1
DENTAL AGE ESTIMATION (DAE): Data Management for Tooth Development
Stages including the Third Molars. Appropriate Censoring of the final S stage of
development – stage H.
Graham J Robertsa,*, Fraser McDonalda, Manoharan Andiappanb, Victoria S Lucasa
Department of Orthodontics, King’s College London Dental Institute, Floor 25, Tower
Wing, Guy’s Campus, London, SE1 9RT, UK
a
b
Biostatistics and Research Methods Centre, Division of Patient and Population Health,
Denmark Hill Campus, King’s College London Dental Institute, Denmark Hill,
London, SE5 9RW, UK
*Corresponding author. Tel: +44 01732 463636
Email addresses: email: [email protected], [email protected],
[email protected], [email protected]
tel +44 020 7188 4432
2
Graphic Abstract
3
Abstract
Introduction.
The final stage of dental development of third molar is usually helpful to indicate whether or
not a subject is aged over 18 years. A complexity is that the final stage of development is
unlimited in its upper border. Investigators usually select an inappropriate upper age limit or
censor point for this tooth development stage.
Materials and Methods
The literature was searched for appropriate data sets for dental age estimation and those that
provide the count (n), the mean (x), and the standard deviation (sd) for each of the tooth
development stages. The Demirjian G and Demirjian H were used for this study. Upper and
lower limits of the stage G and Stage H data were calculated limiting the data to plus or
minus three standard deviations from the mean. The upper border of Stage H was limited by
appropriate censoring at the maximum value for Stage G.
Results
The maximum age at attainment from published data, for stage H, ranged from 22.60 years to
34.50 years. These data were explored to demonstrate how censoring provides an estimate
for the correct maximum age for the final stage of Stage H as 21.63 years for UK Caucasians.
Conclusion
This study shows that confining the data array of individual tooth developments stages to
± 3sd provides a reliable and logical way of censoring the data for tooth developments stages
with a Normal distribution of data. For stage H this is inappropriate as it is unbounded in its
upper limit. The use of a censored data array for stage H using Percentile values is
appropriate. This increases the reliability of using third molar stage H alone to determine
whether or not an individual is over 18 years old. For Stage H, individual ancestral groups
should be censored using the same technique.
1. Introduction
The concept of Dental Age Estimation (DAE) is not new. The assessment of tooth
eruption as a method of estimating age was introduced in the 19th Century1 and is still
occasionally used as a guide to a child's age. The availability of radiographs has enabled
visualization of the mineralization of developing teeth which are then classified into
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identifiable stages from which dental maturity can be determined2. The close link between
dental maturity and chronological age (CA) justifies the use of dental age (DA) as a surrogate
for Chronological Age3. At the 10 year threshold, DA is accurate to within 3 weeks of CA4.
Despite several publications relating to the 18 year threshold, there is little known about the
reliability of estimates made at or near this age5,6,7. A systematic and highly informative
attempt has been made to identify and explore these difficulties in the series of papers from
the University of Leuven8.
The most common way to determine whether or not a subject is over 18 years is to calculate
the probability => 18.00 using the mean () and the standard deviation (sd) of the data array
for the final stage of tooth development. A typical outcome using this approach is that a
subject exhibiting stage H is 0.92 (92%) probability to be over 18 years9. The underlying
assumption is that the data for Stage H is Normally distributed. It has been suggested that an
approach using percentile data would, on theoretical grounds, lead to a conclusion more in
line with the distribution of the data10. The research team in Germany use both Normal
distribution data and some percentile data to display the results for stages of third molar
development11. The Swiss-German research team proposed that because subjects exhibiting
stage H may be below 18 years of age, it is inapproprite to use the presence of stage H alone
as an indication that the subject is over 18 years old12.
An important requirement of statistical analysis is that the data used are effectively
managed13. This is to ensure that inappropriate values are not included in the data array. This
might be because of a grossly incorrect result such as an age value when the data of birth and
data of assessment are reversed, and incorrect assessments that give unjustifiable outliers.
These problems are managed by so-called ‘cleaning’ of the data by visual inspection when
checking the data14.
Common practice in statistics is to use only the central 95% of the data array, the so called
95% Confidence Interval (CI)15. It is common to use this 95% confidence interval,
sometimes called the reference range, as the data array for a given variable to enable
clinicians to determine what is normal and non-normal. With regards to DAE, lawyers
question the appropriateness of this as it excludes 5% of the data or the equivalent of 1 of 20
subjects.
5
Given this concern the research presented here is aimed at encompassing as much of the data
as possible by using plus or minus three standard deviations ( ± 3sd ) as this incorporates
99.9974% of the sample data, and by inference a similar percentage of the population. This
is regarded as an age range for subjects of unknown age whose future will depend upon a fair
and robust assessment of the likelihood of being within or without this stated age range.
A further problem is that of Stage H, the final stage of development which is unbounded in its
upper limit. This raises the issue as to how different investigators have set the upper age limit
for the samples investigated. Publications range from 21 years16, 22 years17, 23 years18, 24
years19, 26 years20, 26.9 years22, and 33.9 years23.
