Multisample estimation of bacterial composition matrices in metagenomics data

Summary Metagenomics sequencing is routinely applied to quantify bacterial abundances in microbiome studies, where bacterial composition is estimated based on the sequencing read counts. Due to limited sequencing depth and DNA dropouts, many rare bacterial taxa might not be captured in the final sequencing reads, which results in many zero counts. Naive composition estimation using count normalization leads to many zero proportions, which tend to result in inaccurate estimates of bacterial abundance and diversity. This paper takes a multisample approach to estimation of bacterial abundances in order to borrow information across samples and across species. Empirical results from real datasets suggest that the composition matrix over multiple samples is approximately low rank, which motivates a regularized maximum likelihood estimation with a nuclear norm penalty. An efficient optimization algorithm using the generalized accelerated proximal gradient and Euclidean projection onto simplex space is developed. Theoretical upper bounds and the minimax lower bounds of the estimation errors, measured by the Kullback–Leibler divergence and the Frobenius norm, are established. Simulation studies demonstrate that the proposed estimator outperforms the naive estimators. The method is applied to an analysis of a human gut microbiome dataset.

Simulation studies for design selection in a simplex space with edge effects on some mixture components

This work proposes an evaluation – through data simulations – of optimality criteria A and D in mixture designs built from a rotational design, considering a normal model and exploring the edge of zero in parts of simplex components, in addition to the analysis of the use of inverse terms in such components. As a function of the mathematical restrictions imposed on such designs, rotationality is obtained by following a specific algebraic procedure, thus preserving the constant prediction variance in all experimental points. When it comes to mixture problems, a response may show extreme alterations when a part of such components tends to the edge of zero and the models may not be suitable to deal with that. The adequate alternative to deal with such response alterations is to include inverse terms into the models. Given the assessed scenarios, the optimum designs were more robust and more promising than the rotational ones, when evaluating the precision of residual mean squares (RMS) in all such scenarios. When a part of the components tends to the edge of zero, RMS was more precise under the D-optimum designs with inverse terms in the components of the normal lineal model.

Compositional Mediation Analysis for Microbiome Studies

Motivated by recent advances in causal mediation analysis and problems in the analysis of microbiome data, we consider the setting where the effect of a treatment on an outcome is transmitted through perturbing the microbial communities or compositional mediators. Compositional and high-dimensional nature of such mediators makes the standard mediation analysis not directly applicable to our setting. We propose a sparse compositional mediation model that can be used to estimate the causal direct and indirect (or mediation) effects utilizing the algebra for compositional data in the simplex space. We also propose tests of total and component-wise mediation effects using bootstrap. We conduct extensive simulation studies to assess the performance of the proposed method and apply the method to a real metagenomic dataset to investigate the effect of fat intake on body mass index mediated through the gut microbiome composition.