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Additional file 1. Summplementary methods.

Supplemental Table 2

Additional file 2. Supplementary Table 1. The log fold change (LFC) of absolute abundances for differentially abundant families (A), (B), (C), (D), (E). *The taxon was declared to be significant since the absolute abundance in the reference group (Time to Develop AIDS > 10 Years) was zero. **NE: not evaluable. Supplementary Table 2. The log fold change (LFC) of absolute abundances for differentially abundant genera (A), (B), (C), (D), (E). *The taxon was declared to be significant since the absolute abundance in the group of interest (Time to Develop AIDS < 5 Years) was zero. **NE: not evaluable. Supplementary Table 3. The log fold change (LFC) of absolute abundances for differentially abundant families (A), (B), (C), (D), (E). *The taxon was declared to be significant since the absolute abundance in the group of interest (Time to Develop AIDS 5 - 10 Years) was zero. **NE: not evaluable. ***The taxon was declared to be significant since the absolute abundance in the reference group (Time to Develop AIDS > 10 Years) was zero.

Supplemental Figure 2. Adjusted associations of second trimester maternal thyroid and placental hCGalpha with expression and receptive communication measured by the Bayley’s Scales at 1 year of age. The x and y axis variables are labeled for each plot. The black lines and gray shaded areas represent the modeled association and 95% confidence intervals, adjusted for confounding. The black dots represent the observed unadjusted values, not controlled for confounders.

Supplemental Figure 1

Supplemental Table 3

BACKGROUND:Early disruption of the microbial community may influence life-long health. Environmental toxicants can contaminate breast milk and the developing infant gut microbiome is directly exposed. We investigated whether environmental toxicants in breastmilk affect the composition and function of the infant gut microbiome at 1month. We measured environmental toxicants in breastmilk, fecal short-chain fatty acids (SCFAs), and gut microbial composition from 16S rRNA gene amplicon sequencing using samples from 267 mother-child pairs in the Norwegian Microbiota Cohort (NoMIC). We tested 28 chemical exposures: polychlorinated biphenyls (PCBs), polybrominated flame retardants (PBDEs), per- and polyfluoroalkyl substances (PFASs), and organochlorine pesticides. We assessed chemical exposure and alpha diversity/SCFAs using elastic net regression modeling and generalized linear models, adjusting for confounders, and variation in beta diversity (UniFrac), taxa abundance (ANCOM), and predicted metagenomes (PiCRUSt) in low, medium, and high exposed groups. RESULTS:PBDE-28 and the surfactant perfluorooctanesulfonic acid (PFOS) were associated with less microbiome diversity. Some sub-OTUs of Lactobacillus, an important genus in early life, were lower in abundance in samples from infants with relative "high" (> 80th percentile) vs. "low" (

Table S1. Characteristics of NoMIC current study population, full cohort and general population of birth-giving mothers in Norway. Table S2. Distribution of diversity measures and short-chain fatty acids in infant fecal samples at 1 month. Table S3. Greengenes lineage for deblurred FASTA sequences. Table S4. Differentially abundant taxa in the high (>80th percentile) vs. low (

Large spatial datasets are typically modelled through a small set of knot locations; often these locations are specified by the investigator by arbitrary criteria. Existing methods of estimating the locations of knots assume their number is known a priori, or are otherwise computationally intensive. We develop a computationally efficient method of estimating both the location and number of knots for spatial mixed effects models. Our proposed algorithm, Threshold Knot Selection (TKS), estimates knot locations by identifying clusters of large residuals and placing a knot in the centroid of those clusters. We conduct a simulation study showing TKS in relation to several comparable methods of estimating knot locations. Our case study utilizes data of particulate matter concentrations collected during the course of the response and clean-up effort from the 2010 Deepwater Horizon oil spill in the Gulf of Mexico.

BackgroundThere is mounting evidence for a connection between the gut and Parkinson's disease (PD). Dysbiosis of gut microbiota could explain several features of PD.ObjectiveThe objective of this study was to determine if PD involves dysbiosis of gut microbiome, disentangle effects of confounders, and identify candidate taxa and functional pathways to guide research.MethodsA total of 197 PD cases and 130 controls were studied. Microbial composition was determined by 16S rRNA gene sequencing of DNA extracted from stool. Metadata were collected on 39 potential confounders including medications, diet, gastrointestinal symptoms, and demographics. Statistical analyses were conducted while controlling for potential confounders and correcting for multiple testing. We tested differences in the overall microbial composition, taxa abundance, and functional pathways.ResultsIndependent microbial signatures were detected for PD (P = 4E-5), participants' region of residence within the United States (P = 3E-3), age (P = 0.03), sex (P = 1E-3), and dietary fruits/vegetables (P = 0.01). Among patients, independent signals were detected for catechol-O-methyltransferase-inhibitors (P = 4E-4), anticholinergics (P = 5E-3), and possibly carbidopa/levodopa (P = 0.05). We found significantly altered abundances of the Bifidobacteriaceae, Christensenellaceae, [Tissierellaceae], Lachnospiraceae, Lactobacillaceae, Pasteurellaceae, and Verrucomicrobiaceae families. Functional predictions revealed changes in numerous pathways, including the metabolism of plant-derived compounds and xenobiotics degradation.ConclusionPD is accompanied by dysbiosis of gut microbiome. Results coalesce divergent findings of prior studies, reveal altered abundance of several taxa, nominate functional pathways, and demonstrate independent effects of PD medications on the microbiome. The findings provide new leads and testable hypotheses on the pathophysiology and treatment of PD. © 2017 International Parkinson and Movement Disorder Society.

