzé and Braga (2007) showed that the quality of both Bayesian methods remains relatively stable regardless of the number of teeth available in each individual. The authors also pointed out that the teeth that complete their development later (i.e. mainly P₄, M₂ and secondly P₃ and C) are more “powerful” (i.e. more useful) in age assessments than teeth that complete their development earlier.

Another problem related to patterning is the fact that dental age cannot be assessed with DBM on an individual whose DMS is not represented in the reference sample, or with IBM, on individuals whose stages of development of the available teeth are not represented at least in one age group of the reference sample. In the test sample, only one child could not be aged using IBM and DBM (specimen# 1448; DMS 55 4 31 53) and three other children could not be aged using DBM. This caveat of the methods is important because there may be a systematic bias in particular teeth and stages which are not being incorporated into the Bayesian estimate. However, such bias could only explain the inability to determine the age of just one child (specimen# 1448), since in the other three, failure to assess dental age is a result of the relative heterochrony between the stages of mineralization of the different teeth compared to the reference sample. For example, on the first child (specimen# 385; DMS 65 4 35 64), P₄ shows a relative advance to C and especially to P₃. The second child (specimen#
1561; DMS 65 5 5_74) shows a relative advance of M₁. On the third child (specimen# 1584; DMS 88 6 87 86), C shows a relative delay and P₄ a relative advance. Interestingly, all four children are boys.

A fairly clear amount of variation can be seen in most reference samples utilized by osteologists and the magnitude of such variation is rarely incorporated into studies (exceptions include Hoppa, 1992). The Bayesian approach used in this study should account for the variation of development time for individual teeth and their stages and for variation that results from random fluctuations in the teeth present for analysis (the relative concordance in dental ages between teeth) and from using combined sexes tooth timings, that could explain what appears to be accelerated or delayed development. Therefore, although environmental effects have not been considered important factors as sources of variation in dental age assessments, the authors believe that the differences in dental development between the reference and Lisbon samples can be ascribed to socioeconomic differences that separate both samples. These differences reflect not only absolute social and economic conditions in populations of both samples, but also secular trends. The reference sample is comprised of modern children, whereas the test sample is comprised of early 20th century deceased children. Therefore, both samples are separated by several decades of history, that reflect social, economical and political transformations in each society, resulting in changes towards better nutrition, especially more protein and caloric intake during infancy, greater overall sanitary conditions and hygiene, lessening of disease as well as delivery of social and medical care. All these improvements are known to modify growth and development by accelerating physical maturation of children over time (Susanne, 1984; Tanner, 1989; Malina, 1990; Bogin, 1999). Even if the reference sample children from Ivory Coast, Iran and Morocco represent populations who have not yet experienced significant secular changes, compared to the reference sample children from France, they do represent the high to middle
1561; DMS 65 5 5_74) shows a relative advance of M₁. On the third child (specimen# 1584; DMS 88 6 87 86), C shows a relative delay and P₄ a relative advance. Interestingly, all four children are boys.

