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. 2021 Jun 3;239(4):920–931. doi: 10.1111/joa.13462

Estimation of age at onset of linear enamel hypoplasia. New calculation tool, description and comparison of current methods

Paweł Dąbrowski 1,✉, Michał Jerzy Kulus 2, Mirosław Furmanek 3, Friedrich Paulsen 4,5, Joanna Grzelak 1, Zygmunt Domagała 1
PMCID: PMC8450483  PMID: 34081785

Abstract

Enamel Hypoplasia (EH) is known to be a useful indicator for wide range of detrimental factors in early childhood in past populations, such as nutritional disturbances, mechanical trauma, disease, metabolic, and/or genetic disorders. EH may be divided into three categories: pits, grooves, and lines, where the last two are referred to as “Linear Enamel Hypoplasia” (LEH). The regularity of enamel formation allows retrospective determination of the age of LEH formation. The current article reviews and compares the best‐known methods used to estimate age at LEH formation and provides a new computational tool. Growth curves for canines and incisors were developed based on tooth growth tables by previous authors. Optimal models were selected using the Akaike Information Criterion. A Microsoft Excel spreadsheet was created to calculate age at LEH formation using the most common methods. All method results were compared with an archaeological sample (44 teeth of 18 individuals from an early modern cemetery from Wrocław, Poland) and a theoretical model. The results of the methods were compared pairwise with Bland‐Altman plots. The current article provides a quick and easy‐to‐use tool for analyzing LEH chronology and comparing the results of different methods. As shown by the Bland‐Altman plots, most methods provide approximately consistent results for LEHs formed at around 2–3 years of age. However, LEHs formed particularly early or late are more prone to discrepancies between different methods. Comparison of the age at LEH formation obtained by different methods should be done carefully ‐ and the new LEH calculation tool with optimized equations provided in this publication can facilitate this process.

Keywords: enamel hypoplasia, mathematical modeling, physiological stress

1. INTRODUCTION

Enamel hypoplasia (EH) can be defined as the enamel thinning caused by partial or complete inhibition of ameloblast function during the secretory phase of enamel formation (Guatelli‐Steinberg, 2015; Hillson, 2014). EH may be divided into three categories: pits, grooves and lines, where the last two are referred to as “Linear Enamel Hypoplasia” (LEH) (Marchewka et al., 2014). LEH is a microscopically or macroscopically visible deformation of the tooth crown surface in the form of bands of varying width and depth running along the circumference of the tooth crown perpendicular to the long axis of a tooth, as shown in Figures 1 and 2 (Goodman & Song, 1999; Hillson, 1996).

FIGURE 1.

FIGURE 1

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Lower canine with two LEHs, scanning electron microscopy image. The scale bar represents 1 mm. Source: own archive

FIGURE 2.

FIGURE 2

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Image of a tooth with LEH. The figure shows an upper canine tooth with visible LEH. When a nutritional stress episode occurs, successive enamel sections thin out and begin to rebuild after homeostasis is regained. The surface of an enamel section between two adjacent Retzius lines is called "perikyma" (pl. "perikymata")

The etiology of EH is associated with factors that interfere with the activity of ameloblasts (enamel‐forming cells), slowing or even stopping their activity (Skinner & Goodman, 1992). Over one hundred factors leading to EH can be listed (El‐Najjar et al., 1978; Skinner & Goodman, 1992). These include: Protein deficiencies (such as: amelogenin, enamelin, and tuftelin) (Neiburger, 1990), vitamin deficiencies (A, C, K. and D) (Tomczyk, 2012), and deficiencies of calcium, phosphorus, magnesium, or fluorine (Nunn, 2001). Subsequently, metabolic disorders associated with diabetes and diseases of the pituitary or thyroid gland and adrenal cortex are mentioned (Tomczyk, 2012). Diseases of viral and bacterial origin (rubella, measles, syphilis, and tetanus) also contribute to disturbances in the activity of the enamel‐forming epithelium (King et al., 2002).

EH has been found to be most commonly caused by nutritional deficiencies, childhood diseases, and injuries (Armelagos et al., 2009; Pindborg, 1970, 1982). For this reason, EH can be considered a general indicator of malnutrition and disease in old populations (Towle & Irish, 2020).