Differential abundance detection false discovery rate with varied library sizes that are approximately even on average between groups. An expanded Fig. 5. (PDF 40 kb)

There are many applications in which a statistic follows, at least asymptotically, a normal distribution with a singular or nearly singular variance matrix. A classic example occurs in linear regression models under multicollinearity but there are many more such examples. There is well-developed theory for testing linear equality constraints when the alternative is two-sided and the variance matrix is either singular or non-singular. In recent years there is considerable, and growing, interest in developing methods for situations in which the estimated variance matrix is nearly singular. However, there is no corresponding methodology for addressing one-sided, i.e., constrained or ordered alternatives. In this paper we develop a unified framework for analyzing such problems. Our approach may be viewed as the trimming or winsorizing of the eigenvalues of the corresponding variance matrix. The proposed methodology is applicable to a wide range of scientific problems and to a variety of statistical models in which inequality constraints arise. We illustrate the methodology using data from a gene expression microarray experiment obtained from the NIEHS' Fibroid Growth Study.

Comparison of common distance metrics and normalization methods when low-coverage samples are excluded. The right axis represents the median library size (NL), while the x-axis effect size is the multinomial mixing proportions of the two classes of samples, ocean and feces. For rarefying, samples below the 15th percentile of library size were dropped from the analysis. See caption for Fig. 2 for further details. (PDF 432 kb)

Pseudocount addition to avoid zero increases FDR. The same data as Fig. 7. a Uneven library sizes, FDR p

Pseudocount addition to avoid zero increases FDR. The same data as Fig. 7. a Uneven library sizes, FDR p

Statistical supplement: statistical details of simulation studies. (DOCX 119 kb)

Differential abundance detection sensitivity with varied library sizes that are approximately even on average between groups. Label the same as Fig. 4, but with more effect sizes. (PDF 44 kb)

Simple example of the reasoning behind differential abundance simulations. a In actual OTU tables generated from sequencing data, the counts (left column) are already compositional and therefore only relative. Application of a constant multiplier to the original multinomial template to create fold-change differences disturbs the distinction between true positive (TP) and true negative (TN) OTUs in the original simulation, but not the balanced simulation. b Creation of compositional data from the multinomial template. The sum constraint that occurs when a researcher samples from the environment can cause, e.g., unchanged OTUs to appear changed in an OTU table. (PDF 199 kb)

Differential abundance detection sensitivity with varied library sizes that are approximately even on average between groups. Label the same as Fig. 4, but with more effect sizes. (PDF 44 kb)

Simple example of the reasoning behind differential abundance simulations. a In actual OTU tables generated from sequencing data, the counts (left column) are already compositional and therefore only relative. Application of a constant multiplier to the original multinomial template to create fold-change differences disturbs the distinction between true positive (TP) and true negative (TN) OTUs in the original simulation, but not the balanced simulation. b Creation of compositional data from the multinomial template. The sum constraint that occurs when a researcher samples from the environment can cause, e.g., unchanged OTUs to appear changed in an OTU table. (PDF 199 kb)

Microarray gene expression data are extremely noisy. Normalization is widely regarded as an essential step before data analysis to remove systematic variations while maintaining biological signals of interest. However, the choice of normalization may substantially impact the detection of rhythmic genes in oscillatory systems. We introduce a rhythmicity measure and a bootstrap methodology to detect rhythmic genes robust with respect to the normalization choice. MINECO grant MTM2015-71217-R Ministerio de Educación, Cultura y Deporte grant FPU14/04534

Differential abundance detection false discovery rate with varied library sizes that are approximately even on average between groups. An expanded Fig. 5. (PDF 40 kb)

Comparison of common distance metrics and normalization methods when low-coverage samples are excluded. The right axis represents the median library size (NL), while the x-axis effect size is the multinomial mixing proportions of the two classes of samples, ocean and feces. For rarefying, samples below the 15th percentile of library size were dropped from the analysis. See caption for Fig. 2 for further details. (PDF 432 kb)

High-throughput microarray technologies are a widely used research tool in gene expression analysis. A large variety of preprocessing methods for raw intensity measures is available to establish gene expression values. Normalization is the key stage in preprocessing methods, since it removes systematic variations in microarray data. Then, the choice of the normalization strategy can make a substantial impact to the final results. Additionally, we have observed that the identification of rhythmic circadian genes depends not only on the normalization strategy but also on the rhythmicity detection algorithm employed. We analyze three different rhythmicity detection algorithms. On the one hand, JTK and RAIN which are widely extended among biologists. On the other hand, ORIOS, a novel statistical methodology which heavily relies on Order Restricted Inference and that we propose to detect rhythmic signal for Oscillatory Systems. Results on the determination of circadian rhythms are compared using artificial microarray data and publicly available circadian data bases.