A fairly clear amount of variation can be seen in most reference samples utilized by osteologists and the magnitude of such variation is rarely incorporated into studies (exceptions include Hoppa, 1992). The Bayesian approach used in this study should account for the variation of development time for individual teeth and their stages and for variation that results from random fluctuations in the teeth present for analysis (the relative concordance in dental ages between teeth) and from using combined sexes tooth timings, that could explain what appears to be accelerated or delayed development. Therefore, although environmental effects have not been considered important factors as sources of variation in dental age assessments, the authors believe that the differences in dental development between the reference and Lisbon samples can be ascribed to socioeconomic differences that separate both samples. These differences reflect not only absolute social and economic conditions in populations of both samples, but also secular trends. The reference sample is comprised of modern children, whereas the test sample is comprised of early 20th century deceased children. Therefore, both samples are separated by several decades of history, that reflect social, economical and political transformations in each society, resulting in changes towards better nutrition, especially more protein and caloric intake during infancy, greater overall sanitary conditions and hygiene, lessening of disease as well as delivery of social and medical care. All these improvements are known to modify growth and development by accelerating physical maturation of children over time (Susanne, 1984; Tanner, 1989; Malina, 1990; Bogin, 1999). Even if the reference sample children from Ivory Coast, Iran and Morocco represent populations who have not yet experienced significant secular changes, compared to the reference sample children from France, they do represent the high to middle
social class of their respective countries, and all the benefits, in terms of access to adequate
nutrition and to health care, that it entails. Similarly, although the French segment of the
sample comprises low socioeconomic status children, they are only 10.3% of the sample
(Heuzé, 2004) and represent an affluent population who had already experienced major
secular changes, including achievements in medical care. Therefore, it is likely that children
in the reference sample show accelerated dental maturity compared to the Lisbon children. In
fact, the last 50 years have witnessed notable improvements in living conditions of European
populations, and those secular changes may explain the acceleration in dental formation that
has been detected in 3- to 9-year-old European boys between 1960 and 1997 (Holtgrave et al.,
1997), and in 8.5- to 14.5-year-old boys and girls in the US, between the 1970s and the 1990s
(Nadler, 1998). In addition, inability to determine age using DBM, due to a certain DMS not
being represented in the reference sample, suggests that socioeconomic status, living
conditions, or secular trends could affect not only dental age, but also relative dental
development (i.e. patterning).

In contrast to the reference sample children, the Lisbon children experienced poor
living conditions and limited access to proper nutrition and health care, which affected their
developmental and growth status (Cardoso, 2005, 2007). However, applying a modified
version of the Moorrees et al.'s (1963a,b) dental aging method using Demirjian et al.'s (1973)
dental stages, Cardoso (2005, 2007) reported a non-significant delay in dental development of
Lisbon children (individuals aged 0 to 12 years) of low socioeconomic status compared to
high socioeconomic status. Overall, dental age of Lisbon children was also not significantly
delayed to chronological age (Cardoso, 2005, 2007) and this contradicts the results in this
study. Results with both Bayesian methods show a dental delay in Lisbon children which does
not seem to derive from methodological bias. Consequently, it seems that the modified
Moorrees et al.'s aging method may be overestimating dental age in the Lisbon children. In
social class of their respective countries, and all the benefits, in terms of access to adequate
nutrition and to health care, that it entails. Similarly, although the French segment of the
sample comprises low socioeconomic status children, they are only 10.3% of the sample
(Heuzé, 2004) and represent an affluent population who had already experienced major
secular changes, including achievements in medical care. Therefore, it is likely that children
in the reference sample show accelerated dental maturity compared to the Lisbon children. In
fact, the last 50 years have witnessed notable improvements in living conditions of European
populations, and those secular changes may explain the acceleration in dental formation that
has been detected in 3- to 9-year-old European boys between 1960 and 1997 (Holtgrave et al.,
1997), and in 8.5- to 14.5-year-old boys and girls in the US, between the 1970s and the 1990s
(Nadler, 1998). In addition, inability to determine age using DBM, due to a certain DMS not
being represented in the reference sample, suggests that socioeconomic status, living
conditions, or secular trends could affect not only dental age, but also relative dental
development (i.e. patterning).

