Machine learning and regression analysis for age estimation from the iliac crest based on computed tomographic explorations in an Indian population

Abstract

Age estimation constitutes an integral parameter of identification. In children, sub-adults, and young adults, accurate age estimation is vital on various aspects of civil, criminal, and immigration law. The iliac crest presents as a suitable age marker within these age cohorts, and the modified Risser method constitutes a relatively novel and unexplored method for iliac crest age estimation. The present study attempted to ascertain the applicability of this modified method for age estimation in the Indian population, an aspect previously unexplored, through computed tomographic examination of the iliac crest. Computed tomography scans of consenting individuals undergoing routine examinations of the pelvis/ abdomen for various clinically indicated reasons were collected and scored using the modified Risser stages. Computed tomographic examinations of the iliac crest indicate that the recalibrated method accurately depicts the temporal progression of ossification and fusion changes. Different regression and machine learning models were subsequently derived and/or trained to evaluate the accuracy and precision associated with the method. Amongst the ten regression models derived herein, compound regression exhibited the lowest inaccuracy (4.78 years) and root mean squared error values (5.46 years). Machine learning yielded further reduced error rates, with decision tree regression achieving inaccuracy and root mean squared error values of 1.88 years and 2.28 years, respectively. A comparative evaluation of error computations obtained from regression analysis and machine learning illustrates the statistical superiority of machine learning for forensic age estimation. Error computations obtained with machine learning suggest that the modified Risser method is capable of permitting reliable age estimation within criminal and civil proceedings.

Keywords

Age estimation computed tomography iliac crest modified Risser stages regression models machine learning

Introduction

Age estimation constitutes one of the crucial prerequisites for human identification.¹ Age estimation in children, sub-adults, and young adults is of paramount significance in cases encompassing various aspects of criminal, civil, and immigration laws.^2–4 Investigations pertain to, but are not limited to, the field of sports medicine,⁵ medico-legal cases of paedopornography,⁶ child trafficking,⁷ child marriage,⁸ illegal immigration,⁹ and assigning criminal responsibility^9–11 all warrant accurate age estimation within these age cohorts. The German Study Group on Forensic Age Diagnostics (AFGAD) advocates relying on the combination of physical examination, scrutiny of dentition status, and X-ray examination of hand and wrist bones for accurate age estimation in criminal proceedings.¹² While dental development^13–15 and ossification of hand and wrist bones^16–19 present as reliable age markers, they each suffer from certain pertinent drawbacks. Eruption and calcification of the second molar and complete ossification of hand and wrist bones are often achieved within sub-adults,^20–22 rendering these markers ineffective for establishing the medico-legally significant 18-year-old threshold. In such scenarios, AFGAD recommends employing computed tomography (CT) scans of the medial clavicle, along with those of any alternate skeletal markers available for scrutiny.¹²

Within the pelvis, the iliac crest, a secondary ossification centre, displays a relatively longer development period and, thus, presents as a reliable age marker in sub-adults and young adults.^4,23–25 Previously undertaken investigations with the iliac crest have indicated a good correlation between apophyseal ossification/ fusion changes and age,^26–29 signifying its utility as an age marker. Numerous scoring approaches for iliac crest ossification and fusion have been devised and researched in the past.^{2–5,8,9,26,29–45} Amongst these methods, Risser scoring constitutes one of the more commonly employed and researched methods.^{3,9,22,24,46–65} However, all such studies utilizing the Risser sign for age estimation reported highly variable findings pertaining to its applicability. Furthermore, these investigations yielded contrasting observations regarding the temporal progression of iliac apophyseal ossification and fusion,^3,9,51 suggesting the need to re-calibrate the staging method in order to permit accurate age estimation. In keeping with these findings, certain pertinent modifications to the original scale were put forth.^59,64 Furthermore, validation of these modified Risser scales is currently lacking. Moreover, an evaluation of the Risser method and/ or its modifications for age estimation in the Indian population remain largely unexplored.⁶⁶