Assessment of LEH can be useful in bioarchaeological studies. It is a fundamental component of recommended standards for data collection in studies of past populations (Tomaszewska & Kwiatkowska, 2019). Important recommendations come from the Skeletal Database Committee of the Paleopathology Association (Rose et al., 1991) and from (Buikstra & Ubelaker, 1994). From the 1980s to the present, enamel hypoplasia has been the common research tool in bioarchaeology, among a number of macroscopically assessed features present in osteological material from archaeological sites (Hillson, 1996; Krenz‐Niedbała, 2000; Krenz‐Niedbała & Kozłowski, 2013; Šlaus et al., 2011; Tomczyk et al., 2014). LEHs are identified in representatives of contemporary human populations as well as in prehuman hominids and archaic humans (De Castro & Pérez, 1995; Guatelli‐Steinberg, 2004; Ogilvie et al., 1989; Skinner, 2019).

Many studies dealing with LEH in human and other primate teeth show that the anterior teeth (especially lower canines and the first upper incisors) are the teeth that are most "sensitive" to stimuli that interfere with enamel development (Goodman et al., 1980; Larsen, 1987; Moggi‐Cecchi et al., 1994; Skinner, 1986; Skinner & Pruetz, 2012; Yamamoto, 1989). This could be due to the different duration of enamel formation of anterior and posterior teeth in the maxilla and mandible and/or the influence of the different degree of genetic determination on the process of tooth crown formation and thus on the exposure time of active ameloblasts to the effects of stressors (Goodman & Rose, 1990; Hillson, 2014; Reid & Dean, 2006). Some researchers suggest observing and assessing hypoplastic defects in all available teeth to obtain a complete picture of the effects of factors that interfere with enamel development (Buikstra & Ubelaker, 1994; Rose et al., 1991).

EH can only be formed during the formation of the tooth crown enamel. Once the dental crown is finally formed, enamel is not subject to remodeling during life or postmortem (Nelson, 2015). Thus, they remain a permanent record of living conditions during enamel formation (Goodman & Armelagos, 1988). Only significant damage to teeth (due to disease or physical injury) or abrasion of dental crowns resulting in a loss of their height may limit the evaluation of LEH (Buikstra & Ubelaker, 1994; Hillson, 1996).

Due to the regularity of enamel formation, each LEH allows us to retrospectively determine the age at its onset and thus reconstruct the entire chronology of physiological stress events in childhood using appropriate methods (Goodman et al., 1980; Krenz‐Niedbała & Kozłowski, 2013; Lukacs et al., 2001; Temple, 2016; Tomczyk et al., 2012). The choice of an appropriate model of LEH chronology estimation still remains a crucial decision that can significantly affect the final outcome of a study (Krenz‐Niedbała, 2000).

In the 1980s, 1990s, and early 21st century, the developmental standard of tooth growth established by Massler (1941) was widely used in studies of LEH (Ritzman et al., 2008). Based on Massler's data, Swärdstedt developed a method for estimating age at LEH formation based on measuring the distance between the LEH and the cementoenamel junction (CEJ). The measurement is compared to the enamel growth chart and assigned to semi‐annual age intervals. The total crown height is not considered in this method (Łukasik & Krenz‐Niedbała, 2014; Swärdstedt, 1966).

Because this method allows the assessment of age at LEH formation with an accuracy of half a year, Goodman and Song (Goodman & Song, 1999) intended to provide a method that would allow a numerical (non‐interval) biological age of LEH formation to be given. They derived linear equations based on Massler's data.

A major limitation of both methods is the omission of individual differences in total crown height, which may lead to over‐ or underestimation of age at LEH development. In addition, the Goodman and Song formula is far too simplistic (it has insufficient parameters) to properly describe tooth growth (Henriquez & Oxenham, 2019). Enamel grows in a nonlinear manner, which has necessitated the development of other methods that better reflect the dynamics of tooth crown development (Reid & Dean, 2006).

A study by Reid and Dean more accurately described the dynamics of tooth crown growth in different tooth types and populations (Reid & Dean, 2000, 2006). Using histological methods, the researchers divided the crown of each tooth into deciles of crown height and then estimated the number of days required for each decile to develop. Reid and Dean provided tooth growth datasets for contemporary northern European and southern African populations and the historical population of Denmark (Reid & Dean, 2000, 2006).