In contrast to the reference sample children, the Lisbon children experienced poor
living conditions and limited access to proper nutrition and health care, which affected their
developmental and growth status (Cardoso, 2005, 2007). However, applying a modified
version of the Moorrees et al.'s (1963a,b) dental aging method using Demirjian et al.'s (1973)
dental stages, Cardoso (2005, 2007) reported a non-significant delay in dental development of
Lisbon children (individuals aged 0 to 12 years) of low socioeconomic status compared to
high socioeconomic status. Overall, dental age of Lisbon children was also not significantly
delayed to chronological age (Cardoso, 2005, 2007) and this contradicts the results in this
study. Results with both Bayesian methods show a dental delay in Lisbon children which does
not seem to derive from methodological bias. Consequently, it seems that the modified
Moorrees et al.'s aging method may be overestimating dental age in the Lisbon children. In
fact, research carried out by Simpson and Kunos (1999) suggests that the standards of
Moorrees et al. may overestimate chronological age. Several studies (Hägg and Mattson,
1986; Poyry et al., 1986; Staaf et al., 1991; Mörnstad et al., 1995; Koshy and Tandon, 1998;
Nykänen et al., 1998; Liversidge et al., 1999; Willems et al., 2001; Eid et al., 2002; Hedge
and Sood, 2002) using different samples (age structures, “geographic origins”) reported that
Demirjian’s method (Demirjian et al., 1973; Demirjian and Goldstein, 1976), another widely
used aging method for subadults, overestimated chronological age, thus providing dental ages
that are advanced relative to chronological age. Applying the Demirjian’s method (Demirjian
et al., 1973; Demirjian and Goldstein, 1976) to the identified juvenile skeletons of the
Spitalfields collection (18th and 19th centuries), Liversidge (1999) reported non-significant
differences between dental age and chronological age and suggested modern dental formation
schedules for Spitalfields children. These children were the sons and daughters of middle- to
upper-class members of the Huguenot congregation buried in the Spitalfields church crypt
(Cox, 1996). However, regardless of the relative wealth of families, these children did not
necessarily receive the best care and the industrial environment of London (overcrowding, air
pollution, and inadequate sewage disposal) contributed significantly to deaths in early
childhood and to growth retardation, exacerbated by the high prevalence of rickets and scurry
(Lewis, 2002). In addition, not only were these middle to high socioeconomic children not
buffered from environmental insults, but they were also living at a time which had not
benefited from recent improvements in sanitation, medical care and food preparation. We can
reasonably conclude, therefore, that this lack of significance between dental and chronological
age in the Spitalfields children (Liversidge, 1999) is due to the tendency of the Demirjian’s
method (Demirjian et al., 1973; Demirjian and Goldstein, 1976) to overestimate dental age (as
the modified Moorrees et al.’s method) and does not represent the biological reality of the
sample. The fact that the Spitalfields children were not found to be dentally delayed relative
fact, research carried out by Simpson and Kunos (1999) suggests that the standards of
Moorrees et al. may overestimate chronological age. Several studies (Hägg and Mattson,
1986; Poyry et al., 1986; Staaf et al., 1991; Mörnstad et al., 1995; Koshy and Tandon, 1998;
Nykänen et al., 1998; Liversidge et al., 1999; Willems et al., 2001; Eid et al., 2002; Hedge
and Sood, 2002) using different samples (age structures, “geographic origins”) reported that
Demirjian’s method (Demirjian et al., 1973; Demirjian and Goldstein, 1976), another widely
used aging method for subadults, overestimated chronological age, thus providing dental ages
that are advanced relative to chronological age. Applying the Demirjian’s method (Demirjian
et al., 1973; Demirjian and Goldstein, 1976) to the identified juvenile skeletons of the
Spitalfields collection (18th and 19th centuries), Liversidge (1999) reported non-significant
differences between dental age and chronological age and suggested modern dental formation
schedules for Spitalfields children. These children were the sons and daughters of middle- to
upper-class members of the Huguenot congregation buried in the Spitalfields church crypt
(Cox, 1996). However, regardless of the relative wealth of families, these children did not
necessarily receive the best care and the industrial environment of London (overcrowding, air
pollution, and inadequate sewage disposal) contributed significantly to deaths in early
childhood and to growth retardation, exacerbated by the high prevalence of rickets and scurry
(Lewis, 2002). In addition, not only were these middle to high socioeconomic children not
buffered from environmental insults, but they were also living at a time which had not
benefited from recent improvements in sanitation, medical care and food preparation. We can
reasonably conclude, therefore, that this lack of significance between dental and chronological
age in the Spitalfields children (Liversidge, 1999) is due to the tendency of the Demirjian’s
method (Demirjian et al., 1973; Demirjian and Goldstein, 1976) to overestimate dental age (as
the modified Moorrees et al.’s method) and does not represent the biological reality of the
sample. The fact that the Spitalfields children were not found to be dentally delayed relative
to the more modern Demirjian standards, also seems contrary to the findings of Holtgrave et
al. (1997) and Nadler (1998), who showed an acceleration in dental maturity during the past
40 years as a consequence of secular trends. Although, at first hand, the socioeconomic status
of the Spitalfields children seems quite different to that of the Lisbon children, they tend to
share several features. They are both comprised of deceased children who were growing up in
poor environments, prior to the era of antibiotics and of other achievements in health care.

