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Compositional data sets are ubiquitous in science, including geology, ecology, and microbiology. In microbiome research, compositional data primarily arise from high-throughput sequence-based profiling experiments. These data comprise…

The interactions among the constituent members of a microbial community play a major role in determining the overall behavior of the community and the abundance levels of its members. These interactions can be modeled using a network whose…

A frequent challenge encountered with ecological data is how to interpret, analyze, or model data having a high proportion of zeros. Much attention has been given to zero-inflated count data, whereas models for non-negative continuous data…

In this work we apply the methodology of integral priors to handle Bayesian model selection in binomial regression models with a general link function. These models are very often used to investigate associations and risks in…

This paper describes a compound Poisson-based random effects structure for modeling zero-inflated data. Data with large proportion of zeros are found in many fields of applied statistics, for example in ecology when trying to model and…

An important goal of environmental health research is to assess the risk posed by mixtures of environmental exposures. Two popular classes of models for mixtures analyses are response-surface methods and exposure-index methods.…

Infectious disease dynamics operate across multiple biological scales, with within-host viral dynamics being a key driver of between-host transmission. However, while models that explicitly link these scales exist, none have been developed…

Microbiome data are complex in nature, involving high dimensionality, compositionally, zero inflation, and taxonomic hierarchy. Compositional data reside in a simplex that does not admit the standard Euclidean geometry. Most existing…

Differential abundance analysis is at the core of statistical analysis of microbiome data. The compositional nature of microbiome sequencing data makes false positive control challenging. Here, we show that the compositional effects can be…

The advent of high-throughput sequencing technologies has made data from DNA material readily available, leading to a surge of microbiome-related research establishing links between markers of microbiome health and specific outcomes.…

Metabonomics time-course experiments provide the opportunity to understand the changes to an organism by observing the evolution of metabolic profiles in response to internal or external stimuli. Along with other omic longitudinal profiling…

Advances in next-generation sequencing technology have enabled the high-throughput profiling of metagenomes and accelerated the microbiome study. Recently, there has been a rise in quantitative studies that aim to decipher the microbiome…

Data for several applications in diverse fields can be represented as multiple matrices that are linked across rows or columns. This is particularly common in molecular biomedical research, in which multiple molecular "omics" technologies…

Mediation analysis is an important tool for studying causal associations in biomedical and other scientific areas and has recently gained attention in microbiome studies. Using a microbiome study of acute myeloid leukemia (AML) patients, we…

Human microbiome studies use sequencing technologies to measure the abundance of bacterial species or Operational Taxonomic Units (OTUs) in samples of biological material. Typically the data are organized in contingency tables with OTU…

The target of inference in microbiome analyses is usually relative abundance (RA) because RA in a sample (e.g., stool) can be considered as an approximation of RA in an entire ecosystem (e.g., gut). However, inference on RA suffers from the…

Compositional data arise in many areas of research in the natural and biomedical sciences. One prominent example is in the study of the human gut microbiome, where one can measure the relative abundance of many distinct microorganisms in a…

Microbiome studies increasingly indicate that disease-associated shifts cannot be understood from compositional changes alone. The functional architecture of microbial communities encoded in patterns of association among microbial gene…

Multiple imputation has become one of the standard methods in drawing inferences in many incomplete data applications. Applications of multiple imputation in relatively more complex settings, such as high-dimensional clustered data, require…

High-dimensional data are crucial in biomedical research. Integrating such data from multiple studies is a critical process that relies on the choice of advanced statistical models, enhancing statistical power, reproducibility, and…