The above methods tended to provide inconsistent results. Age was under‐ or overestimated depending on the research and the type of teeth used to compare the methods (Łukasik & Krenz‐Niedbała, 2014). The main difference between the Swärdstedt method and the Reid and Dean method arises from the consideration of the cusp formation time in the latter method. Krenz‐Niedbała and Kozłowski (2013) found that the Reid and Dean method tends to give lower results than the equations developed by Goodman and Song (1999).

A thorough analysis of differences was also conducted by Ritzman et al., (2008); they found that the determination of LEH chronology varies significantly depending on the method used, which may lead to interpretive differences when comparing studies using different LEH assessment methods.

Recently, a new method for estimating the age of LEH was proposed by Henriques and Oxenham (2019). It is based on datasets derived by Reid and Dean and the equation a*e(b*x) (where x represents growth deciles, a and b stand for constant coefficients fitted for each tooth type, e is Euler's number).

The purpose of this study is to compare the results of existing methods for estimating LEH chronology and to create a tool to facilitate the calculation of LEH chronology and comparison of age at LEH formation obtained by different methods.

2. MATERIALS AND METHODS

2.1. Curve fitting and model selection

Fitting growth curves for the anterior teeth of northern European and southern African populations was previously performed by Henriquez and Oxenham (Henriquez & Oxenham, 2019). However, all curve equations derived by Oxenham and Henriquez were based exclusively on exponential regression [a*e(b*x)], although this was not always an optimal choice. In addition, the curves for canines of medieval northern European populations were not derived. Therefore, in the current study, we derived the new equations and selected the optimal ones.

To calculate the new curves, we used a dataset provided by Reid and Dean (Reid & Dean, 2006) and a nonlinear estimator from Statistica 13.1 (TIBCO Software inc.) based on the Levenberg‐Marquardt algorithm. We fit the curves to the following equations: (1) y = a*x2 + b*x + c; (2) y = a*e(b*x); (3) y = a*e(b*x) + c. In these equations, y represents the age at enamel formation (days), x represents the percentage of tooth crown height at which LEH is present (measured by the CEJ), and a, b, and c are experimentally determined parameters for curve fitting.

To determine the optimal model, we used the Akaike Information Criterion (AIC) with correction for small samples (AICc) (Akaike, 1974; Pan, 2001). The Akaike Information Criterion is an estimate useful for selecting the best mathematical model for a given dataset. Its purpose is to select the model that fits the given data correctly and requires only as many parameters as necessary.

Two factors must be considered in model fitting: the number of parameters and the goodness of fit. Increasing the number of parameters increases goodness of fit, but can lead to "overfitting" of the curve and thus poorer prediction (Lever et al., 2016). AIC can be used to score equations derived from the same dataset ‐ the better the goodness of fit and the lower the number of parameters, the lower the final score. The equation with the lowest AIC can be considered the best equation. An equation where the AIC score is higher by two can be considered the best fit. Equations that have an even higher AIC score should be considered less appropriate (Akaike, 1974; Pan, 2001).

The AIC and AICc for each equation were calculated using the package AICcmodavg (Mazerolle, 2020) in the R program (R Core Team, 2020). The equations with the lowest AICc were selected for further calculations. The equations with the fitted curves are listed in Table 1. The methods with the lowest AICc were considered the best and were further used in the age at LEH calculation tool.

TABLE 1.

Optimal selection of the growth model

Tooth Curve type Equation R AIC AICc Residuals
Northern European (based on Reid & Dean, 2006) 1st upper incisor Quadratic y = (0,0967483)*x^2 + (4,48608)*x + (426,531) 0,99973 90.95 97.61 1213

Exponential

(3 coefficients)

 y = (511,945)*exp((0,0134189)*x) + (−104,553) 0,99942 99.60 106.26 2663

Exponential

(2 coefficients)

 y = (423,849)*exp((0,0148221)*x) 0,99923 100.65 104.08 3517
2nd upper incisor Quadratic y = (0,0752564)*x^2 + (4,41163)*x + (670,112) 0,99975 86.62 93.28 819

