Generalized lambda distribution for flexibly testing differences beyond the mean in the distribution of a dependent...

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Conventional statistical methods often focus on single distribution parameters, typically the mean, and rely on specific distributional assumptions.
• These assumptions may be violated, and parameters beyond the mean can be of significant interest.

Purpose of the Study:

• To introduce a flexible statistical approach using the generalized lambda distribution (GLD) for comparing entire continuous outcome distributions.
• To develop and demonstrate a likelihood ratio test for differences in multiple distribution parameters, including central tendency, dispersion, asymmetry, and steepness.

Main Methods:

• Application of the generalized lambda distribution (GLD) to model continuous outcomes.
• Development of a likelihood ratio test to assess differences in multiple parameters of a distribution.
• Testing for differences in body mass index (BMI) distribution parameters across education categories using the Health and Retirement Study data.

Main Results:

• The proposed GLD-based method detected significant differences in at least one BMI distribution parameter by education category in both a complete dataset (N=13,571, P<0.001) and a smaller, lower-power resampled dataset (N=300 per category, P=0.044).
• A similar analysis using a normal distribution alternative showed significant differences in the complete dataset (P<0.001) but not the smaller dataset (P=0.968).
• The GLD method successfully identified which specific BMI parameters differed significantly across education levels in both datasets.

Conclusions:

• The developed method offers a flexible statistical approach to compare the entire distribution of variables.
• This approach can supplement conventional methods that often have unmet assumptions and focus narrowly on a single parameter.