Debiased high-dimensional regression calibration for errors-in-variables log-contrast models

TL;DR

This paper develops a novel calibration method for high-dimensional log-contrast regression models with compositional data, effectively reducing bias and enabling valid statistical inference despite measurement errors.

Contribution

It introduces a new calibration approach for high-dimensional compositional data with measurement errors, establishing asymptotic normality for inference under mild sparsity conditions.

Findings

The method reduces bias in high-dimensional compositional regression.

It achieves accurate confidence interval coverage in microbiome data.

Numerical experiments validate the approach's effectiveness.

Abstract

Motivated by the challenges in analyzing gut microbiome and metagenomic data, this work aims to tackle the issue of measurement errors in high-dimensional regression models that involve compositional covariates. This paper marks a pioneering effort in conducting statistical inference on high-dimensional compositional data affected by mismeasured or contaminated data. We introduce a calibration approach tailored for the linear log-contrast model. Under relatively lenient conditions regarding the sparsity level of the parameter, we have established the asymptotic normality of the estimator for inference. Numerical experiments and an application in microbiome study have demonstrated the efficacy of our high-dimensional calibration strategy in minimizing bias and achieving the expected coverage rates for confidence intervals. Moreover, the potential application of our proposed methodology extends well beyond compositional data, suggesting its adaptability for a wide range of research contexts.