Enhancement of a Mathematical Model for Predicting Puberty Stage in Boys: A Cross-Sectional Study

Previously, we developed a mathematical model capable of predicting pubertal development (PD) through seven anthropometric variables, with an accuracy of 75%. We believe that it is possible to develop a similar model that uses fewer anthropometric measurements and provides greater precision.

Develop a mathematical model capable of predicting PD through anthropometric variables.

We evaluated the anthropometric profile and PD by medical analysis in 203 boys (Age = 12.6 ± 2.6). Subsequently, we divided the boys into groups: development (n = 121) and cross-validation (n = 82). Data from the development group were subjected to discriminant analysis to identify which anthropometric indicators would be potential predictors of PD. We subsequently developed an equation based on the indicated indicators and tested its validation using data from the cross-validation group.

Discriminant analyses showed that age and sitting-height were the variables with the greatest power to predict PD (p < 0.05). Consequently, the mathematical model was developed: Puberty-score = -17.357 + (0.603 × Age [years]) + (0.127 × Sitting-height [cm]). Based on the scores generated, we classified PD into stage-I (score ≤ -1.815), stage-II (score = -1.816 to -0.605), stage-III (score = -0.606 to 0.695), stage-IV (score = 0.696-3.410), and stage-V (score > 3.410). No differences were found between PD assessments performed by doctors and assessments using the mathematical model (p > 0.5). The prediction model showed high agreement (R ² = 0.867; CCC = 0.899; ICC = 0.900; Kappa = 0.922; α-Krippendorff = 0.885; Bland-Altman LoAs = -2.0, 2.0; pure error = 0.0009) with accuracy of 82.8% and precision of 82%. Analyses in the cross-validation group confirmed the reliability of the prediction model.

The developed mathematical model presents high reliability, validity and accuracy and precision above 80% for determining PD in boys.