A comparison of methods for analysing compositional data with fixed and variable totals: a simulation study using the...

Area of Science:

• Statistics
• Biostatistics
• Data Science

Background:

• Compositional data represent parts of a whole, with either fixed or variable totals.
• Existing analysis methods include isocaloric/isotemporal models, ratio variables, and compositional data analysis (CoDA).
• Previous comparisons relied on real data, limiting understanding of true model performance.

Purpose of the Study:

• To evaluate and compare the performance of different compositional data analysis approaches using simulations.
• To investigate how parameterization matching influences model accuracy under various conditions.
• To assess the impact of fixed versus variable totals on analysis outcomes.

Main Methods:

• Simulated physical activity (fixed total) and dietary (variable total) data.
• Employed linear, log2, and isometric log-ratio relationships between components and an outcome (fasting plasma glucose).
• Evaluated generalized linear/additive models and CoDA for 1-unit and larger reallocations (10- or 100-unit).

Main Results:

• Model performance is contingent on the parameterization aligning with the data-generating process.
• Incorrect parameterization leads to more severe errors with larger reallocations and variable totals.
• Ratio variable models, equivalent to linear models for fixed totals, diverge significantly for variable totals.

Conclusions:

• Compositional data with fixed and variable totals exhibit distinct behaviors.
• All analytical approaches have utility but require careful selection based on data characteristics.
• Investigate the relationship shape and choose the analytical method that best matches it.