Clearly this wide range of age limits for the upper boundary of subjects in studies on DAE,
spanning almost 13 years, raises the question as to what should be the upper boundary for
Stage H of third molars and how this boundary is identified.
Perusal of the literature reveals that investigators do not indicate how the data management
has been carried out to ensure that there are robust data sets using the 8 stage system2 for each
of the 250 plus data arrays for each Tooth Development Stage (TDS).
A further problem is that it is dificult to compare published data sets as the number of Tooth
Development Stages (TDS) used for assessment of dental development varies from 4
stages24, to 21 stages25. (Mahtab M. personal communication). The most frequently used
number of Tooth Development Stages used to estimate Age at Attainment (AaA) of each
stage is the 8 stages described by the Anglo-Canadian research team2. Because of it
widespread use, the 8 stage system of TDS has been selected for this review. It is important
to be aware that the present paper utilises only the anatomical descriptions of the 8 tooth
development stages but does not include the system of mathematical integration to estimate
dental maturity and from that dental age2. In addition the 1973 system of dental age
assessment was limited to teeth in the mandible and excluded third molars. This limitation
was superseded when an American research team applied the 8 stage system to a study of the
development of all four third molars5. This forms the basis for the system of age estimation
at the 18 year threshold currently in use in the United States of America26, and also by many
investigators in Europe including the DARLInG team at King’s College London. The Tooth
Development Stages defined in 1973 are referred to by the letters A, B, C, D, E, F, G, and H.
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Detailed descriptions of each stage are available in the original publication2 and more
recently in a paper at the 16 year threshold27.
The presentation of data follows two formats:
1. Normal distribution summary data
2. Percentile data.
This final stage of tooth development is unbounded in its upper age limit. With regard to third
molars this means that an enquiry about estimating age using a radiograph showing a fully
developed root of a lower left third molar from a male Caucasian who is aged 25 years would
return the same age and probability estimate as an enquiry from someone aged 15 years.
The difficulty with the lack of a natural upper limit to the data array for the AaA of Stage H
is usually overcome by not using stage H for age estimation in children who are still
developing28. This exclusion of stage H is not possibe when estimating age at the 18 year
threshold as the third molar stage H is the principle dental biological marker that can be used
for age prediction for late adolescence and emerging adults. This was the genesis of the
seminal paper on third molars published by the research team in the USA5. In reviewing the
articles on this problem, it is clear that almost all the papers published do not indicate in
sufficient detail the approach used for the curtailment of the upper limit of the AaA for Stage
H. The problem has been touched upon in a paper from South Korea where the authors used
different age ranges to estimate the mean value of stage H29. For example, focusing on the
Lower Left Third Molar Stage H for males, the AaA for the LL8Hm is 21.6 years for the 14
to 24 year band, 22.1 years for the 14 to 25 year age band, and 22.5 years for the 12 to 26
year year age band29. This raises the issue of the amount by which the AaA for stage H is
inflated by using an upper age cut-off or censor point of 26 years when compared to 21 years.
This problem has been explored and led to the concept of ‘appropriate censoring’30. It is
clear from published papers that the issue of censoring the data for the final stage of tooth
development has been ignored or overlooked by the majority of investigators in the field of
DAE.
A further problem is the way in which the uncertaintly uncertainty of the point estimate is
provided. It is conventional to use the 95% confidence interval. The problem with this is
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that it excludes 1 in 20 subjects, a figure that is not acceptable to lawyers. The use of a 100%
confidence interval expressed as a reference range has much to commend it as it places any
estimates of age beyond any reasoanble reasonable doubt. This is important for criminal
procedures but for civil procedures it is necessary only to proivde provide the central 50% of
the data31. This is usually presented as the Interquartile Width (IQW) (Alltman 1991)32.
The purpose of this paper is threefold:
1. To review data management procedures to determine the suitability of a ± 3sd
constraint to the lower and upper limits of the data array for each AaA for all the
tooth development stages.
2. To describe a simple system of censoring to provide a realistic age to the upper
boundary for stage H.
3. To review extant data sets where the 8 stage system of Demirjian2 has been used to
assess the impact of inappropriate censoring of Stage H on the estimation of the lower
and upper limits of AaA for the Lower Left Third Molar (encompassing 100% of the
data array), the estimation of the middle 50% i.e. the Inter Quartile Range, and the
implications of this for DAE at the 18 year threshold.
Materials and Methods
The data for this study are from previous publications thus ethical approaval is not required.
Ethical approval for the previous studies was obtained from the King’s College Hospital NHS
Trust Research and Devlopment Committee – Reference 06DS03, and The Eastman Dental
Hospital – Reference 03/E02.
The dental, medical and forensic literature was searched using both electronic databases and
handsearching of a publications derived form the electronic search.
Timespan of search
The search was limited to the period January 1973 to December 2014.
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Inclusion Criteria
The papers included required that the TDS described by the Anglo-Canadian team was
used2. In addition, the results section provided the count (n-tds), arithmetic mean (-tds) and
the standard deviation (sd-tds).
The subjects providing the data were aged between 4 years and 26 years.
Exclusion Criteria
Publications that did not report the arithmetic mean, and the standard deviation for each AaA.
