Validating dental age estimation in Kenyan black children and adolescents using the Willems method

Abstract

Purpose

This study aimed to validate the Willems Belgian Caucasian (Willems BC) age estimation model in a Kenyan sample, to develop and validate a Kenyan-specific (Willems KB) age estimation model and to compare the age prediction performances of both models.

Methods

Panoramic radiographs of 1038 (523 female, 515 male) Kenyan children without missing permanent teeth and without all permanent teeth fully developed (except third molars) were retrospectively selected. Tooth development of the seven lower-left permanent teeth was staged according to Demirjian et al. The Willems BC model, performed on a Belgian Caucasian sample and a constructed Kenyan-specific model (Willems KB) were validated on the Kenyan sample. Their age prediction performances were quantified and compared using the mean error (ME), mean absolute error (MAE) and root-mean-square error (RMSE).

Results

The ME with Willems BC method equalled zero. Hence, there was no systematic under- or overestimation of the age. For males and females separately, the ME with Willems BC was significantly different from zero, but negligible in magnitude (–0.04 and 0.04, respectively). Willems KB was found not to outperform Willems BC, since the MAE and RMSE were comparable (0.98 vs 0.97 and 1.31 vs 1.29, respectively). Although Willems BC resulted in a higher percentage of subjects with predicted age within a one-year difference of the true age (63.3% vs 60.4%, p=0.018), this cannot be considered as clinically relevant.

Conclusion

There is no reason to use a country-specific (Willems KB) model in children from Kenya instead of the original Willems (BC) model.

Keywords

Forensic dentistry forensic odontology dental age estimation Willems method Caucasian sample Kenyan black sample

Introduction

Estimating the age of an individual has proven useful for several purposes, such as pre- or post-mortem identification of unknown subjects, controlling migration issues such as child trafficking and abuse and other civil, criminal, socio-economic or administrative purposes.¹ The most used forensic methods for chronological age estimation in children are those based on radiographic registrations of dental and bone development.^2,3 While bone development seems to be more influenced by environmental factors such as the diet, teeth have been reported to have a fairly stable maturation track.⁴

Several methods for dental age estimation in children have been reported and validated, such as the ones by Demirjian, Nolla, Nicodemo or Willems,^5–7 which use radiographically observed permanent tooth development and classify it into predefined stages. From these, the Willems model⁷ has been found to provide the most accurate dental age estimations in children.⁸ This model was developed in a Belgian Caucasian (Willems BC) sample of 2116 individuals and has been validated in multiple populations with different ethnical backgrounds.^8–18

One of the limitations of the Willems BC method was its lack of validation in diverse black populations. Recently, this was achieved in a South African and a Somali black sample.^12,15 However, the population of black Somali children was exceptional, since they had been living their whole life in Finland, which makes fair comparisons with other populations of black children difficult. On the other hand, the country-specific prediction method established on the South African black sample (Willems SAB) performed better compared to Willems BC, but the differences were too small to be clinically relevant, especially in males. These results should therefore be confirmed in another black population, since certain studies report differences in age estimation results between black and non-black populations.^19,20 Therefore, in the present study, a sample of panoramic radiographs of Kenyan children was collected.

In Kenya, age estimations in children are particularly requested for a specific age threshold. Children under the age of eight cannot be held criminally responsible, while a child between 8 and 12 years of age can be held criminally responsible if his or her capacity to know right and wrong can be proven. A male person under the age of 12 is presumed incapable of having carnal knowledge, which prevents the prosecution of younger boys for certain sexual offences, while the official age of consent is 18 years old.²¹ Migration of individuals to and from Kenya is also an issue where age estimation is desirable, especially in the case of unaccompanied minors. UNICEF shows in its 2018 Kenya Humanitarian Situation Report that in 2017, approximately 469,000 immigrants came to Kenya from the neighbouring countries of Somalia, South Sudan, Congo or Ethiopia, while 350,000 people migrated from Kenya to the USA, the UK or Canada.²²

The aims of the present study were (a) to use a sample of black children from Kenya to validate the Willems age estimation model (Willems BC), (b) to develop and validate a Kenyan-specific age estimation model (Willems KB) and (c) to quantify and compare the age prediction performances of both models.