Exponential

(3 coefficients)

y = (478,968)*exp((0,0126403)*x) + (179,249) 0,99978 85.04 91.71 709

Exponential

(2 coefficients)

 y = (639,582)*exp((0,0106706)*x) 0,99942 93.77 97.20 1882
upper canine Quadratic y = (0,0772727)*x^2 + (5,25273)*x + (642,818) 0,99925 100.31 106.98 2843

Exponential

(3 coefficients)

 y = (559,213)*exp((0,0121229)*x) + (73,6798) 0,99948 96.27 102.94 1968

Exponential

(2 coefficients)

y = (624,992)*exp((0,0113626)*x) 0,99943 95.35 98.78 2171
1st lower incisor Quadratic y = (0,0654312)*x^2 + (3,70597)*x + (361,42) 0,99681 111.19 117.85 7639

Exponential

(3 coefficients)

 y = (378,619)*exp((0,013249)*x) + (−24,7696) 0,99736 109.13 115.79 6335

Exponential

(2 coefficients)

y = (357,352)*exp((0,0136707)*x) 0,99734 107.19 110.62 6372
2nd lower incisor Quadratic y = (0,075711)*x^2 + (4,20345)*x + (360,566) 0,99961 90.96 97.63 1215

Exponential

(3 coefficients)

 y = (481,162)*exp((0,0125099)*x) + (−135,673) 0,99919 99.06 105.73 2537

Exponential

(2 coefficients)

 y = (365,182)*exp((0,0145167)*x) 0,99881 101.38 104.81 3756
lower canine Quadratic y = (0,112622)*x^2 + (6,17504)*x + (549,888) 0,99967 98.03 104.69 2309

Exponential

(3 coefficients)

 y = (705,773)*exp((0,0125797)*x) + (−178,24) 0,99926 106.80 113.47 5127

Exponential

(2 coefficients)

 y = (553,195)*exp((0,0143502)*x) 0,99896 108.54 111.97 7206
Southern African (based on Reid & Dean, 2006) 1st upper incisor Quadratic y = (0,0674592)*x^2 + (4,52499)*x + (414,462) 0,99938 95.25 101.92 1795

Exponential

(3 coefficients)

 y = (522,741)*exp((0,0116054)*x) + (−121,23) 0,99897 100.75 107.42 2958

Exponential

(2 coefficients)

 y = (416,367)*exp((0,0131966)*x) 0,99873 101.11 104.53 3665
2nd upper incisor Quadratic y = (0,0643473)*x^2 + (4,328)*x + (675,476) 0,99981 81.10 87.76709 495

Exponential

(3 coefficients)

y = (473,023)*exp((0,0119821)*x) + (192,81) 0,99983 79.70 86.37 437

Exponential

(2 coefficients)

 y = (648,198)*exp((0,00990652)*x) 0,99943 91.25 94.68 1496
upper canine Quadratic y = (0,0653147)*x^2 + (5,01399)*x + (616,245) 0,99984 80.46 87.13 468

Exponential

(3 coefficients)

 y = (570,43)*exp((0,0111659)*x) + (35,3005) 0,99968 88.26 94.93 950

Exponential

(2 coefficients)

 y = (602,386)*exp((0,0108063)*x) 0,99967 86.68 90.11 988
1st lower incisor Quadratic y = (0,0633217)*x^2 + (3,12329)*x + (310,301) 0,99963 85.81 92.47 760

Exponential

(3 coefficients)

 y = (350,999)*exp((0,013219)*x) + (−52,6141) 0,99941 90.82 97.48 1199

Exponential

(2 coefficients)

 y = (306,194)*exp((0,0142219)*x) 0,99932 90.46 93.89 1392
2nd lower incisor Quadratic y = (0,0662121)*x^2 + (3,37424)*x + (378,727) 0,99960 87.86 94.53 916

Exponential

(3 coefficients)

 y = (370,743)*exp((0,0132237)*x) + (−3,41833) 0,99957 88.64 95.30 984

Exponential

(2 coefficients)

y = (367,795)*exp((0,0132815)*x) 0,99957 86.65 90.079 984
lower canine Quadratic y = (0,070641)*x^2 + (6,57135)*x + (520,916) 0,99921 101.90 108.57 3285