Electronic Searches
These comprised PubMed, EMBASE, and the Cochrane Collaboration using the terms
‘Demirjian’, Tooth Development Stages’, ‘Tooth Development’, ‘Dental Maturity’.
Hand Searches
Subsequent to this the reference lists in all the articles identified by the electronic searches
were used to identify further articles.
Reference Data Set used for comparison
The Dental Age Research London Information Group (DARLInG) Reference Data Set33 was
used to provide the full data for The Lower Left Third Molar Stage G for males (LL8Gm)
and also the uncensored and censored data for Stage H for males LL8Hm.
Censoring and the Normal distribution
The censoring process for stages A through to G for the DARLInG data was carried out by
identifying the lower limit of the data as minus three standard deviations and the upper limit
as plus three standard deviations (± 3sd). This was achieved by exporting the data from the
DARLInG Access database into Microsoft Excel. Pivot tables were used to isolate individual
data sets e.g. LL8Gm. Following this a simple count of all the data arrays that were within
± 3sd was made and the outcome expressed as a percentage of TDS that fell within the ± 3sd
range for each of the data arrays in the whole dentition.
9
The results presented are those only for stages G and H of the Lower Left Third Molar
(Figure 1) . This is to ensure clarity in presenting and interpreting the findings relating to
Censoring of data.
Censoring of Stage H
The distribution of data for the uncensored stage H was assessed and a proability probability
function plot created in additon to a Stacked (percentage) Bar Graph (see graphic abstract).
The censoring process for Stage H of third molars in the DARLInG datasets was achieved by
first curtailing the upper limit of Stage Data at the age when 100% of subjects in the
DARLInG data set first exhibited Stage H. This is defined as the age immediately above the
oldest subject with stage G30. The data remaining after this censoring of the upper limit of
stage H was then subjected to further scrutiny using the ± 3sd procedure described above.
The resulting data array, limited by ± 3sd was then used to produce the full array of Normal
distribution summary data and percentile data (see DARLInG RDS).
The data were then used to graph a Probability Distribution Histogram on to which is
superimposed a Normal curve (STATA issue 13.0)31. Presentation of the probability
distribution histograms were limited to the LL8Gm censored by ± 3sd and the LL8Hm
uncensored, and censored by the maximum age of LL8Gm (21.64 years). This is for the
purposes of clarity. The appearance and definitions of these two stages are shown (Figure 1.)
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Figure 1.
Stage G:
a. The calcified region of the bifurcation has
developed further down from its semilunar
stage to give the roots a more definite and
distinct outline.
b. The apical end of the root canal is still
partially open (distal root of molars).
Stage H:
a. The apical end of the root canal is
completely closed (distal root of
molars).
b.
The periodontal membrane has a
uniform width around the root apex.
The summary data from publications that provided information on stage H only of lower left
third molars were then used to calculate percentile summary data and Normal distribution
equivalent viz Table 1.
Table 1.
Percentile data
Normal distribution data
minimum
≈ -3 sd
1st quartile
≈ 0.25 cumulative probability
median
≈ mean
3rd quartile
≈ 0.75 cumulative probability
maximum
≈ +3sd
Table 1. Percentile summary point estimates and Normal distribution summary equivalents.
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These data were used to provide population estimates of for the 100% Confidence Interval
(the whole data array), the 50% Confidence Interval (The Interquartile Width [IQW])32 and
the Probability of a Subject with Stage H being under or over 18 years old using the data
from published papers and the DARLInG RDS33. The Percentile equivalent was also
estimated using the PERCENTRANK.INC Function in Microsft Excel34.
Results
The probability distribution histograms for LL8Gm is shown in Figure 2. This is offered as
it is typical of the Normal distribution for all the TDS other than stage H.
Place Figure 2 approximately here.
Figure 2. Probability Distribution Histogram of
the Lower Left Third Molar Stage G- male. This
shows the mean, standard deviation, and the
lower and upper limits defined by ± 3sd.
Figure 2. Probability Distribution Histogram of the Lower Left Third Molar Stage G – male.
This shows the mean (𝑥̅ ), standard deviation (sd), and lower and upper limits defined by
± 3sd.
Of the 256 Tooth Deveolopment Stages present in the UK Caucasian Reference Data Set, 32
were not assessed as there were no data available (due to extreme youth) and a further 32
were not included as these were Stage H which had not been censored. This left 192 TDS of
developing teeth. Of these, 186 (96.88%) gave a data array within the ± 3sd lower and upper
limits. The remaining 6 (3.13%) gave a data array only a small amount outside the ± 3sd
limits.
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The data array for Stage H was censored using the maximum age for Stage G. This is the
point in a cross sectional sample (as should be all DAE Reference Data Sets), where all the
third molars present in the sample first exhibit Stage H. The distribution of this uncensored
data is non-normal and is slightly skewed to the left as is shown in Figure 3. This is owing
to the lack of depletion of Stage H numbers because each tooth, as the subject gets older,
does not move on to a further stage. Thus the upper part of the data array becomes stacked
with fully mature third molars at Stage H. In the uncensored Stage H there are AaA values
up to the age limit of the sample which is 26 years. This shows that in the DARLInG
Reference Data Set (RDS) there are considerable numbers of completed Stage H cases, (n-tds
= 161) inappropriately occuping the upper regions of the array of data (Figure 3).
