A Mathematical Model to Predict Pediatric Macrocephaly

Source abstract

Objective: Macrocephaly is defined as a head circumference (HC) above +2 standard deviations (SD) for age and sex, and a value above +3 SD is generally regarded as clinically relevant. Both thresholds are published only as discrete, month-by-month reference tables. This study aimed to reduce the World Health Organization (WHO) upper reference limits of HC to continuous, closed-form functions of age, and to assess how closely such functions reproduce the tabulated values. Methods: The WHO HC-for-age values corresponding to +2 SD and +3 SD for girls and boys (1–60 months) were used. Six regression models were applied separately to each sex and each threshold. The model with the highest coefficient of determination (R²) was selected as the best fit. Results: Logarithmic regression gave the highest R² in all four datasets (R² = 0.996 throughout). For +2 SD, the models were HC = 38.685 + 3.509 × ln (t) for girls and HC = 39.574 + 3.533 × ln (t) for boys. For +3 SD, they were HC = 39.906 + 3.562 × ln (t) for girls and HC = 40.653 + 3.628 × ln (t) for boys, where t is age in months (all p < 0.001). Deviation from the reference was largest in the first three months (up to 0.57 cm) and did not exceed 0.35 cm beyond the first year. Conclusion: The upper limits of HC follow a logarithmic function of age. Expressing them in closed form allows the thresholds to be embedded in radiological reporting software, evaluated at any age without interpolation, and differentiated to obtain the slope of the threshold curve. A lookup table permits none of these directly. Because the largest deviation from the reference, up to 0.57 cm, occurs within the first three months, a borderline value measured on cross-sectional imaging at that age should be confirmed against the table.