Methods

Digital panoramic radiographs of 1399 children between 3 and 24 years old of Kenyan origin were collected (M_age=11.71±4.63 years, 720 females (F) and 679 males (M)) between 2015 and 2018. Data were collected from the following sites in Nairobi: the School of Dental Sciences of the University of Nairobi, the Dental and Maxillofacial Imaging Centre (DAMIC), the Kenyatta National Hospital and the private practices Millennium Dental Services and JB Dental Clinic. Approval was obtained from the Ethics and Research Committee (ERC) of the Kenyatta National Hospital/University of Nairobi (KNH/UON; approval no. P499/10/2013).

The following selection criteria were applied: age was used to ensure that a sufficient sample could be collected in each age category, which was confirmed by the birthdate on official papers, and radiographs with poor image quality or unclear images were excluded from the study, as well as those corresponding to patients with cleft lip and palate or other craniofacial affectations. The seven permanent teeth of the left mandible were staged on the panoramic radiographs according to the Demirjian technique.⁵ Intra-observer reliability was tested by weighted kappa analysis. Statistical analyses were only performed on individuals without missing permanent teeth and without all permanent teeth on the left mandible fully developed, excluding third molars.

To validate the Willems BC model on the Kenyan sample, the obtained Demirjian stages were used as categorical predictors for age in a weighted analysis of variance (ANOVA) model. Weights were used to handle the non-constant variance (higher variability of age at higher stages). The same approach was used on all included Kenyan individuals to construct a new Kenyan-specific age prediction model, referred to as the Willems KB model. The age prediction performances of both approaches (Willems BC vs. Willems KB method) were quantified and compared in general and by sex and age categories. Therefore, the mean error (ME, calculated by subtracting the estimated age from the chronological age), the mean absolute error (MAE) and the root-mean-square error (RMSE) were used. Leave-one-out cross-validation was used in the validation of the Willems KB model. Note that the validation of the Willems BC model was external and hence did not require a cross-validation strategy. ME and MAE were compared using Wilcoxon signed-rank tests. A McNemar test was used to compare the proportion of children with a MAE ≤1 year. The association between age or mean score and the (absolute) error was evaluated using Spearman correlations. They were compared using the Steiger modification of Dunn & Clark Z test for dependent correlations. All statistical analyses were performed using SAS v9.4 (SAS Institute, Cary, NC).

Results

From the 1399 individuals with collected Demirjian information (720 F, 679 M), 1038 (523 F and 515 M) had no missing permanent teeth and did not have all permanent teeth of the left mandible fully developed. Only these were included in the analysis. If a specific score level did not occur in the training set, no age prediction could be obtained for that subject. In the Willems KB cross-validation, this was the case for two subjects, reducing this validation sample to 1036 (522 F, 514 M) subjects.

The selected subjects were between 3 and 18 years old, with a mean age of 9.85 years old. A total of 1030 (99.23%) subjects were <16 years old, while eight (0.77%) were 16–18 years old. The sex and age distribution of the selected sample is reported in Table 1.

Table 1.

Age and sex distribution of the selected sample.

	Sex
Age (years)	Females	Males	Total
3–3.99	17	9	26
4–4.99	27	37	64
5–5.99	34	41	75
6–6.99	33	32	65
7–7.99	44	43	87
8–8.99	52	45	97
9–9.99	39	47	86
10–10.99	58	56	114
11–11.99	64	61	125
12–12.99	68	50	118
13–13.99	41	35	76
14–14.99	28	27	55
15–15.99	14	28	42
16–16.99	1	4	5
17–17.99	3	0	3
Total	523	515	1038
M_age	9.88	9.82	9.85
SD	3.20	3.28	3.24

SD: standard deviation; M: mean.

