On robust estimation of the location parameter

Preclinical mouse models suggest that the gut microbiome modulates tumor response to checkpoint blockade immunotherapy; however, this has not been well-characterized in human cancer patients. Here we examined the oral and gut microbiome of melanoma patients undergoing anti-programmed cell death 1 protein (PD-1) immunotherapy (n = 112). Significant differences were observed in the diversity and composition of the patient gut microbiome of responders versus nonresponders. Analysis of patient fecal microbiome samples (n = 43, 30 responders, 13 nonresponders) showed significantly higher alpha diversity (P < 0.01) and relative abundance of bacteria of the Ruminococcaceae family (P < 0.01) in responding patients. Metagenomic studies revealed functional differences in gut bacteria in responders, including enrichment of anabolic pathways. Immune profiling suggested enhanced systemic and antitumor immunity in responding patients with a favorable gut microbiome as well as in germ-free mice receiving fecal transplants from responding patients. Together, these data have important implications for the treatment of melanoma patients with immune checkpoint inhibitors.

https://science.sciencemag.org/content/sci/early/2017/11/01/science.aan4236.full.pdf

Gut microbiome modulates response to anti–PD-1 immunotherapy in melanoma patients

Current practice in the normalization of microbiome count data is inefficient in the statistical sense. For apparently historical reasons, the common approach is either to use simple proportions (which does not address heteroscedasticity) or to use rarefying of counts, even though both of these approaches are inappropriate for detection of differentially abundant species. Well-established statistical theory is available that simultaneously accounts for library size differences and biological variability using an appropriate mixture model. Moreover, specific implementations for DNA sequencing read count data (based on a Negative Binomial model for instance) are already available in RNA-Seq focused R packages such as edgeR and DESeq. Here we summarize the supporting statistical theory and use simulations and empirical data to demonstrate substantial improvements provided by a relevant mixture model framework over simple proportions or rarefying. We show how both proportions and rarefied counts result in a high rate of false positives in tests for species that are differentially abundant across sample classes. Regarding microbiome sample-wise clustering, we also show that the rarefying procedure often discards samples that can be accurately clustered by alternative methods. We further compare different Negative Binomial methods with a recently-described zero-inflated Gaussian mixture, implemented in a package called metagenomeSeq. We find that metagenomeSeq performs well when there is an adequate number of biological replicates, but it nevertheless tends toward a higher false positive rate. Based on these results and well-established statistical theory, we advocate that investigators avoid rarefying altogether. We have provided microbiome-specific extensions to these tools in the R package, phyloseq.

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Waste not, want not: why rarefying microbiome data is inadmissible.

Datasets collected by high-throughput sequencing (HTS) of 16S rRNA gene amplimers, metagenomes or metatranscriptomes are commonplace and being used to study human disease states, ecological differences between sites, and the built environment. There is increasing awareness that microbiome datasets generated by HTS are compositional because they have an arbitrary total imposed by the instrument. However, many investigators are either unaware of this or assume specific properties of the compositional data. The purpose of this review is to alert investigators to the dangers inherent in ignoring the compositional nature of the data, and point out that HTS datasets derived from microbiome studies can and should be treated as compositions at all stages of analysis. We briefly introduce compositional data, illustrate the pathologies that occur when compositional data are analyzed inappropriately, and finally give guidance and point to resources and examples for the analysis of microbiome datasets using compositional data analysis.

/pdf/microbiome-datasets-are-compositional-and-this-is-not-vqby06h4cq.pdf

Microbiome Datasets Are Compositional: And This Is Not Optional.

Antibiotics administered in low doses have been widely used as growth promoters in the agricultural industry since the 1950s, yet the mechanisms for this effect are unclear. Because antimicrobial agents of different classes and varying activity are effective across several vertebrate species, we proposed that such subtherapeutic administration alters the population structure of the gut microbiome as well as its metabolic capabilities. We generated a model of adiposity by giving subtherapeutic antibiotic therapy to young mice and evaluated changes in the composition and capabilities of the gut microbiome. Administration of subtherapeutic antibiotic therapy increased adiposity in young mice and increased hormone levels related to metabolism. We observed substantial taxonomic changes in the microbiome, changes in copies of key genes involved in the metabolism of carbohydrates to short-chain fatty acids, increases in colonic short-chain fatty acid levels, and alterations in the regulation of hepatic metabolism of lipids and cholesterol. In this model, we demonstrate the alteration of early-life murine metabolic homeostasis through antibiotic manipulation.