Age estimation using the iliac crest has often been attempted through gross morphological examination of dry bone samples,^39,40 conventional radiography,^{3,4,8,9,22,24,27,33,34,36,38,45,47–51,57,59–61,65,67,68} sonography,^{23,31,53,54,56} magnetic resonance imaging,⁵ and computed tomography.^{2,26,35,37,52,64,69} Digital visualization tools, such as the latter, are particularly advantageous for testing and redefining conventionally derived age estimation methods, particularly, in the absence of large-scale, population-specific, contemporary skeletal repositories. Visualization modalities such as CT have an added advantage as they help eliminate interfering tissue remnants which often impede the appreciation of morphological features during gross and/ or radiological examination.^64,69 Lottering et al. exploited these inherent advantages of computed tomography to recalibrate the temporal progression of apophyseal ossification and fusion described within the Risser method.⁶⁴ This modified Risser scale follows the ossification and fusion of the iliac apophysis through three distinct ossification centres: anterior superior iliac spine, iliac tubercle, and posterior superior iliac spine. Ensuing ossification and fusion changes have been grouped into seven distinct stages, with stage 0 indicative of the lack of any ossification centre. Stages I and II describe the extent of ossification over the crest, i.e. less than 50% and more than 50%, respectively, whereas stage III describes a period wherein the ossification centres have appeared, covering the entire length of the crest, and partial or complete union between centres has commenced. Stages IV, V, and VI describe stages of commenced fusion (<50% of apophyseal cartilage has ossified), active fusion (>50% of the cartilage has ossified), and completed fusion. These stages were appropriately renumbered within the present study and are shown in Figure 1. Subsequent CT-based validation studies for these recalibrated stages are currently lacking.

Figure 1.

3D CT representations of ossification and fusion changes of the iliac crest.

A major portion of previously conducted investigations with the iliac crest utilized descriptive statistics for age estimation.^{2–5,8,9,23,26,27,31,33–36,45,69,70} While this statistical modality permits a simple and straightforward evaluation, it suffers from pertinent issues of age mimicry.⁷¹ On the other hand, a handful of observational studies employed regression analysis^37,38,68 and Bayesian inference^37,64 for the age estimation from the iliac crest. Machine learning is presented as another efficient statistical tool, believed to yield more accurate estimates of age^28,67 by eliminating the influence of human bias.^72–74 Currently, studies utilizing machine learning for iliac crest age estimation are limited to the modified Kreitner–Kellinghaus scoring method.^28,67 A similar investigation with the Risser method, or its modifications, is currently remaining unreported.

The present study was targeted at evaluating the applicability of the modified Risser method for age estimation through computed tomographic examinations of the iliac crest in the Indian population. Different regression models were developed with the aim of assessing the precision and reliability associated with the method. In addition to this, different machine learning models were trained and utilized with the objective of augmenting the precision and reliability associated with the iliac crest age estimation using the modified Risser stages. Error computations obtained with machine learning and regression analysis were comparatively evaluated to establish the superior statistical modality for forensic age estimation.

Materials and methods

Sample collection

The present prospective cross-sectional study was carried out in the Department of Forensic Medicine and Toxicology, and the Department of Diagnostic and Interventional Radiology, All India Institute of Medical Sciences (AIIMS), Jodhpur, India, between January 2020 and January 2022. Ethical approval for conducting the present study was obtained from the Institutional Ethics Committee through Letter no. AIIMS/IEC/2019-20/1007 prior to its commencement. In the present study, individuals aged 10–30 years, residing in the region of Western Rajasthan, India, who were undergoing routine computed tomographic (CT) examinations of the pelvis/ abdomen at the Department of Diagnostic and Interventional Radiology, AIIMS, Jodhpur, for various clinically indicated reasons were approached. The age range of participants incorporated into the present study was pre-decided in accordance with previously undertaken studies pertaining to the iliac crest age estimation.³ Such individuals/ their guardians were informed about the parameters of the study in detail, and their consent was sought for voluntary participation in the study. CT scans of consenting individuals were collected after verifying their chronological age through valid documents. Consenting individuals who could not produce any valid proof of documented age were excluded from the study. In addition to this, CT scans of individuals with a history of congenital bone deformities and/ or metabolic and growth disorders were excluded from the present investigation. Scans with fractures involving the region of interest, and movement induced/ technical artefacts, which became apparent during the CT examination, were also excluded from the study.

A total of 100 CT scans, obtained from 100 consenting individuals, were collected during the preordained study period. This entire sample was divided into a study group of 80 individuals and a test group of 20 individuals using a random number table. All 100 CT scans were coded to blind the observer to patient information capable of inducing bias.

Scanning parameters

CT images were acquired from consenting individuals using a Dual Source CT—SOMATOM Definition Flash^TM system (Siemens Medical Solutions, Erlangen, Germany). The technical specifications associated with each CT scan included a slice thickness of 1.0 mm (a standardized imaging parameter utilized by the healthcare centre for diagnostic purposes). The acquired CT scans were processed, segmented, and analysed using 3D Slicer 4.11.20200930.^75,76 In order to visualize different age-related ossification and fusion changes, the bone window of each scan was selected, following which a 3D volume-rendered (VR) reconstruction of the pelvis was generated. Subsequently, the 3D VR representations were cropped to eliminate any unwanted interfering bony remnants. 3D CT images generated using 3D Slicer were visualized from different planes so as to enable the appreciation of different ossification and fusion changes.

