A Numerical Method for Estimating the Variance of Age at Maximum Growth Rate in Growth Models

Area of Science:

• Human growth and development
• Biostatistics
• Childhood and adolescent health

Background:

• Age at peak height velocity (PHV) is a key indicator for predicting adulthood outcomes.
• Growth models, like the triple logistic function, are used to estimate PHV from stature data.
• Uncertainty in growth model parameters leads to uncertainty in PHV age estimation, requiring accounting in predictive models.

Purpose of the Study:

• To develop and validate a numerical method for estimating the variance of age at peak height velocity (PHV) for non-linear growth functions.
• To address the lack of explicit variance formulas for commonly used growth models like the triple logistic function.
• To demonstrate the utility of incorporating estimated PHV age variance into subsequent statistical modeling.

Main Methods:

• A numerical method was implemented to estimate the variance of the age at PHV.
• The accuracy of the numerical method was validated against models with existing explicit solutions for variance.
• The method was applied to Fels study growth data for estimating PHV age variance.

Main Results:

• The numerical method provides a reliable way to estimate the variance of age at PHV.
• The estimated variances were successfully used as weights in modeling two adulthood outcomes.
• This approach enhances the accuracy of predictive models that utilize PHV age.

Conclusions:

• The developed numerical method effectively estimates the variance in age at peak height velocity (PHV).
• Incorporating this variance improves the accuracy of statistical models predicting adulthood outcomes from growth data.
• This method offers a practical solution for handling uncertainty in PHV age estimation within growth research.