Exponential

(3 coefficients)

 y = (811,591)*exp((0,00993476)*x) + (−303,791) 0,99880 106.57 113.24 5020

Exponential

(2 coefficients)

 y = (538,791)*exp((0,0126587)*x) 0,99807 109.81 113.24 8083
Medieval Northern European (based on Reid & Dean, 2006) Upper canine Quadratic y = (0,0728555)*x^2 + (6,30445)*x + (570,965) 0,99962 93.94 100.61 1593

Exponential

(3 coefficients)

 y = (761,106)*exp((0,0103283)*x) + (−203,564) 0,99922 101.81 108.48 3258

Exponential

(2 coefficients)

 y = (578,114)*exp((0,0121571)*x) 0,99889 103.66 107.09 4622
Lower canine Quadratic y = (0,101981)*x^2 + (6,06732)*x + (481,154) 0,99929 104.77 111.43 4262

Exponential

(3 coefficients)

 y = (706,255)*exp((0,0120728)*x) + (−246,296) 0,99875 111.00 117.67 7513

Exponential

(2 coefficients)

 y = (495,019)*exp((0,0146405)*x) 0,99811 113.56 116.99 11370
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All equations were fitted to the datasets for anterior teeth provided by Reid and Dean. The optimal model (with the lowest AICc value) is shown in bold and is used in the Age at LEH calculation tool (Supplementary Material 1). The selected models should be considered predictive rather than explanatory models, valid only in the range 0%–100% of tooth crown height.

2.2. LEH‐calculation tool

Current study provides a tool for calculating LEH on anterior teeth using the best known methods. A Microsoft Excel spreadsheet was created (File S1) to calculate the age at LEH formation using the methods described by: Swärdstedt (Swärdstedt, 1966), Goodman and Song (Goodman & Song, 1999), Reid and Dean (Reid & Dean, 2006), Henriquez and Oxenham (Henriquez & Oxenham, 2019) and the authors of the present article. The latter two methods are based on melt growth datasets for three populations (northern Europeans, southern Africans, and medieval northern Europeans) provided by Reid and Dean (Reid & Dean, 2006).

The calculations require providing the total crown height and distance from LEH to CEJ (to obtain the percentage of crown height where LEH is present). For the method of Reid and Dean (Reid & Dean, 2006), a result is provided for the nearest decile; e.g., the LEH at 84.9% is assigned to the 8th decile and at 85.1% ‐ to the 9th decile. The results for the methods of Swärdstedt (Swärdstedt, 1966) are provided in two columns: the first gives the semi‐annual intervals and the second gives the mean of the boundaries of the intervals (used later for the purpose of comparing methods). The remaining columns (for methods by Henriquez and Oxenham (Henriquez & Oxenham, 2019), Goodman and Song (Goodman & Song, 1999), and the method developed in the current study) use formulas derived by the respective authors.

The summary results are reported in a separate sheet. File S1 contains the necessary spreadsheet with concise instructions.

2.3. Methods comparison

In this study, the methods were compared on a theoretical model and a real archaeological sample.

The theoretical model consisted of six hypothetical anterior teeth with abundance of LEHs, shown in Figure 3. The distance from the LEH to the CEJ was determined for each line and used to calculate the age at LEH formation.

FIGURE 3.

FIGURE 3

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Theoretical model for method comparison. The black lines on the tooth crowns correspond to an LEH. The lines were measured and their age of origin was calculated using a tool developed in the current study (Supplementary Material 1). Selected Bland‐Altman plots are shown in Figure 4. All possible comparisons can be found in Supplementary Materials 2–7

The real sample consisted of 36 canines (8 upper and 28 lower) with 44 LEHs, from 18 individuals. Teeth were without or with minimal wear (maximal wear score 1b, according to the Wetselaar et al., (2009) tooth wear scale); crown height reduction was neglible and was not included in the calculation. All teeth were excavated from the cemetery of St. Barbara Church (Wrocław, Poland). It was used from the 15th to 18th. Century as a burial place (Burak & Okólska, 2007). The teeth were radioisotopically dated to the 16th‐18th. Century. The total crown height and CEJ‐LEH distance were measured for each line (after Buikstra & Ubelaker, 1994)). For the archaeological sample, measurements were made with a Mitutoyo Absolute Digimatic Caliper, accurate to 0.01 mm. The measurements were made twice.

