A probability model for estimating age in young individuals relative to key legal thresholds: 15, 18 or 21-year

Abstract

Age estimations are relevant for pre-trial detention, sentencing in criminal cases and as part of the evaluation in asylum processes to protect the rights and privileges of minors. No current method can determine an exact chronological age due to individual variations in biological development. This study seeks to develop a validated statistical model for estimating an age relative to key legal thresholds (15, 18, and 21 years) based on a skeletal (CT-clavicle, radiography-hand/wrist or MR-knee) and tooth (radiography-third molar) developmental stages. The whole model is based on 34 scientific studies, divided into examinations of the hand/wrist (15 studies), clavicle (5 studies), distal femur (4 studies), and third molars (10 studies). In total, data from approximately 27,000 individuals have been incorporated and the model has subsequently been validated with data from 5,000 individuals. The core framework of the model is built upon transition analysis and is further developed by a combination of a type of parametric bootstrapping and Bayesian theory. Validation of the model includes testing the models on independent datasets of individuals with known ages and shows a high precision with separate populations aligning closely with the model's predictions. The practical use of the complex statistical model requires a user-friendly tool to provide probabilities together with the margin of error. The assessment based on the model forms the medical component for the overall evaluation of an individual's age.

Keywords: Age distribution; Bayesian theorem; Biological variation; Forensic anthropology; Population; Validation study.

Fig. 1

Probability density functions. Age distributions for hand/wrist, third molar, distal femur and clavicle stages for male (a-d) and female (e–h) individuals in terms of density of developmental stage hand/wrist skeletal age 14–19 and 13.5–18 respectively (Greulich & Pyle) (a and e), third molar stage C-H (Demirjian) (b and f), distal femur reached final stage or not (Krämer) (c and g) and clavicle stage 1–5 (Schmeling) (d and h)

Fig. 2

Probability density functions for combinations. Age distributions for selected combinations in terms of density of developmental stages for distal femur in combination with third molar (males) (a), hand/wrist in combination with third molar (males) (b), hand/wrist in combination with third molar (females) (c), and clavicle in combination with third molar (females) (d). Red dotted line represents age thresholds of interest

Fig. 3

Validation of the third molar model Validation of the third molar model. Distribution of the full validation dataset and the separate studies are shown for males (a) and females (b). Point plots displaying the chronological age and corresponding Demirjian development stage of the third molar together with classification with regard to the 15-or 18- year threshold for males ((c) and (e)) and females ((d) and (f)). Grey bars in (c-f) represents the 95% PI for each development stage. The proportion in the validation set (full line) being under 15(orange) or 18 (blue) for each development stage together with the predicted probability according to the statistical model (dashed lines) for males (g) and females (h). The proportion of the validation set being correctly classified (g-h) with regard to the 15-year threshold (light grey bar) and the 18-year threshold (dark grey bar) is displayed for each development stage for males (g) and females (h)

Fig. 4

Validation of the hand/wrist model. Distribution of the full validation dataset and the separate studies for males(a) and females(b). Point plots displaying the chronological age and corresponding G&P development stage of hand/wrist together with classification with regard to the 15- or 18- year threshold for males (c) and (e) and females (d) and (f). Grey bars in (c-f) represents the 95% PI for each development stage in the model. The proportion in the validation set (full line) being under 15 (orange) or 18 (blue) for each development stage together with the predicted probability according to the statistical model (dashed lines) for males (g) and females (h). The proportion of the validation set being correctly classified with regard to the 15-year threshold (light grey bar) and the 18-year threshold (dark grey bar) displayed for each development stage in the model for males (g) and females (h)

Fig. 5

Validation of the distal femur model. Distribution of the full validation dataset for males (a) and females(b). Point plots displaying the chronological age and corresponding dichotomous development stage of the distal femur together with classification with regard to the 18-year threshold for males (c) and females (d). Grey bars in (c-f) represents the 95% PI for each development stage in the model. The proportion in the validation set (full line) being under 18 (blue) for the development stages together with the predicted probability according to the statistical model (dashed lines) for males (e) and females (f). The proportion of the validation set being correctly classified with regard to the 18-year threshold (dark grey bar) displayed for the two development stages for males (e) and females (f)

Fig. 6

Validation of the clavicle model. Distribution of the full validation dataset for males (a) and females(b). Point plots displaying the chronological age and corresponding dichotomous development stage of the clavicle together with classification with regard to the 18- and 21- year threshold for males (c) and females (d). Grey bars in (c-f) represents the 95% PI for each development stage in the model. The proportion in the validation set (full line) being under 18 (blue) or 21 (orange) for the development stages together with the predicted probability according to the statistical model (dashed lines) for males (e) and females (f). The proportion of the validation set being correctly classified with regard to the 18-(grey bar) or 21-year threshold (dark grey bar) displayed for the five development stages for males (e) and females (f)