The present study showed that ML classification models based on the extended set of cranial measurements in the modern Croatian population could estimate the sex of the unknown skull with 95% accuracy. Those measurements can be easily obtained and do not require additional landmarking out of those included in standard cranial measurements44. Using this approach, calculating all possible combinations of interlandmark distances, and carefully selecting relevant variables and classification models in the ML framework, we increased accuracy compared to the standard approach. Further, in contrast to most ML-based studies that do not include direct model application37,45,46, we provided a web app that can be used to apply best models directly in forensic practice and enable further validation studies.
When considering standard measurements and employing traditional classification models (LR and LDA) without any adjustment, we obtained accuracies of 0.86 and 0.88. This aligns with previous studies where even complete cranium was not a good sex indicator, with accuracies ranging from 82–91%25,27,32. However, when including more classification models, applying hyperparameter tuning, using RFE to select relevant features, and excluding some variables with regional specificities, we could increase the accuracy up to 0.93 with the SVM model, and we constructed one trivariate LR model with accuracy of 0.90 that could be employed even on incomplete crania. This accuracy level overperforms studies that construct the models in the traditional way31,35,47–49, and it is comparable to the studies that used a more advanced ML approach where accuracies without raising decision thresholds (and excluding part of the individuals) ranged from 88–90%45,46,50.
The second approach, which employed 946 interlandmark distances, was not more time-consuming regarding data acquisition as non-standard measurements were automatically obtained as interlandmark distances from the same landmarks used to construct standard ones. At first, accuracy using all the variables was higher but did not exceed 0.93, even after hyperparameter tuning. When we excluded region-specific variables or highly correlated variables and applied RFE to select relevant variables, we obtained two models (one LR and one LDA) for which all classification performance indicators were at least 0.95, which was previously only possible when raising pp thresholds and considering part of the specimens as unidentified45. The only studies that used more inter-landmark distances (n = 1081) were those of Toneva et al. conducted on the modern Bulgarian population37,46. However, these studies included some non-standard landmarks44,51, which hampers the practical use. The first study that employed rule-based classification algorithms (JRIP, Ridor, and J48) along with feature selection techniques (BestFirst and GeneticSearch) achieved a maximum accuracy of 0.9246. The second study on a similar dataset structure employed LR, ANN, and LR over the differently selected features and provided accuracies greater than 0.9537. However, in contrast to our study, the results remained on the prototype level; they were not validated on the independent test sample and were not provided within the infrastructure that would enable practical model implementation or further validations.
When considering state-of-the-art anthropological studies that use the most advanced methods like deep learning and image analysis, it is evident that they outperform described methods based on traditional landmarking and linear measurements. For example, Kondu et al. achieved an accuracy of 93% when using 3D skull images39 and 95% when using 2D lateral images52 but did not provide possibilities for application and validation. Although their approach gave forensically relevant results, similar to our study, the disadvantage, compared to our research, could be their complexity and harder interpretability.
One of the important findings in our study was the importance of variable selection and application of field-specific knowledge. It is reflected in a correlation of cranial dimensions as well as the cognizance of regional differences demonstrated in previous studies26,53,54 in a relatively small and closed population of Croatia. It helped us remove region-specific features that could negatively affect the classification performances and reduce the number of features so we could employ advanced methods to select features and maximize accuracy. Our study used RFE to identify the best variables, considering all the feature numbers and combinations within different classification models and hyperparameters used to maximize the accuracy. This enabled us to identify the best classification models, maximize accuracy up to 0.96, and probably reduce the impact of non-homogenous variables that could not be captured in the previous steps. This could be especially important for the cranium, which, in contrast to most of the postcranial skeleton, has more complex structures that are also more sensitive to population differences55. So, we recommend testing this approach when developing non-population-specific anthropological standards on samples of different backgrounds to increase the accuracy and minimize the impact of population differences.
It is important to highlight that we did not apply statistical model comparison considering AUC, ROC, or similar metrics as they were not relevant in our case, especially as we obtained models that have less than 5% error; instead, we used PPV and NPV. They were chosen for final model selections because they directly reflect the probability of correct classification decisions in practical forensic scenarios. PPV indicates the likelihood that individuals classified into a specific category (e.g., male or female) are correctly identified. NPV provides insight into the accuracy of excluding individuals from a specific category, ensuring that the model reliably identifies when subjects do not belong to a particular group. Given the critical nature of forensic work, where the cost of misclassification extends beyond statistical inaccuracies to real-world implications56, these metrics offer a more relevant and practical assessment of model performance than traditional metrics like AUC and ROC in our study’s context. The choice of the best model for sex estimation was not focused on the statistical superiority of one model over another but on finding a model that offers high accuracy, interpretability, and practical applicability for end users. Our results might imply that when dealing with linear measurements, selecting more complex models is as important as feature selection and hyperparameter tuning, which is rarely done in forensic anthropological studies.
This study was performed on a Croatian population sample, so the results may not be generalizable to other populations. To overcome this limitation, we provided a web application that enables validation of our model on different populations. This application can also overcome model complexity for practical applications since users can directly upload files with landmarks.
Although this study does not aim to prove that certain classification models are optimal for bone measurement analysis, we wanted to demonstrate how forensic anthropology could benefit when combining ML and field knowledge and how ML can provide proof of concepts, theoretical modes, and practical implications. In that sense, with available technologies and tools based on LLM and artificial intelligence, it might not be justifiable anymore to apply basic classification models without adjustments and to generalize that particular measurements of skeletal parts perform better or worse in classifying sex.