Perturbation-based Analysis of Compositional Data

Existing statistical methods for compositional data analysis are inadequate for many modern applications for two reasons. First, modern compositional datasets, for example in microbiome research, display traits such as high-dimensionality and sparsity that are poorly modelled with traditional 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 existing methods for compositional data, we do not transform the data and instead use perturbations to define interpretable statistical functionals on the compositions themselves, which we call average perturbation effects. These average perturbation effects, which can be employed in many applications, 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 data and demonstrate advantages over existing techniques on US census and microbiome data. For all proposed estimators, we provide confidence intervals with uniform asymptotic coverage guarantees.