Age estimation using the modified Risser stages

3D VR reconstructions of the pelvis were scored in accordance with the modified Risser stages described by Lottering et al.⁶⁴ The 3D CT images provided within this original study were utilized as reference images. A detailed description of the modified staging method is given in Table 1. The modified Risser stages described by Lottering et al.⁶⁴ were renumbered as Stages 1–7, as opposed to 0–VI described within the original study, in order to permit logarithmic, inverse, S-curve, and power regression analysis of the data (see Statistical analysis). 3D CT representations of the modified Risser stages 1–7 are shown in Figure 1. Certain stages (stages 2, 6, 7) have been represented by multiple images to demonstrate all plausible forms for the stage.

Table 1.

The iliac crest age estimation method employed in the present study.

Stage	Description
1	No apophysis present.
2	Anterior and/or posterior apophyseal centers have appeared. However, the combined length is approximately half (50%) or less than the length of the superior border of the ilium.
3	The lengthwise measurement of the anterior and posterior apophyseal centers is >50% of the iliac crest. Ossification skip of the posterior superior iliac crest is evident, visualized as a distinct gap >1 cm between the adjacent apophyseal centers.
4	The combined lengthwise apophyseal measurement equals the length of the curvilinear superior border of the ala of the ilium. The apophyseal centers may be partially or completely united, posterior to the most superior point of the mid-crest. In some instances, a small interruption, measuring <1 cm between the anterior and posterior apophyseal centers may be visible. The cartilage between the apophysis and ala of ilium has not ossified
5	Commenced Fusion: Apophyseal fusion to the ala of the ilium has commenced on the anterolateral surfaces of the iliac crest with the apophyseal cartilage ossified to <50% of its maximum length. The apophysis may not extend to the complete width of the superior border of the ilium.
6	Active Fusion: Apophyseal fusion to the ala of the ilium is >50% typically with sporadic disruption of the radiopaque lamellar bone border, in the regions of the iliac tubercle (anterolateral flaring) and/or superior to the iliac tuberosity.
7	Complete Fusion: Complete ossification of the apophyseal cartilage and complete osseous fusion of the iliac apophysis with the ilium with either remnant of a sclerotic margin or no remaining vestige.

The proportion of ossification and fusion described within the method was measured using the ruler-enabled open curve function provided within 3D Slicer. In order to calibrate the same, primarily, the length of the crest was measured using the open curve tool, following which the length of the ossified/ fused region was measured. Subsequently, based on these measurements, the proportion of ossification and fusion was calibrated, and the relevant stage was allotted to the CT image under scrutiny.

Statistical analysis

Statistical analysis for the present study was undertaken using IBM Statistical Package for Social Sciences (SPSS) v26 and R Studio (RStudio Team (2022). RStudio: an integrated development environment for R. RStudio, PBC, Boston, MA, URL http://www.rstudio.com/). For all statistical computations, p < 0.05 was considered significant.

Inter- and intra-observer errors associated with the CT-based scoring of age-related changes within the iliac crest were evaluated using Cohen's weighted κ. In order to compute the inter-observer error, 20 randomly chosen CT scans were scrutinized by the lead investigator. Following this, unprocessed samples for the same 20 participants, a tabular description of the modified Risser stages, and reference CT images provided within the original study were shared with the second author. The second author independently processed and analysed these samples and allotted a stage to each scan based on perceived changes. The stages allotted to the 20 scans by the two observers were evaluated using Cohen's weighted κ which takes into account the degree of disagreement between observers. In order to compute the intra-observer error, the lead investigator scrutinized the same 20 samples after a duration of 2 weeks from the time of the initial assessment. The degree of disagreement between these two sets of observations by the same investigator was subsequently estimated using Cohen's weighted κ. The obtained κ values for inter- and intra-observer errors were evaluated following the system of McHugh⁷⁷: κ < 0.20 indicates no agreement, κ = 0.21–0.39 suggests minimal agreement, κ = 0.40–0.59 implies weak agreement, κ = 0.60–0.79 signifies moderate agreement, κ = 0.80–0.90 represents strong agreement, and κ > 0.91 indicates almost perfect agreement.