The data for stage H censored at the maximum of stage G, 21.64 years, shows a much
narrower age range of data for the probability distribution histogram (Figure 4).
It is clear that these two distributions are markedly different with the LL8Hm (uncensored)
plot being very top heavy in the upper age bracket. A feature of this top heavy data is that the
upper border of the LL8Hm dataset is 26.88 years with a mean of 22.04 years. For the
censored stage H (Figure 4) the data is still top heavy. A Shapiro Wilk test for Normality
shows a non-Normal distribution for both the uncensored (p < 0.00030) and also the censored
stage H data (p < 0.00274 ). The histogram and Shapiro Wilk’s test showed a normal
distribution (p = 0.21) for LL8Gm.
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Lower Left Third Molars Stage H - male
15
Uncensored data
Mean = 22..68 years
Median = 23.46 years
Figure 3. The probability distribution histogram
for LL8Hm [The Lower Left Third Molar Stage H,
10
male] Uncensored.
The mean value for this uncensored stage H is
22.68 years. the Shapiro Wilk test confirms that
5
this is non-Normal with a p value of 0.0003
0
[highly significantly different from Normal].
15
20
25
LL8Hm - uncensored (Years)
30
Lower Left Third Molars Stage H - male
Figure 4. The probability distribution histogram
15
Censored data
Mean = 19.73 years
Median = 20.17 years
for LL8Hm [The Lower Left Third Molar Stage H,
male] Censored at the maximum value of Stage G
10
= 21.64 years. The mean value for this censored
stage H is 19.73 years. the Shapiro Wilk test
confirms that this is non-Normal with a p value of
0
5
0.0027 [significantly different from Normal]
15
20
25
LL8Hm - censored (Years)
30
To illustrate the effect of censoring, the data for LL8Hm was progressively censored by 1
year decrements by reducing the Upper Age (Table 2. a to g).
Table 2.
Row
Upper Age
n- tds
sd-tds
Boundary
(Count)
(Years)
Minimum CPV = 0.25
(Years)
(Years)
Mean CPV = 0.75 Maximum
First
̅- tds)
(𝒙
Third
Quartile
(Years)
Quartile
(Years)
(Years)
(Years)
a
Uncensored
159
2.79
15.47
20.81
22.68
24.57
26.88
b
24.99
138
2.48
15.47
19.89
21.57
23.24
24.89
c
23.99
108
2.19
15.47
19.28
20.76
22.24
23.93
d
22.99
89
1.95
15.47
18.86
20.17
21.48
22.95
e
21.99
72
1.76
15.47
18.42
19.61
20.79
21.96
f
Censored 21.64
65
1.71
15.47
18.58
19.73
20.89
21.63
g
20.99
53
1.53
15.47
17.89
18.92
19.95
20.98
CPV = Cumulative Probability Value;
tds = tooth development stage
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Table 2. This shows the Uncensored stage H data (row a) and the Censored Stage H data
(row f). The reduction (difference) in the mean value is 2.95 years. Rows b to e inclusive
show the descending mean value with the 1 year decrements to the censor point. The
0.25CPV and the 0.75 CPV are the Normal distribution equivalents to the 25th%-ile and the
75th%-ile. The mean is similar in value to the Median which is the 50th%-ile.
Row g shows the effect of over-censoring with a mean value too low at 18.92 years.
To explore these issues on the population estimates the data extracted from the 21 research
reports that contained the relevant information was used to estimate the values shown in
Table 3.
Put the Excel Table here.
Table 3. Calculated and extracted values for - 3sd, 0.25 Cumulative Probability Value (CPV),
the mean (𝑥̅ ), 0.75 cumulative Probability Value, + 3sd, the range, and the Inter Quartile
width. The 0.25 CPV and 0.75 CPV are included to approximate the 25th and 75th
percentiles. All the reports used provided the data for ancestry, gender, mean and standard
deviation. [Table 3 is an Attached Excel File]
The research reports that provided percentile data were used to enable a comparison with the
summary data values derived using Normal distribution statistics (Table 3). In addition for
the DARLInG data sets available, the PERCENTRANK.INC function of Microsoft Excel34
was used to estimate the probability that a subject would be >18 years. This was performed
only for the subjects for whom the full data array was available35,36, 33, 37 -39.
The data reveal large differences for both the Range (Highest minus Lowest) and the
Interquartile Width (25th%-ile to 75th%ile) (Table 3). [Table 3 is an Attached Excel File]
Discussion
The data extracted from the DARLIng RDS show that the data for the AaA for Stages A to G
are Normally distributed33. The example used for this PAPER is the LL8Gm (Figures 1 and
2). The use of ± 3sd to embrace the lower and upper limits was successful as over 96% of the
resulting data arrays were within the limits determined in this way. Although not published
here the remaining data arrays were all very close to being within these limits. This is
important as the results for the minimum and maximum derived in this way, representing
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99.9973% of the data, were subsequently regarded as the 100% Confidence Interval for the
data array for a single TDS. This is particularly important for the third molar as the final stage
of development, stage H, is used to determine whether a subject is below or above the 18 year
threshold. This 100% CI is closely related to the concept of Reference Intervals32.. It
represents the range of data that encompasses all values within this range and are considered
to be normal. (For a detailed exposition of this concept see Altman 1991 Chapter 14).