Additional evidence for the influence of environmental factors in dental development
can be found by comparing the amount of overestimation in chronological age in the several
studies that used Demirjian's method (Demirjian et al., 1973; Demirjian and Goldstein, 1976).
Overestimation seems least in samples of industrialized nations and greatest in samples of
developing countries. For example, while in Indian children overestimation amounted to 3.04
years for boys and 2.82 for girls (Koshy and Tandon, 1998), it only amounted to 0.14 and
0.04 years for Belgian boys and girls, respectively (Hedge and Sood, 2002). It is also
interesting to note that British children of different geographic origins, but who grew up in the
UK, show similar amounts of overestimation when Demirjian's standards are applied
(Liversidge et al., 1999). This suggests that any non-methodological influences on dental age
estimation must be due to overall shared socioeconomic status and living conditions that
affect nutrition and health care that, in turn, impact on dental development.

Using different aging methods (Moorrees et al., 1963a,b; Demirjian et al., 1973; Demirjian and Goldstein, 1976) to estimate dental age of identified skeletal collections, some authors (Saunders et al., 1993; Liversidge, 1999; Cardoso, 2007) reported non-significant differences between dental and chronological ages in non-adult skeletal remains. This seemed to justify the assertion that these dental aging methods were suitable for age assessment of historical and archaeological non-adult skeletal remains. Although problems with the standards of Demirjian et al. and Moorrees et al. may be methodological, results in this study
to the more modern Demirjian standards, also seems contrary to the findings of Holtgrave et
al. (1997) and Nadler (1998), who showed an acceleration in dental maturity during the past
40 years as a consequence of secular trends. Although, at first hand, the socioeconomic status
of the Spitalfields children seems quite different to that of the Lisbon children, they tend to
share several features. They are both comprised of deceased children who were growing up in
poor environments, prior to the era of antibiotics and of other achievements in health care.

Additional evidence for the influence of environmental factors in dental development
can be found by comparing the amount of overestimation in chronological age in the several
studies that used Demirjian's method (Demirjian et al., 1973; Demirjian and Goldstein, 1976).
Overestimation seems least in samples of industrialized nations and greatest in samples of
developing countries. For example, while in Indian children overestimation amounted to 3.04
years for boys and 2.82 for girls (Koshy and Tandon, 1998), it only amounted to 0.14 and
0.04 years for Belgian boys and girls, respectively (Hedge and Sood, 2002). It is also
interesting to note that British children of different geographic origins, but who grew up in the
UK, show similar amounts of overestimation when Demirjian's standards are applied
(Liversidge et al., 1999). This suggests that any non-methodological influences on dental age
estimation must be due to overall shared socioeconomic status and living conditions that
affect nutrition and health care that, in turn, impact on dental development.

Using different aging methods (Moorrees et al., 1963a,b; Demirjian et al., 1973; Demirjian and Goldstein, 1976) to estimate dental age of identified skeletal collections, some authors (Saunders et al., 1993; Liversidge, 1999; Cardoso, 2007) reported non-significant differences between dental and chronological ages in non-adult skeletal remains. This seemed to justify the assertion that these dental aging methods were suitable for age assessment of historical and archaeological non-adult skeletal remains. Although problems with the standards of Demirjian et al. and Moorrees et al. may be methodological, results in this study
show that the application of modern probabilistic dental age methods (Heuzé, 2004; Braga et al., 2005) to archaeological samples can be problematic, due to population differences in socioeconomic status and in living conditions, and to secular trends. When one is dealing with children who experienced poor living conditions, it is likely that delays in dental development will determine a lower accuracy for dental age estimations. Although the children in the test sample do not represent either the affluent or the extremely disadvantaged segments of the 20th century Lisbon society (Cardoso, 2005, 2007), they may serve as a reference sample for many ecologically diverse populations prior to the antibiotic era. It is not implied that this population is representative of prehistoric or historic populations, but it can provide an important test for examining the factors that influence the interpretation of developmental patterns in skeletal samples.