Results of the kappa analysis showed a good intra-observer agreement. The simple and weighted kappa values were 0.84 and 0.94, respectively. The regression coefficients from the weighted ANOVA for the Willems KB model are reported in Table 2, while Table 3 reports the results of the ME, absolute error, RMSE and differences between both Willems BC and KB models. Table 4 reports the error and absolute error per age category and sex. Note that a negative error refers to overestimation of the age, while a positive error is interpreted as underestimation of the age.

Table 2.

Regression coefficients from the weighted ANOVA (Willems KB).

		Demirjian et al. stage
	Tooth	A	B	C	D	E	F	G	H
Males
	t31	–	–	3.092	2.984	3.289	3.754	4.389	4.447
	t32	–	–	0.000	–0.094	0.103	0.148	–0.204	–0.398
	t33	–	0.000	0.071	0.059	0.255	0.660	1.518	2.202
	t34	0.000	0.000	0.236	0.472	1.048	1.241	1.318	1.227
	t35	0.000	0.233	0.325	0.063	–0.047	0.907	0.972	1.364
	t36	–	–	0.000	0.252	0.389	0.704	1.261	1.625
	t37	0.000	0.673	1.029	1.344	1.935	2.286	3.458	–
Females
	t31	–	–	3.650	4.024	4.500	4.340	4.619	4.734
	t32	–	–	0.000	–0.308	–0.335	0.333	0.578	0.109
	t33	–	–	0.000	0.533	–0.003	0.795	1.398	1.572
	t34	–	0.000	0.531	0.469	0.802	1.276	1.776	2.049
	t35	0.000	–0.414	–0.481	–0.627	–0.109	–0.056	–0.085	0.721
	t36	–	–	0.000	–0.080	0.337	0.812	0.848	1.305
	t37	0.000	–0.318	0.424	0.988	1.351	2.236	3.008	–

ANOVA: analysis of variance; t31: central left-lower incisor; t32: lateral left-lower incisor; t33: left-lower canine; t34: first lower-left premolar; t35: second lower-left premolar; t36: first lower-left molar; t37: second lower-left molar.

Table 3.

Absolute error, RMSE and comparison between Willems BC and KB.

		n	M	SD		Med	p
Error
	Males and females
	Willems BC	1036	0.00	1.30		–0.00	–
	Willems KB	1036	0.00	1.31		–0.03	–
	Difference	1036	–0.00	0.39		0.02	0.7411
	Females
	Willems BC	522	0.04	1.35		0.02	–
	Willems KB	522	0.00	1.38		–0.06	–
	Difference	522	0.04	0.37		0.10	0.0228
	Males
	Willems BC	514	–0.04	1.24		–0.03	–
	Willems KB	514	0.00	1.24		–0.02	–
	Difference	514	–0.04	0.41		–0.08	0.0080
Absolute error (y)
	Males and females
	Willems BC	1036	0.97	0.86		0.76	–
	Willems KB	1036	0.98	0.87		0.75	–
	Difference	1036	–0.01	0.37		0.01	0.4209
	Females
	Willems BC	522	0.99	0.91		0.78	–
	Willems KB	522	1.03	0.93		0.78	–
	Difference	522	–0.04	0.35		–0.02	0.0704
	Males
	Willems BC	514	0.95	0.80		0.75	–
	Willems KB	514	0.94	0.81		0.72	–
	Difference	514	0.01	0.39		0.03	0.6612
RMSE			Willems BC			Willems KB
		N	RMSE		CI	RMSE	CI
	Males and females	1036	1.294		1.24;1.35	1.313	1.26;1.37
	Females	522	1.346		1.26;1.43	1.383	1.30;1.47
	Males	514	1.239		1.16;1.31	1.237	1.16;1.31

Note that results were reported for 1036 instead of 1038 subjects, since for two subjects, no age prediction was obtained in the leave-one-out cross-validation procedure (i.e. if the case in the test data set has a score which does not appear in the training data set).

Med: median; p=p-value from Wilcoxon signed rank test comparing absolute error Willems BC and absolute error Willems KB; RMSE: root-mean-square error.