Bilateral and sex differences associated with the allocation of stages to the iliac crest were evaluated using the Wilcoxon test, and the Mann–Whitney U test, respectively. Spearman's rho was employed to establish the correlation between observed ossification and fusion changes and the documented age of participants. Each of these statistical analyses was undertaken using the total study sample of 100 CT scans.

A total of ten regression models i.e. linear, logarithmic, inverse, quadratic, cubic, compound, power, S-curve, growth, and exponential regression models, were derived using the study group of 80 individuals. The basis for deriving these multiple models instead of the commonly utilized simple linear regression models was the study by Zhang et al.⁶⁸ This study concluded that cubic regression models present a better fit for iliac crest age estimation, in comparison with the commonly utilized linear models. However, further empirical validations of the same are currently lacking.

In order to derive each of these models, the age of individuals was treated as the dependent variable, and the stage assigned to the iliac crest was considered the independent variable. The generated regression models were subsequently applied to the test group (N = 20) and the precision and reliability associated with these models were established through computations of inaccuracy and root mean square error (RMSE). Inaccuracy values, representative of the absolute error between estimated age and documented age, were computed as follows:

∑ (|Estimated mean point age- Chronological age|)/n

Root mean squared error (RMSE), a measure of how accurately the model predicts the response i.e. the age of individuals in this case, was computed as

[∑ (Estimated mean point age- Chronological age)²/n]^1/2

Different Machine learning models including Support Vector Regression (SVR), Decision Tree Regression (DTR), and K Nearest Neighbour Regression (KNNR) were trained to estimate the age of individuals. Inaccuracies and RMSE values associated with each of these machine learning approaches were computed for the study group (N = 80) and the test group (N = 20), separately.

The inaccuracies and RMSE values obtained with machine learning approaches and different regression models were comparatively evaluated to establish the superior statistical approach for the age estimation from the iliac crest.

Results

The total study sample in the present study comprised 65 males and 35 females, with a mean age and standard deviation of 22.98 ± 5.488 years and 23.34 ± 5.589 years, respectively. The age and sex distribution of the total study sample are shown in Table 2.

Table 2.

Age and sex distributions of the study population (N = 100).

Age class (years)	Males (%)	Females (%)	Combined population (%)
10–12	06 (09.20)	02 (05.70)	08 (07.90)
13–15	-	03 (08.60)	03 (03.00)
16–18	06 (09.20)	04 (11.40)	10 (09.90)
19–21	10 (15.40)	02 (05.70)	12 (11.90)
22–24	15 (23.10)	04 (11.40)	19 (18.80)
25–27	11 (16.90)	12 (34.30)	23 (22.80)
28–30	17 (26.20)	08 (22.90)	25 (24.80)

An assessment of intra-observer error yielded a Cohen's weighted κ value of 0.810, indicating strong agreement in the allotment of modified Risser stages through CT images. The corresponding inter-observer weighted κ value of 0.716 suggests moderate agreement between the two observers for a CT-based analysis of the modified Risser stages. Spearman's rho yielded a correlation of 0.571 between ossification and fusion changes of the right iliac crest and documented age, and a correlation of 0.535 between that of the left iliac crest and age. No significant bilateral (p = 0.564; Z-score = −0.577) or sex differences (right iliac crest: p = 0.715; Z-score = −0.365; left iliac crest: p = 0.538; Z-score = −0.616) were observed in the allocation of modified Risser stages. Owing to the observed bilateral symmetry, only the left iliac crest was considered for further statistical analysis. Due to the low sample size of the study group, sex-pooled age estimation models alone are reported herein.

All ten regression models derived for the age estimation are shown in Table 3. Amongst the different models, the highest (0.770) and lowest (0.627) R² values (proportion of variance in age explained by regression models) were obtained with the power regression model and the inverse regression model, respectively. The strongest correlation between estimated age and documented age was obtained with power regression models (0.879), whereas inverse regression models yielded the weakest correlation (0.795) in comparison. The standard error of estimates (SEE) computed for different regression models garnered the lowest value of 0.140 years with the power regression. The highest SEE values of 3.387 years were obtained with inverse regression models. On applying these models to the test group (N = 20), compound regression models yielded lowest inaccuracy and RMSE values of 4.78 years, and, 5.46 years, respectively. Highest error rates were observed with inverse regression models. Inaccuracy and RMSE values pertaining to all ten regression models are shown in Table 4.

Table 3.

Regression models derived for age estimation (N = 80).