## CONCLUSION

The two main purposes of this study were to test two Bayesian dental aging methods (with dependent or independent assumptions) in a large identified skeletal collection, and to interpret the origin of the potential discrepancies between the chronological and dental ages in the test sample. The subadults of the Lisbon collection provided an appealing opportunity to test those methods and examine their overall accuracy. Our results showed a general tendency of the Lisbon children to be consistently and systematically one-year delayed relative to the reference sample, regardless of the method utilized. This suggests that skeletal biologists should be very careful when determining the age of non-adult skeletal remains. Dental age may be the best indicator of chronological age but differences between populations may occur due to differences in living conditions, overall socioeconomic status or to secular trends that affect the accuracy of the dental age estimates. This is particularly true for archaeological studies, where older material is being examined and less information can be gathered from
show that the application of modern probabilistic dental age methods (Heuzé, 2004; Braga et al., 2005) to archaeological samples can be problematic, due to population differences in socioeconomic status and in living conditions, and to secular trends. When one is dealing with children who experienced poor living conditions, it is likely that delays in dental development will determine a lower accuracy for dental age estimations. Although the children in the test sample do not represent either the affluent or the extremely disadvantaged segments of the 20th century Lisbon society (Cardoso, 2005, 2007), they may serve as a reference sample for many ecologically diverse populations prior to the antibiotic era. It is not implied that this population is representative of prehistoric or historic populations, but it can provide an important test for examining the factors that influence the interpretation of developmental patterns in skeletal samples.

## CONCLUSION

The two main purposes of this study were to test two Bayesian dental aging methods (with dependent or independent assumptions) in a large identified skeletal collection, and to interpret the origin of the potential discrepancies between the chronological and dental ages in the test sample. The subadults of the Lisbon collection provided an appealing opportunity to test those methods and examine their overall accuracy. Our results showed a general tendency of the Lisbon children to be consistently and systematically one-year delayed relative to the reference sample, regardless of the method utilized. This suggests that skeletal biologists should be very careful when determining the age of non-adult skeletal remains. Dental age may be the best indicator of chronological age but differences between populations may occur due to differences in living conditions, overall socioeconomic status or to secular trends that affect the accuracy of the dental age estimates. This is particularly true for archaeological studies, where older material is being examined and less information can be gathered from
archaeological or written sources to infer the population's living standards. This issue may
also affect forensic applications, particularly if the remains that need to be identified belong to
a child of lower socioeconomic status in an under-developed country and the reference
standard used to estimate dental age has been developed on the affluent segment of more
developed nations. Moreover, more attention has to be given to the potential influence of
socioeconomic status, living conditions and secular trends over relative dental development
and dental sequences.

ACKNOWLEDGEMENTS

The authors would like to thank the anonymous reviewers for their helpful comments
and Sandra Albanese for editorial suggestions.
archaeological or written sources to infer the population's living standards. This issue may
also affect forensic applications, particularly if the remains that need to be identified belong to
a child of lower socioeconomic status in an under-developed country and the reference
standard used to estimate dental age has been developed on the affluent segment of more
developed nations. Moreover, more attention has to be given to the potential influence of
socioeconomic status, living conditions and secular trends over relative dental development
and dental sequences.