Then, the spreadsheet from File S1 was used to estimate the age at LEH formation using all of the above methods.

Bland‐Altman plots were used to compare the results of the different methods (Bland & Altman, 1986). The purpose of each Bland‐Altman plot is to compare and visualize the output of two methods and determine their agreement. Creation and interpretation of the Bland‐Altman plots is explained on Figure 4.

FIGURE 4.

FIGURE 4

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Bland‐Altman plots explanation. (a) age at each LEH formation was estimated with two methods. Then mean of every pair of estimates was calculated as well as differences between results. (b) calculated data put on Bland‐Altman plots. Bolded‐dashed line marks mean difference between methods’ outputs. X‐axis presents the mean of both methods’ outputs for each LEH, Y‐axis presents the relative differences between both methods’ output

The X‐axis shows the mean of each pair of estimates and the Y‐axis shows the difference between the results of the two methods for a given pair of measurements.

When interpreting Bland‐Altman plots, the following features should be considered first and foremost: mean difference of the methods’ results, maximum/minimum difference, and confidence interval. Subsequently, one should look for visible trends (or lack thereof); when the difference between methods changes in different ranges of mean outputs. Plots were created using a BlandAltmanLeh package (Lehnert, 2015) in the R program (R Core Team, 2020).

Selected Bland‐Altman plots for the theoretical model are shown in Figure 4 and for the archaeological sample in Figure 5. Plots for all possible method pairs are shown in Files S2–S8.

FIGURE 5.

FIGURE 5

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Selected Bland‐Altman plots for the theoretical model. Bolded‐dashed line marks mean difference in methods output, doted lines – confidence interval. The results of all methods were compared for the 1st maxillary incisor (except for the last line). (a‐c) Comparison of different methods based on the same, South African, dataset. (d‐e) Comparison of different datasets within a single method. (g‐i) Evaluation of older methods. (j‐l) Selected comparisons for upper canines. (j) this plot shows the largest discrepancies among all plots produced in this study, ranging from −1 to 1 year. (k) the most extreme discrepancies between the Reid and Dean and Henriquez and Oxenham methods

3. RESULTS

3.1. Method‐output comparison

Figure 5 shows the Bland‐Altman plots comparing selected pairs of methods, for the 1st maxillary incisor and the maxillary canine. It shows the main differences and similarities. The comparison of the results of the methods on a real archaeological sample is shown in Table 2, and selected Bland‐Altman plots for it are shown in Figure 6.

TABLE 2.

Results of estimating age at LEH on the archaeological sample. The table shows the results for all evaluated methods and source datasets

Method: Mean: Median Standard deviation Min Max
% of total crown high at LEH (measuring from CEJ) 44,92 42,16 15,51 20,88 74,56

Northern European

(Reid & Dean, 2006)

 3,37 3,39 0,81 1,95 4,88

Southern African

(Reid & Dean, 2006)

 3,01 3,14 0,65 1,68 4,18

Medieval Northern European, canines only

(Reid & Dean, 2006)

 3,09 3,28 0,75 1,82 4,53
Northern European (Henriquez & Oxenham, 2019 based on Reid & Dean, 2000) 3,30 3,33 0,75 1,82 4,62

Southern African

Henriquez & Oxenham, 2019 based on Reid & Dean, 2006)

 2,85 2,69 0,64 1,54 3,98
Goodman & Song, 1999 4,01 4,07 0,92 1,95 5,55
Swärdstedt, 1966 (means) 2,99 3,25 1,06 1,25 4,75
Medieval Northern European (Dąbrowski et al. 2021, based on Reid & Dean, 2006) 3,16 3,21 0,72 1,92 4,38
Northern European (Dąbrowski et al. 2021, based on Reid & Dean, 2006) 3,36 3,37 0,80 1,83 4,78
Southern African (Dąbrowski et al. 2021, based on Reid & Dean, 2006) 3,00 3,07 0,64 1,60 4,06
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FIGURE 6.