Model type	Regression model	SEE	R²	R
Linear regression	9.529 + (2.470 × RS)	3.057	0.696	0.837
Logarithmic regression	10.811 + [7.965 × ln (RS)]	3.107	0.686	0.831
Inverse regression	28.383 – (17.918/ RS)	3.387	0.627	0.795
Quadratic regression	7.833 + (3.765 × RS) – (0.156 × RS²)	3.049	0.698	0.840
Cubic regression	13.016 – (2.329 × RS) + (1.456 × RS²) – (0.121 × RS³)	3.028	0.702	0.845
Compound regression^a	ln (10.458) + [ln (1.145) × RS]	0.142	0.761	0.874
Power regression^a	ln (11.120) + [0.443 × ln (RS)]	0.140	0.770	0.879
S-curve regression^a	3.389 – (1.008/ RS)	0.154	0.722	0.852
Growth regression^a	2.347 + (0.136 × RS)	0.142	0.761	0.874
Exponential regression^a	ln (10.458) + (0.136 × RS)	0.142	0.761	0.874

RS: modified Risser stage allotted to the left iliac crest; SEE: standard error of estimate; R2: proportion of variance in age explained by regression models; R: correlation between estimated age and documented age; ln: natural log; ^aestimated ages were in the natural logarithmic scale.

Table 4.

Error computations associated with different regression models (N = 20).

Model type	Regression model	Inaccuracy (years)	RMSE (years)
Linear regression	9.529 + (2.470 × RS)	5.09	5.72
Logarithmic regression	10.811 + [7.965 × ln (RS)]	5.57	6.17
Inverse regression	28.383 – (17.918/ RS)	5.87	6.46
Quadratic regression	7.833 + (3.765 × RS) – (0.156 × RS²)	5.46	5.98
Cubic regression	13.016 – (2.329 × RS) + (1.456 × RS²) – (0.121 × RS³)	5.84	6.20
Compound regression	ln (10.458) + [ln (1.145) × RS]	4.78	5.46
Power regression	ln (11.120) + [0.443 × ln (RS)]	5.25	5.85
S-curve regression	3.389 – (1.008/ RS)	5.55	6.12
Growth regression	2.347 + (0.136 × RS)	4.83	5.52
Exponential regression	ln (10.458) + (0.136 × RS)	4.84	5.52

RS: modified Risser stages allotted to the left iliac crest; ln: natural log; RMSE: root mean squared error.

Inaccuracy, RMSE, and R² values obtained with different machine learning approaches for the study group and the test group are shown in Table 5. Decision Tree Regression (DTR) yielded the lowest computations of inaccuracy (1.88 years) and RMSE (2.28 years) with the test group. On the other hand, Support Vector Regression (SVR) garnered the highest inaccuracy (2.33 years) and RMSE values (2.74 years). In comparison with other machine learning models, K-Nearest Neighbour Regression (KNNR) generated higher R² values for the study group, and DTR yielded the highest R² values for the test group.

Table 5.

Proportion of variance and error computations garnered with different machine learning models.

	Inaccuracy (years)		RMSE (years)		R²
Model	Study group (N = 80)	Test group (N = 20)	Study group (N = 80)	Test group (N = 20)	Study group (N = 80)	Test group (N = 20)
Support Vector Regression	2.68	2.33	3.38	2.74	0.600	0.179
Decision Tree Regression	2.63	1.88	3.25	2.28	0.650	0.432
K Nearest Neighbour Regression	2.44	2.12	3.08	2.37	0.718	0.221

RMSE: root mean squared error; R2: proportion of variance in age explained by machine learning models.

A comparative evaluation of inaccuracy and RMSE values computed with machine learning and regression analysis for the test group indicates that all three machine learning approaches garner more precise estimates of age. R² values obtained with machine learning and regression models for the study group suggest that all ten regression models account for a greater variation in age in comparison with Support Vector Regression. Similarly, all regression models, except inverse regression, accounted for a greater variation in age, when compared to Decision Tree Regression. On the other hand, compound, power, S-curve, growth, and exponential regression models accounted for a greater variation in age, in comparison with K Nearest Neighbour Regression.

