A semiparametric model for between-subject attributes: Applications to beta-diversity of microbiome data.

The human microbiome plays an important role in our health and identifying factors associated with microbiome composition provides insights into inherent disease mechanisms. By amplifying and sequencing the marker genes in high-throughput sequencing, with highly similar sequences binned together, we obtain operational taxonomic units (OTUs) profiles for each subject. Due to the high-dimensionality and nonnormality features of the OTUs, the measure of diversity is introduced as a summarization at the microbial community level, including the distance-based beta-diversity between individuals. Analyses of such between-subject attributes are not amenable to the predominant within-subject-based statistical paradigm, such as t-tests and linear regression. In this paper, we propose a new approach to model beta-diversity as a response within a regression setting by utilizing the functional response models (FRMs), a class of semiparametric models for between- as well as within-subject attributes. The new approach not only addresses limitations of current methods for beta-diversity with cross-sectional data, but also provides a premise for extending the approach to longitudinal and other clustered data in the future. The proposed approach is illustrated with both real and simulated data.

A Test of Foraging Models Using Dietary Diversity Indices for the Lomako Forest Bonobos.

Optimal diet and functional response models are used to understand the evolution of primate foraging strategies. The predictions of these models can be tested by examining the geographic and seasonal variation in dietary diversity. Dietary diversity is a useful tool that allows dietary comparisons across differing sampling locations and time periods. Bonobos (Pan paniscus) are considered primarily frugivorous and consume fruits, leaves, insects, vertebrates, terrestrial herbaceous vegetation, and flowers. Frugivores, like bonobos, are valuable for examining dietary diversity and testing foraging models because they eat a variety of species and are subject to seasonal shifts in fruit availability. Frugivorous primate species thus allow for tests of how variation in dietary diversity is correlated with variation in ecological factors. We investigated measures of dietary diversity in bonobos at two research camps across field seasons within the same protected area (N'dele and Iyema) in Lomako Forest, Democratic Republic of the Congo. We compared the results of behavioral observation (1984/1985, 1991, 1995, 2014, and 2017) and fecal washing analysis (2007 and 2009) between seasons and study period using three diversity indices (Shannon's, Simpson's, and SW evenness). The average yearly dietary diversity indices at N'dele were Shannon's H' = 2.04, Simpson's D = 0.82, and SW evenness = 0.88 while at Iyema, the indices were Shannon's H' = 2.02, Simpson's D = 0.82, and SW evenness = 0.88. Behavioral observation data sets yielded significantly higher dietary diversity indices than fecal washing data sets. We found that food item (fruit, leaf, and flower) consumption was not associated with seasonal food availability for the 2017 behavioral observation data set. Shannon's index was lower during periods when fewer bonobo dietary items were available to consume and higher when fruit was abundant. Finally, we found that optimal diet models best-explained patterns of seasonal food availability and dietary diversity. Dietary diversity is an essential factor to consider when understanding primate diets and can be a tool in understanding variation in primate diets, particularly among frugivores. Dietary diversity varies across populations of the same species and across time, and it is critical in establishing a complete understanding of how primate diets change over time.

The effect of vaccine on COVID-19 spread by function-on-scalar regression model: a case study of Africa.

Aim: This paper aimed to study the effect of the vaccine on the reproduction rate of coronavirus in Africa from January 2021 to November 2021. Subject and methods: Functional data analysis (FDA), a relatively new area in statistics, can describe, analyze, and predict data collected over time, space, or other continuum measures in many countries every day and is increasingly common across scientific domains. For our data, the first step of functional data is smoothing. We used the B-spline method to smooth our data. Then, we apply the function-on-scalar and Bayes function-on-scalar models to fit our data. Results: Our results indicate a statistically significant relationship between the vaccine and the rate of virus reproduction and spread. When the vaccination rate falls, the reproduction rate also decreases. Furthermore, we found that the effect of latitude and the region on the reproduction rate depends on the region. We discovered that in Middle Africa, from the beginning of the year until the end of the summer, the impact is negative, implying that the virus spread due to a decrease in the vaccination rates. Conclusion: The study found that vaccination rates significantly impact the virus's reproduction rate.

A Functional Approach to Deconvolve Dynamic Neuroimaging Data.

Positron emission tomography (PET) is an imaging technique which can be used to investigate chemical changes in human biological processes such as cancer development or neurochemical reactions. Most dynamic PET scans are currently analyzed based on the assumption that linear first-order kinetics can be used to adequately describe the system under observation. However, there has recently been strong evidence that this is not the case. To provide an analysis of PET data which is free from this compartmental assumption, we propose a nonparametric deconvolution and analysis model for dynamic PET data based on functional principal component analysis. This yields flexibility in the possible deconvolved functions while still performing well when a linear compartmental model setup is the true data generating mechanism. As the deconvolution needs to be performed on only a relative small number of basis functions rather than voxel by voxel in the entire three-dimensional volume, the methodology is both robust to typical brain imaging noise levels while also being computationally efficient. The new methodology is investigated through simulations in both one-dimensional functions and 2D images and also applied to a neuroimaging study whose goal is the quantification of opioid receptor concentration in the brain.