Table 4.

Error and absolute error as a function of age and sex.

		Error			Absolute error
Sex	Age (years)	n	M	SD	n	M	SD
F	3–3.99	17	–0.83	1.17	17	0.96	1.06
	4–4.99	27	–0.44	0.80	27	0.62	0.67
	5–5.99	34	–0.15	0.90	34	0.63	0.66
	6–6.99	33	–0.27	0.82	33	0.69	0.51
	7–7.99	44	–0.40	1.52	44	1.06	1.15
	8–8.99	52	–0.22	1.22	52	0.80	0.93
	9–9.99	39	–0.08	1.48	39	1.01	1.07
	10–10.99	58	–0.23	1.25	58	1.00	0.77
	11–11.99	64	–0.10	1.28	64	1.05	0.74
	12–12.99	68	0.11	1.16	68	0.99	0.59
	13–13.99	41	0.50	0.99	41	0.82	0.74
	14–14.99	28	1.61	1.27	28	1.61	1.27
	15–15.99	14	1.80	0.54	14	1.80	0.54
	16–16.99	1	2.85		1	2.85
	17–17.99	3	4.39	1.70	3	4.39	1.70
M	3–3.99	9	–0.34	0.76	9	0.67	0.44
	4–4.99	37	–0.39	0.71	37	0.54	0.60
	5–5.99	41	0.06	0.62	41	0.51	0.34
	6–6.99	32	–0.40	1.12	32	0.91	0.74
	7–7.99	43	–0.53	1.02	43	0.89	0.72
	8–8.99	45	–0.39	1.04	45	0.83	0.73
	9–9.99	47	–0.27	1.01	47	0.82	0.64
	10–10.99	56	–0.17	1.50	56	1.14	0.98
	11–11.99	61	–0.28	1.16	61	0.96	0.70
	12–12.99	50	–0.09	1.35	50	1.10	0.77
	13–13.99	35	0.10	1.02	35	0.87	0.53
	14–14.99	27	1.25	1.38	27	1.30	1.33
	15–15.99	28	1.63	0.93	28	1.63	0.93
	16–16.99	4	1.97	0.37	4	1.97	0.37

Note that a negative error refers to overestimation of the age, while a positive error is interpreted as underestimation of the age.

The ME with Willems BC method was found to equal zero. Hence, we can conclude that there is no systematic under- or overestimation of the age. For males and females separately, the MEs are significantly different from zero but negligible in magnitude (–0.04 and 0.04, respectively). The MAE and RMSE between the Willems BC and KB methods were comparable (0.97 vs 0.98 (p=0.4209) and 1.29 vs 1.31, respectively). Although the Willems BC model resulted in a higher percentage of subjects with the predicted age within a one-year difference of the true age (63.3% vs 60.4%, p=0.018), this cannot be considered as clinically relevant. There were no important differences in calibration slope between both approaches (Table 5), although the calibration slope when using Willems KB was closer to 1, but also when using the Willems BC method the slope did not differ significantly from 1 within males and females separately.

Table 5.

Comparison calibration slope.

		Calibration slope	95% CI
Females	Willems KB	0.984	0.94;1.02
	Willems BC	0.973	0.93;1.01
Males	Willems KB	0.990	0.95;1.03
	Willems BC	0.971	0.94;1.01
Males and females	Willems KB	0.988	0.96;1.01
Males and females	Willems BC	0.972	0.95;1.00

Calibration slope: regression line of age regressed on predicted age; CI: confidence interval.

In both Willems BC and KB, there was a significant relation between age and the absolute error (r=0.274 vs r=0.247, p=0.13; Table 6), meaning that the older the subject the larger the discrepancy between true and predicted age but without significant difference between both approaches. The same is observed for the relation between the mean score and the absolute error (r=0.285 vs r=0.263, p=0.21).

Table 6.

Dependence of error and absolute error on age (Spearman correlations).