Discussion

Risser, through a series of investigations,^30,78,79 devised a scoring system for grading iliac apophyseal changes with the aim of utilizing it for monitoring the progression of scoliosis in children. The underlying basis for developing such a grading system was the observed concordance between the completion of vertebral growth, progression of spinal curvature, and ossification of the iliac apophysis. This observed conformity permitted an indirect assessment of vertebral growth in children, by circumventing limitations centered around the visualization of vertebral growth plates using conventional radiography. Risser's stages of iliac apophyseal ossification were subsequently utilized within clinical settings to monitor vertebral growth in patients presenting with adolescent idiopathic scoliosis.^46,80 Research investigations, which followed, attempted to establish the correlation of Risser stages with bone age computed from hand and wrist bones and indicated a good correlation between the two markers.^22,47,58,63 In contrast, certain other research studies questioned the ability of Risser stages in accurately assessing skeletal maturation in children, within forensic and clinical settings.^{50,55,58,62,81,82} These highly variable findings regarding the applicability of the Risser method could be attributed to the temporal discrepancies associated with apophyseal ossification and fusion,^3,9,51 as well as limitations stemming from the use of radiographic modalities for examination.^{9,48,50,52,81} With the aim of overcoming these methodological and imaging limitations, Lottering et al.⁶⁴ formulated their modified Risser method through a computed tomographic examination of the iliac crest, wherein they described the temporal progression of age-related changes within the iliac crest. However, subsequent validation studies for this described temporal progression are currently lacking. The present study attempted to evaluate the applicability of the modified Risser stages in describing the progression of age-related changes within the iliac crest, as well as the forensic suitability of the method for age estimation.

In order to do so, the present study utilized multi-slice computed tomography (MSCT) and modified ossification and fusion stage descriptions formulated by Lottering et al.⁶⁴ Such 3D CT-based investigations enable evaluation from multiple planes and rotations within a single clinically obtained scan, permitting an unambiguous assessment of transpiring changes. Similar examinations with X-rays warrant procuring multiple scans from different radiographic views, including, but not limited to, the antero-posterior, postero-anterior, and lateral views; these are often not attainable and ethical within a clinical setting. Furthermore, computed tomographic examinations are not affected by superimposition-induced artefacts such as those resulting from foreign material, decomposition-induced gaseous by-products and/ or microbial activity, bodily tissues and organs,^64,69 and magnification errors,⁸³ complications commonly encountered with radiography. Previously undertaken CT-based investigations validate these advantages of computed tomography for age estimation.^{2,26,35,37,52,64,69,84–86} Comparative evaluations between computed tomography and plain radiography for iliac crest age estimation, too, have demonstrated that the overall repeatability and accuracy associated with CT supersedes that of X-ray examination.^52,64 Inter- and intra-observer error values computed within the present study demonstrate moderate to strong agreement between and within observers for CT-based iliac crest age estimation.⁷⁷

The ontogeny of iliac apophyseal ossification observed within our study is in agreement with that reported by Lottering et al.⁶⁵ In 100% of scrutinized cases, the appearance of the anterior ossification centres preceded that of the posterior centre, with the iliac tubercle ossifying first within all CT scans (Figure 1(c) and (d)). With stage 3, a characteristic skip ossification was observed i.e. a distinct gap between all three ossification centres: iliac tubercle, anterior superior iliac spine, and the posterior apophysis (Figure 1(e)). Fusion of the apophyseal centres to the crest was observed to commence from the anterior aspect (Figure 1(g)). With stages of active fusion, for a marginal fraction of 16.67% of cases, fusion completed posteriorly first (Figure 1(h)), whereas for another 16.67% of cases, active fusion was first observed simultaneously within the anterior superior iliac spine and the posterior superior iliac spine, with an unfused iliac tubercle (Figure 1(i) and (j)). Apophyseal fusion changes observed herein corroborate the sporadic disruptions described by Lottering et al.⁶⁴ Our findings pertaining to ossification and fusion changes, as well as those reported within previous investigations,^3,9,51 suggest that the temporal progression described by Risser^30,78,79 fails to accurately account for age-related changes transpiring within the iliac crest. It is prudent to mention here that the representation of each stage within the present study was relatively lower in comparison. Thus, these findings should be further verified through subsequent investigations.

In the present study, a moderate correlation was obtained between iliac apophyseal stages and the documented age of individuals.^87,88 No significant sex or bilateral differences were observed during the allocation of modified Risser stages to an Indian population. Lottering et al.⁶⁴ demonstrated in their study that females achieved advanced apophyseal development, in comparison with males. Mean ages pertaining to stages 1, 4, 5, and 6 of this study substantiate this finding, with lower mean ages found in females. However, for stages 0, 2, and 3, the opposite was observed, which could be attributed to the limited representation of females in these stages. Stage-wise descriptions for both sexes have not been incorporated here as the smaller and unequal representation of females impedes effectively demonstrating any sex-specific aging patterns for the method. Owing to the relatively smaller sample size in our study, sex-pooled statistical models for age estimation, alone, have been reported here. Such sex-pooled models enable age estimation even in cases wherein fragmented remains are present for examination, rendering sex estimation problematic. Furthermore, the unequal representation of males and females within our study hinders empirical and reliable derivation of accurate sex-specific age estimation models. It is prudent to mention that the earlier maturation in females obtained herein and in similar investigations indicates that the lack of any statistically significant sex differences obtained within our study could largely be a result of the under-representation of females. Similar investigations employing an equally represented male and female population are currently lacking in order to better illustrate sex-specific patterns associated with the modified Risser method.

