Improved Centile Estimation by Transformation And/Or Adaptive Smoothing of the Explanatory Variable

Area of Science:

• Biostatistics
• Statistical modeling
• Growth curve analysis

Background:

• The Lambda-Mu-Sigma (LMS) method is a standard for growth reference centile estimation.
• It models distribution parameters (location, scale, shape) as smooth functions of an explanatory variable.
• High curvature in these functions can reduce estimation accuracy.

Purpose of the Study:

• To develop and evaluate methods for improving centile estimation accuracy when the LMS method encounters high curvature.
• To provide practical solutions for smoother and better-fitting centiles in growth references.

Main Methods:

• Introduced a transformation method: transforming the explanatory variable (X) to T to reduce curvature before fitting LMS parameters.
• Described three distinct transformations for X.
• Developed an adaptive smoothing method where the smoothing parameter varies with the response variable (Y).
• Utilized simulations to compare the performance of both methods.

Main Results:

• Both transformation and adaptive smoothing methods demonstrated effectiveness in reducing high curvature issues.
• Simulations indicated that these methods lead to substantially smoother and better-fitting centiles compared to standard approaches.
• Case examples illustrated the practical benefits of the proposed methods.

Conclusions:

• The proposed transformation and adaptive smoothing methods offer significant improvements for centile estimation in the presence of high curvature.
• These methods enhance the reliability and accuracy of growth references.
• The findings support the adoption of these techniques for more robust statistical modeling.