FIGURE 6

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Selected Bland‐Altman plots for the archaeological sample. The sample consisted of upper and lower canines. The following plots compare the results obtained using the method of Reid and Dean (medieval Northern European dataset) and (a) Reid and Dean for the contemporary Northern European population. (b) Goodman and Song method (c) equations derived in the current study for the medieval Northern European dataset

Figure 5a‐c shows the comparison of different methods based on the same, South African dataset. All methods give strongly agreed results; the mean difference in results between the methods is close to 0. Figure 5d‐e show the comparison of different datasets within a single method. The mean difference in results is close to 0.2–0.3 years and ranges from −0.2 to 0.6 years. Figure 5g‐i: Evaluation of older methods. Although the mean difference in the output of the methods is close to 0 in most graphs, the range of possible differences is as large as 1 year. Figure 5 j‐l: Method comparison for upper canines. J: This plot shows the largest discrepancies among all the plots produced in this study, ranging from −1 to 1 year. Figure 5 k‐l: Although the method of Henriquez and Oxenham tends to give reliable results, in some cases their equations can be replaced by better ones. Figure 5k shows the most extreme discrepancies between the methods of Reid and Dean (Reid & Dean, 2006) and Henriquez and Oxenham (Henriquez & Oxenham, 2019). All possible Bland‐Altman plots for distinct teeth created in theoretical model are included in Files S3–S7.

As shown in Table 2, the results obtained for the archaeological sample provide similar results. The Reid and Dean dataset derived for the medieval northern European population (Reid & Dean, 2006) should be considered the most appropriate for evaluating the archaeological sample and treated as a reference point. The Bland‐Altman plots shown in Figure 6 illustrate the difference between two different datasets (Figure 6a), the most divergent methods (Figure 6b), and between the method of Reid and Dean and the method derived in the current study.

All possible Bland‐Altman plots for the archaeological sample are included in File S8.

4. DISCUSSION

The comparison of the methods used for estimation of age in LEH formation was performed earlier. Martin et al (2008) compared Reid and Dean method with linear equations derived by Walker (similar to those published by Goodman and Song), whereas Krenz‐Niedbała and Kozłowski, in the study of the population from Rogów, compared the results of the assessment of the biological age of the LEH by the Swärdstedt method with the results obtained with the regression equations proposed by Goodman and Song (Krenz‐Niedbała & Kozłowski, 2013). Ritzman et al. conducted another comparison of Dean, pointing out the importance of methods and datasets used to estimate age in LEH formation and emphasizing the problem of comparing results in studies that use different methods (Ritzman et al., 2008). However, the current study uses a more comprehensive methodology and involves more tooth types and more recent methods than previous articles, moreover, compares all methods at once.

For archaeological samples from the early modern cemetery of Wrocław, all compared methods provide mostly consistent results. The most appropriate dataset for this population is the one obtained from the medieval northern European population. The mean result obtained with the original method of Reid and Dean (Reid & Dean, 2006) is 3.09 years and with the equation derived in the current article ‐ 3.16 years. As shown in Table 2, only Goodman & Song (Goodman & Song, 1999) gave an apparently overestimated result (4.01 years). For the other methods, the difference depends more on the source dataset used (based on South African/Northern European/Medieval Northern European populations) than on the methods themselves‐at least for the study population. Martin et al (2008) reached similar conclusions, indicating the necessity for using population‐specific tooth‐growth standards.

Bland‐Altman plots generated for the theoretical model show that in some cases, the methods used to estimate LEH chronology can strongly influence the final results. As shown in Figure 6, most methods provide similar results for LEH formed in the middle of the teeth (at about 2–3 years), but for the earliest and the latest growth periods (about 1‐2/3‐4 years), the differences increase, regardless of the methods. As shown in Figure 6, the differences can be as large as 1 year in extreme cases (Figure 6j).

Previous studies comparing different methods tend to compare differences in means only, ignoring the min/max range. In Martin et al study (2008) mean differences between Walker's linear equations and Reid and Dean method ranged from 1 to 4 months, whereas the differences between linear equations and Reid and Dean methods can be as big as one year (Figures [Link], [Link], [Link], [Link], [Link], [Link]). Populations in which the mean LEH formation age is particularly late or early would produce larger discrepancies between method results, where in populations with more diverse age at LEH formation even divergent methods may give similar results.

The Bland‐Altman plots confirm the different source datasets as the main source of the discrepancies. Different methods based on the same data set tend to produce similar results (Figure 6a‐c), with a narrow range of differences between methods, while another data set produces quite different results even with the same method (Figure 6d‐f).

