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One important problem in microbiome analysis is to identify the bacterial taxa that are associated with a response, where the microbiome data are summarized as the composition of the bacterial taxa at different taxonomic levels. This paper considers regression analysis with such compositional data as covariates. In order to satisfy the subcompositional coherence of the results, linear models with a set of linear constraints on the regression coefficients are introduced. Such models allow regression analysis for subcompositions and include the log-contrast model for compositional covariates as a special case. A penalized estimation procedure for estimating the regression coefficients and for selecting variables under the linear constraints is developed. A method is also proposed to obtain de-biased estimates of the regression coefficients that are asymptotically unbiased and have a joint asymptotic multivariate normal distribution. This provides valid confidence intervals of the regression coefficients and can be used to obtain the $p$-values. Simulation results show the validity of the confidence intervals and smaller variances of the de-biased estimates when the linear constraints are imposed. The proposed methods are applied to a gut microbiome data set and identify four bacterial genera that are associated with the body mass index after adjusting for the total fat and caloric intakes.

Regression analysis with compositional data containing zero values

This study will examine the effect of changes in racial composition of a US county over time on the average life satisfaction of different racial/ethnic groups (White, Black, Asian, Hispanic, Other), with data over the 2008-2017 period.

Objective: The objective of the scoping review is to provide an overview of studies that have used a compositional isotemporal substitution model (CISM) to investigate the modelled effect of reallocating time between different time-use behaviours on health. The three specific objectives of the scoping review will be (1) to review and summarise findings from studies that have applied a CISM to time-use behaviours; (2) describe the study designs, populations, health outcomes, and the time reallocations investigated (duration/s and pattern/s of reallocation); and (3) identify research gaps.

This paper is motivated by the recent interest in the analysis of high dimen- sional microbiome data. A key feature of this data is the presence of `structural zeros' which are microbes missing from an observation vector due to an underlying biological process and not due to error in measurement. Typical notions of missingness are insufficient to model these structural zeros. We define a general framework which allows for structural zeros in the model and propose methods of estimating sparse high dimensional covariance and precision matrices under this setup. We establish error bounds in the spectral and frobenius norms for the proposed esti- mators and empirically support them with a simulation study. We also apply the proposed methodology to the global human gut microbiome data of Yatsunenko (2012).

This paper is motivated by the recent interest in the analysis of high dimen- sional microbiome data. A key feature of this data is the presence of `structural zeros' which are microbes missing from an observation vector due to an underlying biological process and not due to error in measurement. Typical notions of missingness are insufficient to model these structural zeros. We define a general framework which allows for structural zeros in the model and propose methods of estimating sparse high dimensional covariance and precision matrices under this setup. We establish error bounds in the spectral and frobenius norms for the proposed esti- mators and empirically support them with a simulation study. We also apply the proposed methodology to the global human gut microbiome data of Yatsunenko (2012).

The Near Earth Asteroid Rendezvous (NEAR) spacecraft is to orbit the S-class asteroid 433 Eros for about one year beginning on February 14, 2000. The X-ray/gamma-ray O, Mg, Al, Si, Fe, and K; possibly H, Ca, S, Ti, and Th) of Eros with a spatial resolution ranging from a few km for X-rays to approx. 25% of the asteroid's surface for gamma-rays. The major scientific goals for the NEAR XGRS are to relate the composition of Eros to known classes of meteorites, to assess compositional heterogeneity and to identify geological processes that have occurred on the asteroid. Comparing remote-sensing data from asteroids to laboratory data from meteorites requires that the latter be well determined and understood. How well particular classes of meteorites can be identified as analogues of Eros depends not only on the error of the XGRS measurement, but also on the spread in abundances observed among different members of a given meteorite class. To prepare for the return of XGRS data from Eros, we have compiled a large database of bulk elemental compositions of meteorites, using data from a wide variety of published and unpublished sources. Custom software was developed to easily extract statistical information and make plots of data from different meteorite classes. Here, we use the meteorite compositional database to investigate which abundances and abundance ratios, of those measureable by the NEAR XGRS, are most diagnostic for distinguishing meteorite classes and identifying geological processes that have occurred on the samples' parent asteroids.

This article is from Microbiome , volume 2 . Abstract Background: Experimental designs that take advantage of high-throughput sequencing to generate datasets include RNA sequencing (RNA-seq), chromatin immunoprecipitation sequencing (ChIP-seq), sequencing of 16S rRNA gene fragments, metagenomic analysis and selective growth experiments. In each case the underlying data are similar and are composed of counts of sequencing reads mapped to a large number of features in each sample. Despite this underlying similarity, the data analysis methods used for these experimental designs are all different, and do not translate across experiments. Alternative methods have been developed in the physical and geological sciences that treat similar data as compositions. Compositional data analysis methods transform the data to relative abundances with the result that the analyses are more robust and reproducible. Results: Data from an in vitro selective growth experiment, an RNA-seq experiment and the Human Microbiome Project 16S rRNA gene abundance dataset were examined by ALDEx2, a compositional data analysis tool that uses Bayesian methods to infer technical and statistical error. The ALDEx2 approach is shown to be suitable for all three types of data: it correctly identifies both the direction and differential abundance of features in the differential growth experiment, it identifies a substantially similar set of differentially expressed genes in the RNA-seq dataset as the leading tools and it identifies as differential the taxa that distinguish the tongue dorsum and buccal mucosa in the Human Microbiome Project dataset. The design of ALDEx2 reduces the number of false positive identifications that result from datasets composed of many features in few samples. Conclusion: Statistical analysis of high-throughput sequencing datasets composed of per feature counts showed that the ALDEx2 R package is a simple and robust tool, which can be applied to RNA-seq, 16S rRNA gene sequencing and differential growth datasets, and by extension to other techniques that use a similar approach.