Development of Gender- and Age-Specific Ponderal Index (PI)Percentile Curves Using Quantile Regression (QR) in Pakistan

Abstract

Background: Accurate assessment of human growth and nutritional status is critical for early detection of malnutrition, over nutrition, and metabolic disorders. Traditional anthropometric indices such as Body Mass Index (BMI) have recognized limitations, particularly in pediatric and ethnically diverse populations, necessitating the development of more sensitive and population-specific measures. The Ponderal Index (PI), which normalizes body mass relative to height cubed, offers a potentially superior metric for evaluating proportionality, especially in neonates and children. However, population specific growth references for PI are lacking in Pakistan, where unique growth patterns influenced by genetic, environmental, and socioeconomic factors prevail.

Objectives: This study aims to develop gender- and age-specific percentile reference curves for PI in the Pakistani population utilizing advanced statistical modelling techniques, specifically quantile regression, to accurately characterize the distributional properties across the lifespan. The primary objectives include establishing normative standards, comparing the performance of different percentile estimation methods, and validating the utility of PI as a growth and health risk indicator.

Methods: A cross-sectional, nationally representative sample of approximately 10,000 apparently healthy Pakistani individuals aged 2 years to over 60 years was recruited via multistage stratified random sampling across diverse geographic, socioeconomic, and ethnic strata. Anthropometric measurements including weight and height were obtained following standardized protocols, and PI was calculated as body weight (kg) divided by height (m) cubed. Data quality assurance involved double data entry, validation, and outlier management. Descriptive analyses characterized the distribution of PI across subgroups. Separate gender-specific quantile regression models were fitted for key percentiles (5th, 10th, 25th, 50th, 75th, 85th, 90th, 95th), incorporating fractional polynomial transformations of age to capture non-linear growth trajectories. Model selection was guided by AIC, BIC, residual diagnostics, and bootstrap validation to ensure robustness. Normative percentile curves were generated and visually depicted for clinical and epidemiological applications.

Results: The dataset exhibited a right-skewed distribution of PI, with mean values of 14.80 (SD=3.57) overall, and significant gender differences females demonstrating higher PI than males across all age groups (p<0.001). PI peaked during early childhood (mean =18.75 at 2–5 years) and declined progressively with age, with distinct sex-specific trajectories. Quantile regression (QR) models revealed non-linear, heteroscedastic relationships between age and PI, with polynomial and fractional polynomial terms providing optimal fit. The generated percentile curves demonstrated a characteristic decline in PI during adolescence, stabilization in early adulthood, and gradual reduction thereafter, with females consistently maintaining higher proportionality indices. Validation procedures confirmed the models' predictive accuracy, stability, and applicability.

Conclusions: The study successfully establishes comprehensive, gender- and age-specific percentile standards for PI in the Pakistani population using robust QR techniques. These population-specific growth references offer enhanced sensitivity over traditional indices for early identification of growth abnormalities, nutritional deficiencies, and metabolic risks. Implementation of these standards in clinical practice and public health monitoring can improve individualized growth assessment, facilitate early intervention, and inform health policy tailored to Pakistan’s demographic needs. Future longitudinal studies are recommended to validate the predictive utility of PI percentiles for metabolic and non-communicable disease outcomes.