It is proposed that for future publications the data management procedures for TDS are
explained by authors in sufficient detail to enable readers to assess the ‘fitness for purpose’ of
such an approach. Within the UK Caucasian RDS33 there were 192 data arrays for the TDS
present representing all the Tooth Morphology Types in the human dentition. The remaining
arrays, taking the total number up to 258, are for Stage H for which the ± 3sd approach is
inappropriate.
The use of ± 3sd satisfies the requirements of lawyers not to exclude 5% of the data (1 in 20).
The additional finding in this paper are the large differences in the data for stage H when
looking at the range of data. Values for the range as high as 15.72 years and 13.26 years
(Table 3) respectively for females and males raise concerns as to the appropriateness of the
data leading to these large and biologically untenable differences. It is clear that these
extreme values are in part the consequence of using the Minimum and Maximum values (±
3sd). In the context of DAE this broader CI is appropriate as it provides clients with a broad
and justifiable range within which age estimation may be provided with only a very small
risk of error at either end of the distribution (0.0013 [0.13%]) or approximately less than 1 in
1000.
Censoring of stage H is an important problem in relation to determining child or adult status
for asylum seekers. Asylum seekers who are assessed as children have the right to stay in the
UK with the associated benefits of domestic care, education, and financial support.
The first approach was to follow the procedure first reported in the UK30. In this study it was
considered that once the whole sample of subjects in the RDS had achieved the status of
Stage H then any further (older) subjects were contributing to the data array inappropriately
and inflating the mean and median value. The identification of this age or censor point is the
oldest age for Stage G. For the UK Reference Data Set, it is 21.64 years. This is clearly
shown in Figures 3 and 4 where the mean value for the uncensored data is 22.68 years and
the mean value for the censored data is 19.73 years, a difference of 2.95 years. This is clearly
16
a difference which has an impact on estimates of the probability that a subject is over 18
years using current methodology26. These probability estimates for the 18 year threshold are
0.9533 [95.33%] for the uncensored value and 0.9512 [95.12%] for the censored values
respectively. This is a very small difference and is probably the result of the heavily skewed
data for stage H for both the uncensored and censored data.
The difficulty with this approach is that the calculation of the probability values are
dependent on the data array for Stage H being Normally distributed. As is shown in Figures
3 and 4 it is clear that this is not the case. For this reason it is necessary to use the Percentile
Summary Data. There is no simple calculation that indicates that the probability of a subject
being over 18. Instead, the investigator has to use the PERCENTRRANK.INC function in
Excel34 to identify the value in the data array that is closest to the 18 year threshold. For the
LL8Hm this is estimated as p = 0.7593 [75.93%] that the subject is older than 18 years or p =
0.2407 [24.07%] that the subject is under 18 years old. Because access to the original data
array is required this is more taxing than using the NORM.DIST function of Excel which
requires only the summary data. On logical grounds it gives a result consistent with the nonNormal distribution of Stage H.
In this study the abstracted data presented in this paper show a very wide span for the time
over which Stage H extends in the Lower Left Third Molar in the 1st nations people of
Canada. The main purpose of this paper is to establish how this has come about. In the data
extracted and calculated for females it extends from 14.43 years to 32.97 years, a spread of
18.54 years47. This is over three times the spread when compared to similar estimates for the
UK Caucasian RDS33 for which females extends from 16.50 years to 24.90 years, an interval
of 8.4 years.
To understand the implications of this, it is helpful to appreciate that the UK Caucasian RDS
is systematically redacted to remove unsuitable data that may inappropriately influence the
outcome summary data. This was achieved by first ensuring that any negative values arising
from mistaken data entry are corrected. Second, extreme values that are likely to be
untenable in terms of clinical growth and development are also excluded. The most efficient
way to do this is to limit the data set to ‘plus or minus’ three standard deviations from the
mean value for each of the TDSs present in the data set. As can be seen (Figure 2), the
Normal distribution is clearly discernible from the ± 3sd censored data for LL8Gm is a
17
considerable contrast with the uncensored data for LL8Hm (Figure 3) which is severely left
skewed. The reason for this is that the data in the upper region of the data set are from
mature subjects where root maturity was completed some months or even years previously.
Appropriate censoring of LL8Hm eliminates the redundant data but the distribution remains
non-Normal (Figure 4).
The identification of the end point i.e. when all third molars have become mature is
straightforward. The age at which Stage G ceases to be present is the age when Stage H is
present in 100% of the population is determined by the oldest age at which stage G is present.
This is represented by the 99.7th % Cumulative Probability Value (CPV) for Stage G in the
worksheet of summary data (Table 3).
