Analyzing differences between microbiome communities using mixture distributions

Abstract

In this paper, we present a method to assess differences between microbiome communities that effectively models sparse count data and accounts for presence-absence bias frequently encountered when zeros are present. We assume that the observed data for each operational taxonomic unit is Poisson generated with the rate for each sample originating from an underlying rate distribution. We propose to model this distribution using a mixture model, specifying the components based on the posterior rate distribution of a count and estimating the optimal weights using a least squares objective function. The distribution incorporates varying resolutions of samples, a point mass for differentiating structural and nonstructural zeros, and a truncation point mass to account for high values that are too sparse to model. As mixture component specification is not always straightforward, a method to estimate a joint model from several mixture distributions using minimum distances of bootstrap iterates is proposed. Once the population rate distribution is approximated, we obtain sample-specific distributions by conditioning on the observed operational taxonomic unit count, resolution, and estimated mixture distribution and then use these to estimate pairwise distances for a permutation test. The method gives an accurate estimate of the true proportion of zeros for presence-absence, effectively models the distribution of low counts using the mixture distribution, and achieves good power for detecting differences in a variety of scenarios. The method is tested using a simulation study and applied to two microbiome datasets. In each case, the results are compared with a number of existing methods.

DCMD: Distance-based classification using mixture distributions on microbiome data

“…The main steps of the model include mixture distribution specification and parameter estimation for modelling observed data, calculation of conditional distributions for each sample, and calculating distances between samples and cluster centres to use in distance-based classification methods. The mixture model and conditional distribution estimation are described in Shestopaloff et al [21]. It is proposed to model the underlying population rate structure of the observed count data using a mixture distribution with Poisson-Gamma components, then conditioning on observed sample counts and resolution to obtain sample-specific distributions.…”

“…We estimate the joint mixture model using a nonparametric bootstrap algorithm. As stated in Shestopaloff et al [21], we can obtain the weight v(l) of each candidate model, which is the proportion of times each model is selected as optimal relative to the observed data, and calculate the weights for the joint mixture distribution. Let w l be the estimated weights for each candidate model, F l , with zeros assigned to the weights of components not included in a specific model, then the weights of the joint model are…”

“…This paper aims to address these problems in a classification framework, where predictors are sparse and heterogeneous count data. Shestopaloff et al [21] proposed representing count data using a mixture distribution to analyze the differences between microbiome communities. We extend the method to distance-based classification using mixture distributions (DCMD) that specifically addresses the uncertainty in sparse and low-count data.…”

Clustering on Human Microbiome Sequencing Data: A Distance-Based Unsupervised Learning Model

“…To deal with the unique characteristics of microbiome data—sparsity with abundant zeros, we incorporate a mixture model proposed by Shestopaloff [ 40 ] to attain the beta diversity measures for partition. The mixture model focuses on the distribution of a single OTU across a population which can address the problem of sparsity between samples.…”

“…The -C CDF norms can be computed by where is a matrix such that represents the two components in the mixture model. See details of the derivation in [ 40 ].…”