Robust Regression with Compositional Covariates

TL;DR

This paper introduces RobRegCC, a robust regression framework for compositional biological data that effectively detects outliers and identifies associations with covariates, demonstrated on microbiome data with theoretical guarantees.

Contribution

The paper presents RobRegCC, a novel robust regression method with outlier detection and sparse modeling for compositional data, extending existing models with new penalties and validation schemes.

Findings

RobRegCC accurately detects outliers in simulated data.

It identifies meaningful microbial associations in HIV microbiome data.

The method provides theoretical guarantees for estimator performance.

Abstract

Many biological high-throughput data sets, such as targeted amplicon-based and metagenomic sequencing data, are compositional in nature. A common exploratory data analysis task is to infer statistical associations between the high-dimensional microbial compositions and habitat- or host-related covariates. We propose a general robust statistical regression framework, RobRegCC (Robust Regression with Compositional Covariates), which extends the linear log-contrast model by a mean shift formulation for capturing outliers. RobRegCC includes sparsity-promoting convex and non-convex penalties for parsimonious model estimation, a data-driven robust initialization procedure, and a novel robust cross-validation model selection scheme. We show RobRegCC's ability to perform simultaneous sparse log-contrast regression and outlier detection over a wide range of simulation settings and provide theoretical non-asymptotic guarantees for the underlying estimators. To demonstrate the seamless applicability of the workflow on real data, we consider a gut microbiome data set from HIV patients and infer robust associations between a sparse set of microbial species and host immune response from soluble CD14 measurements. All experiments are fully reproducible and available on GitHub at https://github.com/amishra-stats/robregcc.