This issue of utilizing data from the 0.05th to 99.5th CPV is potentially difficult. As explained
earlier, the data are censored at these two extremes to incorporate the information from TDS
that are developing normally. The use of CPV expands the range of the data to the population
estimates usually cover a noticeably wider range of ages than the sample data expressed in
percentiles. In this sense the CPV values are a more reliable estimate than the percentiles for
the data span in the population. However, clinically, in normal patients, such extreme values
have not been observed by any of the authors in a combined ‘lifework’ of 112 years.
It is recommended by the DARLInG team that the population estimates used are based on the
mid 50% of data spread around the mean value as 0.25 CPV to 0.75 CPV as this is usually
broader than the interquartile width that is based on percentile data (25th %-ile to the 75th %ile). Further work is in progress to identify the appropriate range of values from which a
DAE is made by carrying out estimates of masked radiographs for whom the CA is known,
but not the assessors.
The censoring of data within the ± 3sd is sometimes criticized ‘… as it excludes potentially
important data … ’32. This is certainly a consideration as outliers will be discarded. In
clinical dental practice such outliers are regarded as ‘abnormal’. Therefore the decision to
exclude such extreme values is justified. Furthermore, as regards the RDS of UK Caucasians,
it is clear that for almost every data set, LL8Gf, LL8Gm etc. numbering up to 258 data sets is
within the upper and lower limits set by the ± 3sd33. That is to say the upper and lower limits
set by this calculation are, respectively lower and higher than the values retrieved from the
18
DARLInG data set. Thus the calculated limits of ± 3sd are more extreme than the minimum
and maximum values obtained in the DARLInG UK Caucasian Dataset. The concern about
excluding high or low values is a theoretical rather than a practical issue.
A remaining concern is the confusion often apparent between the burden of proof for criminal
cases and civil cases in the law courts. For criminal cases the legal dictum is ‘beyond
reasonable doubt’. In terms of probability this of the order of 0.92 (92%) certainty48. For
civil cases the burden of proof is greater than 50%. This is described as ‘the balance of
probability in the UK, and ‘the preponderance of the evidence’ in the USA50. This concept
needs to be considered within the framework of legal proceedings51.
It is to provide information on these different levels of proof between Criminal proceedings
and civil proceedings. An interesting corollary to this is that subjects accused of a serious
crime are subject to the ‘beyond reasonable doubt’ dictum, but if, subsequent to conviction
are claiming to be under 18 years of age, subject to the ‘balance of probability’ threshold
when the court determines if the convicted subject should be detained under the adult penal
system or the ‘youth court’ penal system. This is an example of criminal justice and civil
justice combining to ensure just and fair treatment of the convict subject.
A comment on other final stage systems and their utility is tempting but outside the scope of
this paper as these used systems of tooth development using 10, 12, or even 15 stages52
although a cursory examination of these papers reveals similar problems with censoring the
final stage of development of the third permanent molars.
It is also clear that the distribution of data for AaA for Stage H is not Normally distributed.
This is because the usual growth change of the data is that a tooth will transfer, for example,
from stage F to Stage G thus there is a natural ‘entry’ and ‘exit’ pattern which results in a
Normal distribution (Figure 2). However, even where the AaA data for LL8Hm censored is
plotted, the resulting graph still appears top heavy over the upper fifty percent (Figure 4).
This is because in normal circumstances the numbers in the upper half of the population
distribution reduce as the tooth transforms into the next dental stage. The consequence of this
is the increased number of Stage H in the upper part of the plot.
19
The main finding from this review is that the age span for Stage H is, for many papers, too
large to be realistic. This is because of a failure by investigators to scrutinize the AaA values
close to the upper boundary of Stage H. Failure to do this has resulted in inappropriate
censoring of the data. The consequence of this is that the mean age at attainment for Stage H
is usually too large. The implications of this are that subjects at the 18 year threshold are
assigned an age that is too high and therefore possibly unfair to the subject. This injustice
translates into a probability value that is too high. The details of this are in a paper currently
in preparation (Lucas VS personal communication)
The recommendations on using summary data based on percentiles is not new, this has been
used extensively by the team in Germany for stage H11, 47. However, no detail of the
implications of using the extreme values (Minimum and Maximum) has previously been
discussed. In the present review it is discussed in detail in relation to the Normal distribution
summary data and the Percentile summary data.
Finally, this raises the issue of the numerical status of estimates of the median (and mean) of
Stage H. An average value provided with 100% CI (for criminal cases) or 50% CI (for civil
cases) rests on an estimate for a single tooth in a single individual only. This is because a
subject with an estimated age of 19.64 years and with a 50% confidence interval from17.94
years to 20.67 years indicates that the individual subject falls within these values or could be
higher. This ambiguity means that once estimated these values are not proper numbers in the
sense that they can be added together to provide an averaged age for developing third molars.
Further work is in progress to test the reliability of age estimations using the lower third
molar in a blind study of assessments, and the impact of other age markers related to third
molars, is in progress.
Conclusions
1. The summary data for Tooth Development stages should be clearly limited by an
appropriate statistical method viz. ±3sd.
2. For the final stage of tooth development the use of ±3sd is inappropriate as the data
for this final stage of dental development does not display a Normal distribution.
