Perturbation-based Effect Measures for Compositional Data

Existing effect measures for compositional features are inadequate for many modern applications for two reasons. First, modern datasets with compositional covariates, for example in microbiome research, display traits such as high-dimensionality and sparsity that can be poorly modelled with traditional parametric approaches. Second, assessing -- in an unbiased way -- how summary statistics of a composition (e.g., racial diversity) affect a response variable is not straightforward. In this work, we propose a framework based on hypothetical data perturbations that addresses both issues. Unlike many existing effect measures for compositional features, we do not define our effects based on a parametric model or a transformation of the data. Instead, we use perturbations to define 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. For all proposed estimators, we provide confidence intervals with uniform asymptotic coverage guarantees.