Enhancement of a Mathematical Model for Predicting Puberty Stage in Boys: A Cross‐Sectional Study
Bibliographic record
Abstract
ABSTRACT Background 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. Objective Develop a mathematical model capable of predicting PD through anthropometric variables. Methods 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. Results 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. Conclusion The developed mathematical model presents high reliability, validity and accuracy and precision above 80% for determining PD in boys.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".