	Willems BC	Willems KB	p-value (comparison)
Correlation with age
Absolute error	0.274 (p<0.0001)	0.247 (p<0.0001)	0.1328
Error	0.315 (p<0.0001)	0.357 (p<0.0001)	<0.0001
Correlation with mean score
Absolute error	0.285 (p<0.0001)	0.263 (p<0.0001)	0.2078
Error	–0.052 (p=0.0965)	0.006 (p=0.8353)	<0.0001

In both approaches there was a significant relation (comparable in magnitude) between age and the error (significantly larger when using Willems BC (0.315) vs Willems KB (0.357; p<0.0001)) which is due to underestimation of the age of older subjects. This does not hold for the relation between the mean score and the error (–0.052 vs 0.006, p<0.001).

Discussion

The Willems BC method for dental age estimation has been validated in many geographical and ethnical populations, such as Bosnia-Herzegovina,¹⁶ Bangladesh,⁸ India,¹⁰ Brazil,¹¹ Japan,¹³ Arab Emirates¹⁴ and Malaysia,¹⁷ yielding consistent results. The validations provided overestimation of age between 0.10¹⁸ and 0.46¹⁷ years in females and between 0.05⁸ and 0.55¹⁷ years in males.

Due to these validation results, which greatly simplify the practical application, the Willems BC model is one of the most frequently used in forensic age estimation practice in children. The fact that this model is restricted to no missing scores and to subjects without all permanent teeth fully developed, instead of using age as a selection criterion, has been reported as a limitation. However, this actually ensures fair comparison, since in a practical setting age is not known.

Recently, the method was also validated in a SAB sample, where small but significant age overestimation was only found in females.¹² The results from the present study confirm that in another black (Kenyan) population, there is also no need to develop a country-specific dental age estimation model.

In the Kenyan sample, a very slight age overestimation is found between the ages of 8 and 12 (0.08–0.23 for F, 0.17–0.39 for M). The younger the individual, the higher the overestimation and vice versa, which is typical for age prediction using a regression model. From the age of 12 years, there is a slight underestimation that increases from 16 years and is more accentuated for females than males (Table 4). Despite results of particular age categories, no systematic under- or overestimation of the age was detected in the present study when using Willems BC on the Kenyan sample. Also, contrary to the findings in the SAB sample, Willems KB did not outperform Willems BC.

In our study, no linearity assumption has been made with respect to the Demirjian scores, and a weighted ANOVA has been used to handle the non-constant variance (higher variability of age at higher stages), as suggested in the original article of Willems et al.⁷ As such, this linear model is the same as an ANOVA model (using the scores as categorical predictors for age). Allowing non-linearity (by using the score as a categorical predictor in the regression model) increases the risk of overfitting. This phenomenon will be stronger the smaller the training data set. The difference between the prediction from Willems BC and the prediction from the model on the current dataset (Willems KB) not only reflects the usefulness of the Belgian population as reference, but also the difference in size of the current data set and the set of subjects used with Willems BC⁷ to develop the prediction model.

It has been reported that adding the information of third molars may result in a decrease of the RMSE, especially during the teenage years (i.e. in those 14–16 years old).¹¹ This can be explained by the fact that in this age range, most permanent teeth are already developed, yielding no extra information regarding dental age. Therefore, adding the third molar information is encouraged for a more accurate age prediction, taking into consideration that this age period shows the largest error and the teenage years may be especially relevant regarding legal issues in several countries, such as those mentioned in the introduction.

Conclusion

No reason was found to use a country-specific model for juveniles from Kenya (Willems KB) instead of using the Willems BC method. The ME with Willems BC method was zero. Hence, no important systematic under- or overestimation of the age was found for the Kenyan black sample. Even more importantly, the absolute error was not increased using the Willems BC method.

Footnotes

Acknowledgements

We would like to thank the participating centres: the School of Dental Sciences of the University of Nairobi, the Dental and Maxillofacial Imaging Centre (DAMIC), the Kenyatta National Hospital, Millennium Dental Services and JB dental clinic (Dr James Ngesa).