Antibiotics in early life alter the murine colonic microbiome and adiposity

UniFrac is a β-diversity measure that uses phylogenetic information to compare environmental samples. UniFrac, coupled with standard multivariate statistical techniques including principal coordinates analysis (PCoA), identifies factors explaining differences among microbial communities. A recent simulation study concluded that UniFrac is unsuitable as a distance metric and should not be used for multivariate analysis (Schloss, 2008). We counter this argument by reassessing the data that led to this conclusion and by providing a mathematical proof showing that UniFrac is a distance metric. However, we confirm with actual sequence data that UniFrac values can be influenced by the number of sequences/sample, and recommend sequence jackknifing (that is, determining how often the cluster results are recovered using random subsets of the data) to avoid this issue.

/pdf/unifrac-an-effective-distance-metric-for-microbial-community-49tbdwjkw4.pdf

UniFrac: an effective distance metric for microbial community comparison

Advances in sequencing technologies have enabled novel insights into microbial niche differentiation, from analyzing environmental samples to understanding human diseases and informing dietary studies. However, identifying the microbial taxa that differentiate these samples can be challenging. These issues stem from the compositional nature of 16S rRNA gene data (or, more generally, taxon or functional gene data); the changes in the relative abundance of one taxon influence the apparent abundances of the others. Here we acknowledge that inferring properties of individual bacteria is a difficult problem and instead introduce the concept of balances to infer meaningful properties of subcommunities, rather than properties of individual species. We show that balances can yield insights about niche differentiation across multiple microbial environments, including soil environments and lung sputum. These techniques have the potential to reshape how we carry out future ecological analyses aimed at revealing differences in relative taxonomic abundances across different samples. IMPORTANCE By explicitly accounting for the compositional nature of 16S rRNA gene data through the concept of balances, balance trees yield novel biological insights into niche differentiation. The software to perform this analysis is available under an open-source license and can be obtained at https://github.com/biocore/gneiss. Author Video: An author video summary of this article is available.

/pdf/balance-trees-reveal-microbial-niche-differentiation-1bbahfbyt0.pdf

Balance Trees Reveal Microbial Niche Differentiation

RNA motifs typically consist of short, modular patterns that include base pairs formed within and between modules. Estimating the abundance of these patterns is of fundamental importance for assessing the statistical significance of matches in genomewide searches, and for predicting whether a given function has evolved many times in different species or arose from a single common ancestor. In this manuscript, we review in an integrated and self-contained manner some basic concepts of automata theory, generating functions and transfer matrix methods that are relevant to pattern analysis in biological sequences. We formalize, in a general framework, the concept of Markov chain embedding to analyze patterns in random strings produced by a memoryless source. This conceptualization, together with the capability of automata to recognize complicated patterns, allows a systematic analysis of problems related to the occurrence and frequency of patterns in random strings. The applications we present focus on the concept of synchronization of automata, as well as automata used to search for a finite number of keywords (including sets of patterns generated according to base pairing rules) in a general text.

Multiple pattern matching: A Markov chain approach

Let (X t ) be a one-dimensional Ornstein-Uhlenbeck process with initial density function f: R + → R + , which is a regularly varying function with exponent -(1 + η), η ∈ (0, 1). We prove the existence of a probability measure v with a Lebesgue density, depending on η, such that for every A E B(R + ): formula math.

Domain of attraction of the quasi-stationary distributions for the Ornstein-Uhlenbeck process

Let S ⊂ {−1, 0, 1}2 \ {(0, 0)}. We address the enumeration of plane lattice walks with steps in S, that start from (0, 0) and remain in the first quadrant {(i, j) : i 0, j 0}. A priori, there are 28 models of this type, but some are trivial. Some others are equivalent to models of walks confined to a half-plane, and can therefore be treated systematically using the kernel method, which leads to a generating function that is algebraic. We focus on the remaining models, and show that there are 79 inherently different ones. To each of the 79, we associate a group G of birational transformations. We show that this group is finite (in fact dihedral, and of order at most 8) in 23 cases, and is infinite in the other 56 cases. We present a unified way of dealing with 22 of the 23 models associated with a finite group. For each, we find the generating function to be D-finite; and in some cases, algebraic. The 23rd model, known as Gessel’s walks, has recently been proved by Bostan et al. to have an algebraic (and hence D-finite) generating function. We conjecture that the remaining 56 models, each associated with an infinite group, have generating functions that are non-D-finite. Our approach allows us to recover and refine some known results, and also to obtain new ones. For instance, we prove that walks with N, E, W, S, SW and NE steps yield an algebraic generating function.

Manuel E. Lladser

Papers

UniFrac: an effective distance metric for microbial community comparison

Balance Trees Reveal Microbial Niche Differentiation

Multiple pattern matching: A Markov chain approach

Domain of attraction of the quasi-stationary distributions for the Ornstein-Uhlenbeck process

Algorithmic Probability and Combinatorics