Regression models have often been utilized in the past for age estimation using the mandible,⁸⁹ molars,^90–93 premolars,⁹⁴ knee,⁹⁵ hand bones,⁹⁶ clavicle⁹⁷ and sternum.⁹⁸ Previously undertaken regression-based analyses with the acetabulum yielded reduced error rates in comparison with the use of descriptive statistics for age estimation,^84,85 illustrating the advantages of this statistical modality in medico-legal investigations. Zhang et al.,⁶⁸ in a pilot study, assessed the performance of different regression models for iliac crest age estimation using the modified Kreitner–Kellinghaus stages and reported that cubic regression generates the best-fit models. They, however, did not comment on the error computations associated with different regression models. The present study attempted a similar scrutiny with ten regression models derived using the modified Risser stages. In addition to this, inaccuracy and RMSE values associated with each of these ten models were computed in order to establish the most accurate regression model for age estimation. The correlation between estimated and documented age obtained with all ten regression models was observed to be significantly higher than those obtained with a direct scoring of iliac changes for age estimation. While power regression models garnered the strongest R² and correlation values, the lowest error rates were obtained with compound regression models, even lower than those obtained with the conventionally utilized linear and cubic approaches. The correlation between estimated and documented age, SEE, and R² values obtained with compound, exponential, and growth regression models differed only marginally from those attained with power regression models. Exponential and growth regression models, in addition to this, yielded inaccuracy and RMSE values comparable to those obtained with compound regression. These findings indicate that ossification and fusion changes occurring within the iliac crest exhibit a characteristic non-linear relationship with age. Thus, employing alternate non-linear regression models for iliac crest age estimation might help augment the overall precision and reliability associated with this marker.

Machine learning has been employed in the past for age estimation using dental markers,^90,99,100 femur,¹⁰¹ knee,¹⁰² and hand and wrist bones.^103–105 In comparison, limited investigations have undertaken pelvic age estimation with different machine learning approaches.^28,67,106 Within the present study, the lowest inaccuracy and RMSE values were obtained with Decision Tree Regression (DTR). Decision Tree constitutes one of the more commonly employed supervised learning approaches, utilized for both regression and classification problems. This encompasses an algorithm targeted towards creating a simplified model which predicts the target variable/ outcome by imbibing decision rules inferred from the data in hand. Decision trees, previously employed for pubic symphyseal age estimation, similarly yielded high accuracy percentages.¹⁰⁶ K-Nearest Neighbour Regression (KNNR), another supervised learning technique, makes predictions concerning the grouping of individual data points based on the classification of their neighbours. In the present study, the KNNR model yielded the highest R² values for the study group. Support Vector Regression (SVR), which explored the non-linear relationship between age and stage within the present study, yielded the highest error computations and the lowest R² values. Contrary to our findings, Fan et al. reported lower inaccuracy and RMSE values with Support Vector Regression, in comparison to Decision Tree Regression, using the modified Kreitner–Kellinghaus stages.²⁸

Error computations obtained with different machine learning approaches in the present study exhibited a significant improvement over all ten regression models. Li et al., similarly, reported lower inaccuracy and RMSE values with machine learning, in comparison to cubic regression models derived using the modified Kreitner-Kellinghaus stages.⁶⁷ Given the increase in precision obtained with different machine learning approaches, it would be beneficial to rely on this statistical approach for forensic age estimation. In addition to eliminating the component of human bias, machine learning does not suffer from issues of age mimicry, a commonly encountered problem even with regression models.^{37,71,107,108} Inaccuracy values obtained herein with different machine learning models are comparable to those reported by Lottering et al. using a Bayesian approach.⁶⁴ While a Bayesian investigation with the modified Risser stages was not attempted herein, future investigations that comparatively evaluate the performance of Bayesian inference and machine learning for iliac crest age estimation should be undertaken.

