Comparative Analysis of Quantile Regression Using GAMLSS and QGAM

This major paper evaluates the accuracy of two statistical modeling techniques for estimating head circumference growth curves across several age groups: Quantile Generalized Additive Models (QGAM) and the Box-Cox Cole and Green (BCCG) distribution. The quantiles (0.01, 0.05, 0.25, 0.5, 0.75, 0.95, and 0.99) of the head circumference distribution and their corresponding confidence intervals, which provide an indication of the degree of uncertainty in the estimations, were used to evaluate the models. The results demonstrate that although QGAM provides greater flexibility at lower quantiles and closely resembles actual data, its confidence intervals greatly expand as quantiles get closer to the extremes, especially above the 95th quantile and below the 5th quantile, suggesting increased uncertainty and possible sensitivity to outliers. On the other hand, BCCG offers more consistent forecasts with smaller confidence intervals across all quantiles but is less adaptable than QGAM. This implies that QGAM might be more likely to overfit at the distribution's extremes. These findings suggest that the quantile range of interest influences the decision between QGAM and BCCG. BCCG offers a more reliable fit at extreme quantiles (both close to 0 and 1) where stability is crucial. On the other hand, the flexibility of QGAM might be useful at intermediate quantiles, where it is crucial to capture minor patterns in growth. To enhance quantile-based growth projections, future studies will investigate hybrid modeling techniques, incorporate more factors, and carry out empirical validation. In addition to providing insightful information for model selection in pediatric growth studies, this work emphasizes the significance of striking a balance between flexibility and stability across quantile ranges to generate trustworthy, data-driven health assessments.