The method derived by Henriquez and Oxenham (2019) is ingenious. However, in some cases it was possible to provide more optimal equations (especially for the estimation of the earliest and latest LEH) without overfitting the curve (which is supported by the AIC/AICc score). The most pronounced discrepancies between their equations and those of Reid and Dean are shown in Figure 3k. However, in most cases, the difference is negligible, and the equations derived by Oxenham and Henriquez should still be considered valid. Furthermore, the curves derived in our study should be considered only as predictive equations; they should not be considered explanatory equations under any circumstances. The curves derived in the current study are valid only in the range from 0% to 100% of the tooth crown height‐which is satisfactory given that the LEH appearance is limited to the tooth crown surface only.

To the best of our knowledge, the LEH calculation tables provided in the current article (file S1) are the fastest possible tool for estimating LEH age at formation. It would be particularly useful for comparing the current work with previous studies that based their LEH chronology estimates on older methods. Comparison of results obtained using different methods may be biased in some cases, as noted earlier and shown in the Bland‐Altman plots (Figure 6 and Files S3–S8), so calculation using all possible methods is warranted and useful to ensure comparability with all LEH studies.

Bland‐Altman plots, provided in the current study as files S3–S8, can be used for the opposite reasoning, i.e., to predict what the age at LEH formation would be if estimated using a more accurate method (such as Reid & Dean or Oxenham and Henriquez) instead of an old/biased method (such as Swärdstedt or Goodman & Song). However, such a prediction requires the mean age at LEH formation calculated for each tooth type ‐ which is not always provided in the publications.

Further optimization is still possible. First of all, the dynamics of enamel growth varies between populations. To our knowledge, there is not yet a suitable dataset for Asian, Native American, and other populations. There is also a problem with tooth wear ‐ most methods require total crown height for calculations and tooth wear can bias the estimate of age at LEH formation. A study presenting an appropriate model to estimate the percentage of enamel worn as a function of biological age could further increase the precision of LEH chronology estimation.

5. CONCLUSIONS

Different methods can give similar results on average, especially for those formed around 2–3 years of age. However, for LEHs formed particularly early or late in life, the discrepancies are more pronounced. The datasets on which the different methods are based are an important source of discrepancies in the results. Providing new datasets for Asian, Indian, and other populations could increase the accuracy of estimating age at LEH formation in these populations.

The comparison of age at LEH formation obtained by different methods should be done carefully and a new LEH calculation tool with optimized equations provided in this work can facilitate this process.

Conflict of interest

Authors declare no conflict of interests.

AUTHOR CONTRIBUTIONS

All authors contributed significantly to current manuscript. Conceptualization of the manuscript was conducted by PD and MK. Introduction was written by PD, MK, and JG. MK performed statistical inference and necessary computations, which were verified by PD, JG, and MF. MK and JG prepared age‐at‐LEH calculation tool, which were tested and verified by PD, FP, and ZG. Figures were prepared by MK with conceptualization of PD and ZG. Discussion was written by PD, ZG, FP, and MK. Language editing and proofreading: ZG and FP. All authors approved the submission of this work.

Supporting information

Supplementary Material

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Fig S2

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Fig S3

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Fig S4

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Fig S5

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Fig S6

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Fig S7

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Fig S8

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Supplementary Material

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ACKNOWLEDGMENTS

We thank the archaeological company Delfa for help in obtaining unique material, Piotr Kmiecik for his help in dating the cemetery based on architecture, Aleksandra Królicka for illustrative pictures of the SEM, Marek Krąpiec for help in dating material, and Joanna Grzelak for help in obtaining necessary references. The research was funded by the National Science Center, Poland, under the project "OPUS 13", decision no: DEC‐2017/25/B/HS3/02006, grant acquired from PD, Wrocław Medical University.

Dąbrowski, P., Kulus, M.J., Furmanek, M., Paulsen, F., Grzelak, J. & Domagała, Z. (2021) Estimation of age at onset of linear enamel hypoplasia. New calculation tool, description and comparison of current methods. Journal of Anatomy, 239, 920–931. 10.1111/joa.13462

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supplementary Material

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Fig S2

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Fig S3

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Fig S4

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Fig S5

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Fig S6

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Fig S7

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Fig S8

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Supplementary Material

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Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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