Perturbation-based Effect Measures for Compositional Data

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. We show how average perturbation effects can be estimated efficiently by deriving a perturbation-dependent reparametrization and applying semiparametric estimation techniques. We analyze the proposed estimators empirically on simulated and semi-synthetic data and demonstrate advantages over existing techniques on data from New York schools and microbiome data.