Applications of circular regression models appear in many different fields such as evolutionary psychology, motor behavior, biology, and, in particular, in the analysis of gene expressions in oscillatory systems. Specifically, for the gene expression problem, a researcher may be interested in modeling the relationship among the phases of cell-cycle genes in two species with differing periods. This challenging problem reduces to the problem of constructing a piecewise circular regression model and, with this objective in mind, we propose a flexible circular regression model which allows different parameter values depending on sectors along the circle. We give a detailed interpretation of the parameters in the model and provide maximum likelihood estimators. We also provide a model selection procedure based on the concept of generalized degrees of freedom. The model is then applied to the analysis of two different cell-cycle data sets and through these examples we highlight the power of our new methodology., Ministerio de Ciencia e Innovación grant (MTM2012-37129), Junta de Castilla y León, Consejería de Educación and the European Social Fund, Intramural Research Program of the National Institute of Environmental Health Sciences (NIEHS) [Z01 ES101744-04]

Supplementary Materials. Section S1. The mathematical notations and definitions used in the paper are described in this section. The hypotheses tested in different steps of the testing procedure are formulated and interpreted. Section S2. The mathematical proof of the theorem that states that the general testing algorithm controls mdFDR. Section S3. The details of the statistical methodology developed for the testing and analysis of the FGS microarray data. Section S4. The supplementary results for the simulation study performed to evaluate the power of the developed statistical methodology compared to several other competing methods. (PDF 270 kb)

This work is motivated by a problem encountered in Molecular Biology where researchers are interested in correlating angular data from two oscillatory systems. The observations are the time to peak expression (also known as phase angle) of periodic genes under two different conditions (dose levels, organs or even species). In particular, we deal here with expression data from genes participating in the cell-cycle. Cell-biologists are often interested in drawing inferences regarding the phase angle of cell-cycle genes since they are considered to be associated with the gene’s biological function (Jensen et al 2006).

In recent years there has been considerable interest in drawing inferences regarding order relationships among angular parameters. In particular, in biology the interest is to understand genes participating in cell cycle across multiple species and whether they are functionally conserved. The time to peak expression, known as phase angle, of such a gene can be mapped onto a unit circle. Biologists are not only interested in estimating the phase angles but in determining the relative order of expression of various genes. The final aim is to know whether the order of peak expression among cell cycle genes is conserved evolutionarily across species. These questions are challenging due to large variability among studies and to the circular nature of the data. A methodology to find the underlying circular order in a population is presented. We also propose a solution for the problem of testing equality of circular orders among two or more populations. Unbalanced samples and differences in distributions are taken into consideration. The proposed methodology is illustrated by analyzing data sets from three species: Schizosaccharomyces Pombe, Schizosaccharomyces Cerevisiae and Humans. As a result a set of genes is presented where the circular order is conserved across these three species.

A word document containing supplementary information including details of DNA processing, statistical methods, R-code, supplementary tables and figures cited in the article. (DOC 331 kb)

A word document containing supplementary information including details of DNA processing, statistical methods, R-code, supplementary tables and figures cited in the article. (DOC 331 kb)

Benzene, a ubiquitous environmental pollutant, causes acute myeloid leukemia (AML). Recently, through transcriptome profiling of peripheral blood mononuclear cells (PBMC), we reported dose-dependent effects of benzene exposure on gene expression and biochemical pathways in 83 workers exposed across four airborne concentration ranges (from 10 ppm) compared with 42 subjects with non-workplace ambient exposure levels. Here, we further characterize these dose-dependent effects with continuous benzene exposure in all 125 study subjects. We estimated air benzene exposure levels in the 42 environmentally-exposed subjects from their unmetabolized urinary benzene levels. We used a novel non-parametric, data-adaptive model selection method to estimate the change with dose in the expression of each gene. We describe non-parametric approaches to model pathway responses and used these to estimate the dose responses of the AML pathway and 4 other pathways of interest. The response patterns of majority of genes as captured by mean estimates of the first and second principal components of the dose-response for the five pathways and the profiles of 6 AML pathway response-representative genes (identified by clustering) exhibited similar apparent supra-linear responses. Responses at or below 0.1 ppm benzene were observed for altered expression of AML pathway genes and CYP2E1. Together, these data show that benzene alters disease-relevant pathways and genes in a dose-dependent manner, with effects apparent at doses as low as 100 ppb in air. Studies with extensive exposure assessment of subjects exposed in the low-dose range between 10 ppb and 1 ppm are needed to confirm these findings.