The present study indicates that MSCT-based modifications to the original Risser scale help appropriately re-calibrate the ontogenic pattern of apophyseal ossification and fusion. CT examinations of the iliac crest additionally help overcome limitations associated with the use of conventional radiography for age estimation. The use of the open curve tool helped place points along the entire length of the S-shaped crest, enabling measurement of the extent of ossification and fusion. Despite these advantages, we do not recommend CT examination of the pelvic region in living individuals for age diagnosis. In lieu of this, clinically undertaken CT examinations can be relied upon as additional corroborative evidence for age estimation. Post-mortem CT examination of contemporary fleshy remains/ bodies can also be undertaken to permit age estimation using non-invasive procedures.¹⁰⁹ Radiography-based investigations, in amalgamation with deep learning models, directed towards automated age estimation, have also shown to circumvent issues of superimposition, effectively increasing the accuracy associated with this modality for age estimation.²⁸ However, in the absence of any actual legal basis for authorizing X-ray examinations in civil investigations, radiographic age estimation in such scenarios is also not feasible.²³ As an alternative to this dilemma, radiation-free visualization techniques such as ultrasonography (USG)^23,31,54 and MRI⁵ may be administered for age estimation. The applicability of modified Risser stages for iliac age estimation using USG and MRI should be investigated, and appropriate modality-based re-calibrations, if any, should be incorporated.

The present investigation incorporated clinically undertaken CT scans of consenting individuals, aged between 10 and 30 years, undergoing therapeutic examinations at the healthcare centre during the ordained study period. For this reason, large, homogeneously represented study and test groups could not be ensured within our study. Similar population specific studies employing a larger, contemporary dataset comprising a more homogeneous representation for each stage and age are required to help substantiate our findings. Furthermore, machine learning based investigations traditionally require a large dataset to appropriately train models for age estimation. While the general rule of thumb indicates that a minimum sample size equivalent to ten times the number of parameters/ features being scrutinized can be employed, more accurate and reliable results are primarily furnished with larger data sets.¹¹⁰ The present study is merely a pilot attempt at demonstrating the utility of alternative regression models for iliac crest age estimation, as well as the increased performance of machine learning over regression analysis. Our findings pertaining to the performance of the aforementioned should be further validated, either through larger training sets, or data augmentation steps. The smaller study set also hampered the utilization of sex-specific models for age estimation or commenting on sex-specific aging patterns. Future investigations will attempt to incorporate a larger study set to corroborate the error computations obtained herein, as well as employ deep learning models to further augment the applicability associated with the modified Risser stages.

Currently available iliac crest age estimation methods which employ ossification and fusion changes of the crest often restrict themselves to the age group of 10–30 years, primarily, as age-related ossification and fusion changes are observed within this age cohort alone. Future investigations should attempt to incorporate older individuals i.e. beyond 30 years, and extend their analysis to the scrutiny of different sub-surface trabecular changes as well. Previous investigations with different trabecular parameters within the iliac crest for the age group of 13–58 years have yielded promising results in the past.⁴³ Incorporating trabecular changes, alongside the standard ossification and fusion changes, may help extend the forensic applicability of the iliac crest beyond the 30-year cut-off.

Conclusion

A computed tomographic evaluation of the modified Risser method in the Indian population indicates that the re-calibrated method accurately accounts for apophyseal ossification and fusion changes occurring within the iliac crest. No statistically significant bilateral differences were observed during the allotment of the modified Risser stages, indicating that either half of the pelvis can be utilized for the age estimation with equal vigour. No significant sex differences were obtained with the grading of age-related iliac crest changes, circumventing the quandary of estimating the sex of fragmented pelvic remains, which is often a prerequisite for accurate age estimation. Regression models derived within the present study garnered stronger correlations with documented age, in comparison with a direct scoring of apophyseal changes for age estimation. Amongst the ten regression models, compound regression models yielded the lowest error rates, even lower than those obtained with the commonly utilized linear and cubic models. Different machine learning approaches garnered further reduced error computations, with Decision Tree Regression furnishing the lowest inaccuracy and RMSE values. A comparative evaluation of inaccuracy and RMSE values obtained with regression analysis and machine learning illustrates the statistical superiority associated with the latter.

Footnotes

Acknowledgements

This research article is a part of an ongoing doctoral research being conducted by the first author (VW) in the Department of Forensic Medicine and Toxicology, All India Institute of Medical Sciences, Jodhpur, India. The PhD scholar is grateful to the University Grants Commission, New Delhi, for awarding the research fellowship (UGC-JRF) for pursuing PhD. The authors are also thankful to the individuals who participated in this study and to the authorities of the institution for allowing them to conduct this research.

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 iDs

Varsha Warrier

Rutwik Shedge

Kewal Krishan

Tanuj Kanchan

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