Using Cross-Validation to Find the Optimal Polynomial Model for Pediatric Anthropometric Time-Series Data

Abstract 496

Background: A single function describing the distribution of growth parameters in children is desirable for clinical and population studies. However, such a function needs to avoid being too specific for the population sampled. Our objective was to find the optimal polynomial modeling the distribution of pediatric anthropometric parameters.

Methods: Program was created in Matlab. Using cross-validation and testing models by calculating squared-error, the program finds the optimal model that best fits the training data without over-fitting. Tested models ranged from first-order (linear) to 11th order polynomials; error decreases as models fit better, then increases with over-fitting, as shown in figure.

Fig 1

Distribution of Height Velocities in Males with Constitutional Delay

This was used to model the distribution of arm-span and height velocities over age from data collected in an endocrinology clinic in a large children's hospital between 1992 and 1998. Inclusion criteria were all patients over age 4 years diagnosed with constitutional-delay with consecutive encounters 120 to 365 days apart. Annualized velocities were calculated and outliers were removed in an automated manner.

Results: 33 male and 14 female arm-span velocities and 224 male and 94 female height velocities were calculated. The optimal polynomial model for the distribution of male arm velocities was 3rd order and female was 2nd order; optimal for male height velocities was 7th order and female was 4th order.

Conclusion: Using cross-validation to find the optimal function is an effective way to find an accurate, but not over-fit, model for pediatric anthropometric time-series data. Future research will involve comparisons between these models.