Declaration of conflicting interests

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

Funding

The authors received no financial support for the research, authorship and/or publication of this article.

ORCID iD

Maria Cadenas de Llano-Pérula

References

Willems

A review of the most commonly used dental age estimation techniques. J Forensic Odontostomatol 2001; 19: 9–17.

Tanner

JM.

Normal growth and techniques of growth assessment.

Clin Endocrinol Metab 1986; 15: 411–451.

Varshosaz

Ehsani

Nouri

, et al. Bone age estimation by cervical vertebral dimensions in lateral cephalometry. Prog Orthod 2012; 13: 126–131.

Garn

Lewis

Blizzard

RM.

Endocrine factors in dental development. J Dent Res 1965; 44: 243–258.

Demirjian

Goldstein

Tanner

JM.

A new system of dental age assessment. Hum Biol 1973; 45: 211–227.

Rai

The evaluation of two radiographic methods for age determination of children in an Indian population. J Forensic Odontostomatol 2008; 26: 30–33.

Willems

Van Olmen

Spiessens

, et al. Dental age estimation in Belgian children: Demirjian’s technique revisited. J Forensic Sci 2001; 46: 893–895.

Maber

Liversidge

Hector

MP.

Accuracy of age estimation of radiographic methods using developing teeth. Forensic Sci Int 2006; 159: S68–73.

Yusof

MYPM

Thevissen

Fieuws

, et al. Dental age estimation in Malay children based on all permanent teeth types. Int J Legal Med 2014; 128: 329–333.

10.

Grover

Marya

Avinash

, et al. Estimation of dental age and its comparison with chronological age: accuracy of two radiographic methods. Med Sci Law 2012; 52: 32–35.

11.

Franco

Thevissen

Fieuws

, et al. Applicability of Willems model for dental age estimations in Brazilian children. Forensic Sci Int 2013; 231: 401.e1–4.

12.

Willems

Lee

S-S

Uys

, et al. Age estimation based on Willems method versus new country-specific method in South African black children. Int J Legal Med 2018; 132: 599–607.

13.

Ramanan

Thevissen

Fleuws

, et al. Dental age estimation in Japanese individuals combining permanent teeth and third molars. J Forensic Odontostomatol 2012; 30: 34–39.

14.

Altalie

Thevissen

Fieuws

, et al. Optimal dental age estimation practice in United Arab Emirates’ children. J Forensic Sci 2014; 59: 383–385.

15.

Metsaniitty

Waltimo-Siren

Ranta

, et al. Dental age estimation in Somali children using the Willems et al. model. Int J Legal Med 2018; 132: 1779–1786.

16.

Galic

Vodanovic

Cameriere

, et al. Accuracy of Cameriere, Haavikko, and Willems radiographic methods on age estimation on Bosnian-Herzegovian children age groups 6–13. Int J Legal Med 2011; 125: 315–321.

17.

Mani

Mohsin

WSY

John

Prevalence and patterns of tooth agenesis among Malay children.

Southeast Asian J Trop Med Public Health 2014; 45: 490–498.

18.

Nik-Hussein

Kee

Gan

Validity of Demirjian and Willems methods for dental age estimation for Malaysian children aged 5–15 years old. Forensic Sci Int 2011; 204: 208.e1–6.

19.

Angelakopoulos

De Luca

Palacio

LAV

, et al. Age estimation by measuring open apices in teeth: a new formula for two samples of South African black and white children. Int J Legal Med 2019; 133: 1529–1536.

20.

Esan

Schepartz

LA.

The timing of permanent tooth development in a Black Southern African population using the Demirjian method. Int J Legal Med 2019; 133: 257–268.

21.

National Legislative Bodies of Kenya. Kenya: The Constitution of Kenya, https://www.refworld.org/docid/4c8508822.html (2010, accessed 24 March 2020).

22.

UNICEF. KENYA humanitarian situation report – 1 January to 30th June 2018, https://www.unicef.org/appeals/files/UNICEF_Kenya_Humanitarian_Situation_Report_Dec_2018.pdf