ACKNOWLEDGEMENTS

The authors would like to thank the anonymous reviewers for their helpful comments
and Sandra Albanese for editorial suggestions.
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<table><caption>TABLE 1. Age and sex distribution of the reference and test samples.</caption><thead><tr><th rowspan="2">Age interval (years)</th><th colspan="3">Reference sample</th><th colspan="3">Test sample</th></tr><tr><th>Females</th><th>Males</th><th>Sexes combined</th><th>Females</th><th>Males</th><th>Sexes combined</th></tr></thead><tbody><tr><td>[1-2[</td><td>1</td><td>0</td><td>1</td><td>-</td><td>-</td><td>-</td></tr><tr><td>[2-3[</td><td>2</td><td>5</td><td>7</td><td>-</td><td>-</td><td>-</td></tr><tr><td>[3-4[</td><td>20</td><td>34</td><td>54</td><td>-</td><td>-</td><td>-</td></tr><tr><td>[4-5[</td><td>50</td><td>57</td><td>107</td><td>3</td><td>3</td><td>6</td></tr><tr><td>[5-6[</td><td>69</td><td>72</td><td>141</td><td>2</td><td>1</td><td>3</td></tr><tr><td>[6-7[</td><td>86</td><td>74</td><td>160</td><td>1</td><td>1</td><td>2</td></tr><tr><td>[7-8[</td><td>109</td><td>77</td><td>186</td><td>0</td><td>2</td><td>2</td></tr><tr><td>[8-9[</td><td>164</td><td>107</td><td>271</td><td>1</td><td>1</td><td>2</td></tr><tr><td>[9-10[</td><td>170</td><td>129</td><td>299</td><td>2</td><td>2</td><td>4</td></tr><tr><td>[10-11[</td><td>177</td><td>117</td><td>294</td><td>3</td><td>1</td><td>4</td></tr><tr><td>[11-12[</td><td>178</td><td>126</td><td>304</td><td>3</td><td>4</td><td>7</td></tr><tr><td>[12-13[</td><td>134</td><td>103</td><td>237</td><td>2</td><td>1</td><td>3</td></tr><tr><td>[13-14[</td><td>95</td><td>78</td><td>173</td><td>2</td><td>1</td><td>3</td></tr><tr><td>[14-15[</td><td>50</td><td>37</td><td>87</td><td>1</td><td>3</td><td>4</td></tr><tr><td>[15-16[</td><td>41</td><td>24</td><td>65</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Total</td><td>1,346</td><td>1,040</td><td>2,386</td><td>20</td><td>20</td><td>40</td></tr></tbody></table>
<table><caption>TABLE 1. Age and sex distribution of the reference and test samples.</caption><thead><tr><th rowspan="2">Age interval (years)</th><th colspan="3">Reference sample</th><th colspan="3">Test sample</th></tr><tr><th>Females</th><th>Males</th><th>Sexes combined</th><th>Females</th><th>Males</th><th>Sexes combined</th></tr></thead><tbody><tr><td>[1-2[</td><td>1</td><td>0</td><td>1</td><td>-</td><td>-</td><td>-</td></tr><tr><td>[2-3[</td><td>2</td><td>5</td><td>7</td><td>-</td><td>-</td><td>-</td></tr><tr><td>[3-4[</td><td>20</td><td>34</td><td>54</td><td>-</td><td>-</td><td>-</td></tr><tr><td>[4-5[</td><td>50</td><td>57</td><td>107</td><td>3</td><td>3</td><td>6</td></tr><tr><td>[5-6[</td><td>69</td><td>72</td><td>141</td><td>2</td><td>1</td><td>3</td></tr><tr><td>[6-7[</td><td>86</td><td>74</td><td>160</td><td>1</td><td>1</td><td>2</td></tr><tr><td>[7-8[</td><td>109</td><td>77</td><td>186</td><td>0</td><td>2</td><td>2</td></tr><tr><td>[8-9[</td><td>164</td><td>107</td><td>271</td><td>1</td><td>1</td><td>2</td></tr><tr><td>[9-10[</td><td>170</td><td>129</td><td>299</td><td>2</td><td>2</td><td>4</td></tr><tr><td>[10-11[</td><td>177</td><td>117</td><td>294</td><td>3</td><td>1</td><td>4</td></tr><tr><td>[11-12[</td><td>178</td><td>126</td><td>304</td><td>3</td><td>4</td><td>7</td></tr><tr><td>[12-13[</td><td>134</td><td>103</td><td>237</td><td>2</td><td>1</td><td>3</td></tr><tr><td>[13-14[</td><td>95</td><td>78</td><td>173</td><td>2</td><td>1</td><td>3</td></tr><tr><td>[14-15[</td><td>50</td><td>37</td><td>87</td><td>1</td><td>3</td><td>4</td></tr><tr><td>[15-16[</td><td>41</td><td>24</td><td>65</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Total</td><td>1,346</td><td>1,040</td><td>2,386</td><td>20</td><td>20</td><td>40</td></tr></tbody></table>
<table><caption>TABLE 2. Quality of dental age assessments of both reference and test samples according to dependent and independent Bayesian methods.</caption><thead><tr><th rowspan="2"></th><th colspan="2">Reference sample</th><th colspan="2">Test sample</th></tr><tr><th>DBM</th><th>IBM</th><th>DBM</th><th>IBM</th></tr></thead><tbody><tr><td>Number of individuals</td><td>2,259</td><td>2,259</td><td>40</td><td>40</td></tr><tr><td>Percentage of response (%)</td><td>91.9</td><td>100.0</td><td>90.0</td><td>97.5</td></tr><tr><td>95% CI (months)<sup>1</sup></td><td>84</td><td>84</td><td>84</td><td>84</td></tr><tr><td>Performance (%)</td><td>34.3</td><td>35.5</td><td>25.0</td><td>23.1</td></tr><tr><td>Symmetry to rank 0<sup>2</sup></td><td>0.00 (+)</td><td>0.14</td><td>0.03 (-)</td><td>0.01 (-)</td></tr></tbody></table>