3. The appropriate censoring of Stage for Lower Third Molars brings down the
estimated mean or median age to below 20 years.
20
4. The way in which data for the AaA for Stage H of third molars needs to be managed
in such a way that the interests of justice and the needs of asylum seekers are met
appropriately and equitably need to be reviewed and restated to take proper account of
appropriately censored data for the final stage of dental development.
Acknowledgements
We are grateful to Dr Eric Whaites, Clinical Director of the Dental Hospital, for granting
access to the dental radiological archive at Guy’s and St Thomas’ NHS Trust.
This article is based on a paper presented to the American Academy of Forensic Science at a
meeting held in Orlando, Florida, USA in February 2015.
References
1.
Saunders E. The teeth a test of age, considered with reference to the factory children:
Addressed to both Houses of Parliament, Westminster, London UK. 1837. London: H.
Renshaw.
2.
Demirjian A, Goldstein H, Tanner JM. A New System of Dental Age Assessment. Hum
Biol. 1973; 45(2): 211-27.
3.
Gustafson G. Age determination on teeth. J Amer Dent Ass. 1950; 41: 45-54.
4.
Roberts GJ, McDonald F, Lucas VS, Neill M. The weighted average method 'WAM' for
Dental Age Estimation: a simpler method for children at the 10 year threshold. J Forensic
Leg Med. 2014; 26: 56-60.
5.
Mincer HH, Harris EF, Berryman HE. The ABFO study of third molar development and
its use as an estimator of chronological age. J Forensic Sci. 1993; 38(2):379-90.
21
6.
Garamendi PM, Landa MJ, Ballasteros J, Solano MA. Reliability of methods applied to
assess age minority in living subjects around 18 years old. A survey on a Moroccan
origin population. Forensic Sci Int. 2005: 154: 3-12.
7.
Blankenship JA, Mincer HM, Anderson KM, Woods MA, Burton EL. Third molar
development in the estimation of chronological age in American Blacks as compared
with Whites. J Forensic Sci. 2007; 52(2): 428-33. doi 10.1111/j.1556-4029.2006.00356.x
8.
Thevissen P. 2013. Dental Age Estimation in Sub-Adults: striving for an optimal
approach. Acta Biomedica Lovaniensia 605. Leuven University Press.
ISBN 978 94 6165 087 0.
9.
Lewis JM, Senn DR. Dental Age Estimation. In – Manuel of Forensic Odontology.
American Society of Forensic Odontology. 2013. Chapter 8. New York. ISBN 978-14398-5133-3.
10.
Roberts GJ & Petrie A. Dental Age Assessment: A Practical Approach. 2011.
Chapter 11 in Digital Forensic Science. IGI Global USA. ISBN 978-1-60960-483-7.
11.
Olze A, Schmeling A, Taniguchi M, Maeda H, Niekerk P van, Wernecke KD,
Geserick G. Forensic age estimation in living subjects: the ethnic factor in wisdom
tooth mineralization. Int J Leg Med. 2004; 118: 170-3.
12.
Knell B, Ruhstaller P, Prieels F, Schmeling A. Dental age diagnostics by means of
radiographical evaluation of the growth stages of lower wisdom teeth.
Int J Leg Med. 2009; 123: 465-69.
13.
O'Brien PMS, Broughton Pipkin F. Introduction to research methodology.
2nd Edition 2007. Royal College of Obstetricians and Gynaecologists Press.
London. ISBN 978-1-904752-01-1.
14.
Gore SM & Altman DG. Statistics in Practice. 1982. British Medical Association.
London. ISBN 0 7279 0085 4
22
15.
Kirkwood BR, Sterne JAC. Essential Medical Statistics. 1988. Blackwell Publishing.
Oxford. ISBN 0-86542-871-9.
16.
Prieto JL, Barberia E, Ortega R, Magana C. Evaluation of chronological age based
on third molar development in the Spanish population.
Int J Leg Med. 2005; 119(6):349-54.
17.
Thevissen PW, Fieuws S, Willems G, et al. Human dental age estimation using third
molar developmental stages: accuracy of age predictions not using country specific
information. Forensic Sci Int. 2010; 201: 106-11.
18.
Altalie S, Thevissen P, Fieuws S, Willems G. Optimal age estimation practice in
United Arab Emirates children. J Forensic Sci. 2014; 59(2): 383-85.
19.
Thevissen PW, Fieuws S, Willems G. Third molar development: measurements versus
scores as age predictor. Arch Oral Biol. 2011; 56: 1035-40.
20.
Zandi M, Shokri A, Malekzadeh H, Amini P, Shafiey P. Evaluation of third molar
development and its relation to chronological age: a panoramic radiographic study
J Maxillofac Oral Surg. 2014. November 21. Epub. PMID 25409631.
22. Zeng DL, Wu ZL, Cui MY. Chronological age estimation of third molar mineralization
on Han in southern China. Int J Leg Med. 2010; 124(2): 119-23.
23.
Thevissen PW, Fieuws S, Willems G. Third molar development: evaluation of nine
tooth development registration techniques for age estimations.
J Forensic Sci. 2013; 58(2): 393-7.
