Bayesian hierarchical modelling of root canal morphology in mandibular first premolars across 21 countries

Abstract

Background: Understanding root canal morphology is crucial for successful endodontic treatment; however, the anatomy of mandibular first premolars (M1Ps) remains one of the most variable and challenging aspects. The Vertucci classification provides a standardised framework for describing canal configurations; however, population-level data integrating multiple countries are scarce. This study aimed to evaluate the global distribution and determinants of Vertucci canal morphology in M1Ps using a Bayesian hierarchical model.

Methods: Cone-beam computed tomography (CBCT) data of M1Ps from 21 countries were analysed. The Vertucci classification was used as the categorical outcome variable. The predictors included tooth side (34/44), voxel size, field of view (FOV), sex and age, with the country modelled as a random intercept. A Bayesian hierarchical multinomial logistic regression was fitted using the brms package (rstan backend) with weakly informative priors. Posterior estimates were expressed as odds ratios (OR) and 95% credible intervals (CrI), and model-based predicted probabilities were computed for each Vertucci type.

Results: Bayesian modelling estimated the posterior probability of Vertucci Type I configuration at 73.4% (95% CrI: 63.8%-81.5%). Non-Type I configurations showed lower but credible probabilities, including Type V (8.2%, 3.6%-15.9%), Type III (3.7%, 1.6%-7.7%), Type IV (2.9%, 1.2%-6.3%) and Type II (1.3%, 0.5%-3.1%). Unclassified canal patterns accounted for approximately one-tenth of the MnP1s (9.9%, 3.9%-19.2%). Substantial variability was observed between countries for non-Type I and unclassified configurations, whereas Type I remained consistently predominant. Sex and age exerted modest effects, whereas tooth side and field of view showed no meaningful associations. Increasing the voxel size was associated with a slight reduction in the probability of Type I and marginal increases in Type V and unclassified configurations.

Conclusions: Although Vertucci Type I configuration predominates globally in MnP1s, clinically relevant non-Type I and unclassified canal patterns occur with non-negligible frequency and vary across populations. Bayesian hierarchical modelling enables the robust quantification of anatomical heterogeneity and uncertainty, supporting more reliable cross-country comparisons and cautious interpretation of less common canal configurations.