<footnote n="1">¹Credible interval (CI)</footnote>

<footnote n="2">² Significance level of the difference between positive and negative rank proportions (symmetry to rank 0). Majority of negative ranks is shown as (-), majority of positive ranks as (+).</footnote>
<table><caption>TABLE 2. Quality of dental age assessments of both reference and test samples according to dependent and independent Bayesian methods.</caption><thead><tr><th rowspan="2"></th><th colspan="2">Reference sample</th><th colspan="2">Test sample</th></tr><tr><th>DBM</th><th>IBM</th><th>DBM</th><th>IBM</th></tr></thead><tbody><tr><td>Number of individuals</td><td>2,259</td><td>2,259</td><td>40</td><td>40</td></tr><tr><td>Percentage of response (%)</td><td>91.9</td><td>100.0</td><td>90.0</td><td>97.5</td></tr><tr><td>95% CI (months)<sup>1</sup></td><td>84</td><td>84</td><td>84</td><td>84</td></tr><tr><td>Performance (%)</td><td>34.3</td><td>35.5</td><td>25.0</td><td>23.1</td></tr><tr><td>Symmetry to rank 0<sup>2</sup></td><td>0.00 (+)</td><td>0.14</td><td>0.03 (-)</td><td>0.01 (-)</td></tr></tbody></table>

<footnote n="1">¹Credible interval (CI)</footnote>

<footnote n="2">² Significance level of the difference between positive and negative rank proportions (symmetry to rank 0). Majority of negative ranks is shown as (-), majority of positive ranks as (+).</footnote>
<figure><img src="image_1.png" /><figcaption>**Fig. 1.** Distribution of ranks in the test sample compared to the distribution of ranks in the reference sample (dependent Bayesian method, sexes combined).</figcaption></figure>

<figure><img src="image_2.png" /><figcaption>**Fig. 2.** Distribution of ranks in the test sample compared to the distribution of ranks in the reference sample (independent Bayesian method, sexes combined).</figcaption></figure>
<figure><img src="image_2.png" /><figcaption>**Fig. 1.** Distribution of ranks in the test sample compared to the distribution of ranks in the reference sample (dependent Bayesian method, sexes combined).</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Distribution of ranks in the test sample compared to the distribution of ranks in the reference sample (independent Bayesian method, sexes combined).</figcaption></figure>