Perturbation-based Effect Measures for Compositional Data

Understand

Existing effect measures for compositional features are inadequate for many modern applications, for example, in microbiome research, since they display traits such as high-dimensionality and sparsity that can be poorly modelled with traditional parametric approaches.

• Further, assessing -- in an unbiased way -- how summary statistics of a composition (e.g., racial diversity) affect a response variable is not straightforward.
• We propose a framework based on hypothetical data perturbations which defines interpretable statistical functionals on the compositions themselves, which we call average perturbation effects.
• These effects naturally account for confounding that biases frequently used marginal dependence analyses.