24.
Gustafson G, Koch G. Age estimation up to 16 years of age based on dental
development. Proc Finn Dent Soc. 1974; 25: 297-306.
25.
Mahtab M 2011 – Personal communication
26.
Senn DR, Weems RA. 2013. Manual of Forensic Odontology. 5th Edition. CRC
23
United States of America. ISBN 978-1-4398-5133-3.
27.
Mitchell JC, Roberts GJ, Donaldson ANA, Lucas VS. Dental age assessment (DAA)
for British Caucasians at the 16 year threshold. Forensic Sci Int 2009; 189: 19 – 23.
28.
Moze K, Roberts GJ. Dental Age Assessment (DAA ) of Afro-Trinidadian children and
adolescents. Development of a reference data set and comparison with Caucasians
resident in London UK. J Forensic Leg Med. 2012; 19: 272-79.
29.
Lee SS, Byun YS, Park MJ, Choi JH, Yoon CL, Shin KJ. The chronology of second
and third molar development in Koreans and its application to forensic age estimation.
Int J Leg Med 2010; 124:659-65.
30.
Boonpitaksathit T, Hunt N, Roberts GJ, Petrie A, Lucas VS. 2011 Dental age
assessment of adolescents and emerging adults in UK Caucasians using censored data
for stage H of third molar roots. Eur J of Orthod. 2010; 33(5): 503 –8.
31.
STATA Statistical Software. Issue 13.0 www.stata.com Texas. USA.
32.
Liversidge HM, Marsden PH. Estimating age and likelihood of having attained 18
years of age using mandibular third molars. Br Dent J. 2010; 209: E13.
32.
Altman D. Practical statistics for medical research. 1st edn. London: Chapman & Hall,
1991. p51 et seq.
33.
DARLInG Reference Data Set www.dentalage.co.uk/+R/RDS-UK-Caucasian
34.
Jelen B. Microsoft Excel 2013. QUE Publishing. USA. ISBN 978-0-78974857-7.
35.
Alsaffar H, Camilleri S. Dental Age Assessment of Maltese subjects between the ages
of 4 and 14 years. MSc Dissertation. University of Malta and King’s College
London 2013.
24
36.
El-Shewahi W, Camilleri S. Dental Age Assessment of Maltese subjects between the
ages of 15 and 26 years. MSc Dissertation. University of Malta and King’s College
London 2013.
37.
Jayaraman J. Development and Validation of Reference Dataset for Dental Age
Assessment in a Southern Chinese Population. PhD Thesis. 2014 University
of Hong Kong.
38.
Karimi A. Development of a Reference Data Set for Kuwaiti children, adolescents and
emerging adults agage assessment ed 3 – 26 years MSc dissertation 2015. King’s
College London.
39.
Oiknine S. Dental age assessment (DAA): development of a Reference Data set for
Israeli children between 3 and 26 years old. MSc dissertation. 2013.
King’s College London.
40.
Prieto JL, Barberia E, Ortega R, Magana C. Evaluation of chronological age based on
third molar development in the Spanish population.
Int J Leg Med. 2005; 119(6): 349-54.
41.
Alshihri AM, Kruger E, Tennant M. Western Saudi adolescent age estimation utilising
third molar development. Eur J Dent. 2014; 8(3):296-301.
42.
Knell B, Ruhstaller P, Prieels F, Schmeling A. Dental age diagnostics by means of
radiographical evaluation of the growth stages of lower wisdom teeth.
Int J Leg Med. 2009; 123: 465-9.
43.
Bai Y, Mao J, Zhu S, Wei W. Third-molar development in relation to chronologic age
in young adults of central China. J Huazh Uni Sci Tech Med Sci. 2008; 28(4):487-90.
44.
Lee SS, Byun YS, Park MJ, Choi JH, Yoon CL, Shin KJ. The chronology of second and
third molar development in Koreans and its application to forensic age estimation.
Int J Leg Med. 2010; 124:659-65
25
45.
Sisman Y, Uysal T, Yagmur F, Ramoglu SI. Third molar development in relation to
chronological age of Turkish children and young adults.
Angle Orthod. 2007; 77(6): 1040-45.
46.
Zeng DL, Wu ZL, Cui MY. Chronological age estimation of third molar mineralisation
on Han in southern China. Int J Leg Med. 2010; 124(2):119-23.
47.
Olze A, Pynn BR, Kraul V, Schulz R, Heinecke A, Pfeiffer H, Schmeling A. Studies
on chronology of third molar mineralisation in First Nations people of Canada.
Int J Leg Med. 2010; 124(5): 433-7
48.
Aitken CGG. Statistics and the evaluation of evidence for forensic scientists.
Statistics in Practice. 1995. John Wiley & Sons. Chichester. ISBN 0-471-95532-9
50.
Kadane JB. Statistics in the Law. 2008. Oxford University Press. Oxford.
52.
Roberts GJ, McDonald F, Lucas VS
51. Vito GF, Letessa EJ. Statistical applications in criminal justice. 1989. Law and
Criminal Justice Series. Sage Publications. Newbury Park. ISBN 0-8039-2983-8
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