An investigation into the statistical precision attainable with a distribution-free method of constructing...

Area of Science:

• Biostatistics
• Statistical Methods

Background:

• The distribution-free approach for age-dependent reference centiles (Wellek & Merz, 1995) lacks sample-size planning guidance.
• Previous applications have been in numerous large-scale studies without sample-size optimization.
• This study addresses the gap in sample-size determination for this established method.

Purpose of the Study:

• To investigate sample-size requirements for the distribution-free construction of age-dependent reference centiles.
• To evaluate the efficiency of the distribution-free method compared to quantile regression for reference range determination.
• To provide sample-size recommendations based on precision criteria and Monte Carlo simulations.

Main Methods:

• Utilized the precision criterion (Jennen-Steinmetz & Wellek, 2005; Jennen-Steinmetz, 2014) for sample-size estimation.
• Employed Monte Carlo simulations to determine sample sizes due to the lack of an exact analytical representation.
• Assessed various conditional distributions (symmetric, skewed) and linear relationships between conditional standard deviation and age.

Main Results:

• Sample sizes required are generally within practical limits, comparable to recent large reference-value studies.
• The distribution-free approach demonstrates higher sample-size efficiency compared to quantile regression.
• Efficiency gains are notable across various tested distributions and age-dependent standard deviation models.

Conclusions:

• The distribution-free method for age-dependent reference ranges is sample-size efficient.
• Monte Carlo simulations provide reliable sample-size estimates for this statistical approach.
• The findings support the use of the distribution-free method in future reference range studies.