We model the Alzheimer\'s Disease-related phenotype response variables observed on irregular time points in longitudinal Genome-Wide Association Studies as sparse functional data and propose nonparametric test procedures to detect functional genotype effects while controlling the confounding effects of environmental covariates. Our new functional analysis of covariance tests are based on a seemingly unrelated kernel smoother, which takes into account the within-subject temporal correlations, and thus enjoy improved power over existing functional tests. We show that the proposed test combined with a uniformly consistent nonparametric covariance function estimator enjoys the Wilks phenomenon and is minimax most powerful. Data used in the preparation of this article were obtained from the Alzheimer\'s Disease Neuroimaging Initiative (ADNI) database, where an application of the proposed test lead to the discovery of new genes that may be related to Alzheimer\'s Disease.

Recently, two-way or longitudinal functional data analysis has attracted much attention in many fields. However, little is known on how to appropriately characterize the association between two-way functional predictor and scalar response. Motivated by a mortality study, in this paper, we propose a novel two-way functional linear model, where the response is a scalar and functional predictor is two-way trajectory. The model is intuitive, interpretable and naturally captures relationship between each way of two-way functional predictor and scalar-type response. Further, we develop a new estimation method to estimate the regression functions in the framework of weak separability. The main technical tools for the construction of the regression functions are product functional principal component analysis and iterative least square procedure. The solid performance of our method is demonstrated in extensive simulation studies. We also analyze the mortality dataset to illustrate the usefulness of the proposed procedure.

In this paper we propose a new semiparametric function-on-function quantile regression model with time-dynamic single-index interactions. Our model is very flexible in taking into account of the nonlinear time-dynamic interaction effects of the multivariate longitudinal/functional covariates on the longitudinal response, that most existing quantile regression models for longitudinal data are special cases of our proposed model. We propose to approximate the bivariate nonparametric coefficient functions by tensor product B-splines, and employ a check loss minimization approach to estimate the bivariate coefficient functions and the index parameter vector. Under some mild conditions, we establish the asymptotic normality of the estimated single-index coefficients using projection orthogonalization technique, and obtain the convergence rates of the estimated bivariate coefficient functions. Furthermore, we propose a score test to examine whether there exist interaction effects between the covariates. The finite sample performance of the proposed method is illustrated by Monte Carlo simulations and an empirical data analysis.

Host-microbe biology (HMB) stands on the cusp of redefinition, challenging conventional paradigms to instead embrace a more holistic understanding of the microbial sciences. The American Society for Microbiology (ASM) Council on Microbial Sciences hosted a virtual retreat in 2023 to identify the future of the HMB field and innovations needed to advance the microbial sciences. The retreat presentations and discussions collectively emphasized the interconnectedness of microbes and their profound influence on humans, animals, and environmental health, as well as the need to broaden perspectives to fully embrace the complexity of these interactions. To advance HMB research, microbial scientists would benefit from enhancing interdisciplinary and transdisciplinary research to utilize expertise in diverse fields, integrate different disciplines, and promote equity and accessibility within HMB. Data integration will be pivotal in shaping the future of HMB research by bringing together varied scientific perspectives, new and innovative techniques, and \'omics approaches. ASM can empower under-resourced groups with the goal of ensuring that the benefits of cutting-edge research reach every corner of the scientific community. Thus, ASM will be poised to steer HMB toward a future that champions inclusivity, innovation, and accessible scientific progress.

Compared with the conditional mean regression-based scalar-on-function regression model, the scalar-on-function quantile regression is robust to outliers in the response variable. However, it is susceptible to outliers in the functional predictor (called leverage points). This is because the influence function of the regression quantiles is bounded in the response variable but unbounded in the predictor space. The leverage points may alter the eigenstructure of the predictor matrix, leading to poor estimation and prediction results. This study proposes a robust procedure to estimate the model parameters in the scalar-on-function quantile regression method and produce reliable predictions in the presence of both outliers and leverage points. The proposed method is based on a functional partial quantile regression procedure. We propose a weighted partial quantile covariance to obtain functional partial quantile components of the scalar-on-function quantile regression model. After the decomposition, the model parameters are estimated via a weighted loss function, where the robustness is obtained by iteratively reweighting the partial quantile components. The estimation and prediction performance of the proposed method is evaluated by a series of Monte-Carlo experiments and an empirical data example. The results are compared favorably with several existing methods. The method is implemented in an R package robfpqr.

We propose a new non-parametric conditional independence test for a scalar response and a functional covariate over a continuum of quantile levels. We build a Cramer-von Mises type test statistic based on an empirical process indexed by random projections of the functional covariate, effectively avoiding the \"curse of dimensionality\" under the projected hypothesis, which is almost surely equivalent to the null hypothesis. The asymptotic null distribution of the proposed test statistic is obtained under some mild assumptions. The asymptotic global and local power properties of our test statistic are then investigated. We specifically demonstrate that the statistic is able to detect a broad class of local alternatives converging to the null at the parametric rate. Additionally, we recommend a simple multiplier bootstrap approach for estimating the critical values. The finite-sample performance of our statistic is examined through several Monte Carlo simulation experiments. Finally, an analysis of an EEG data set is used to show the utility and versatility of our proposed test statistic.

Considering the context of functional data analysis, we developed and applied a new Bayesian approach via the Gibbs sampler to select basis functions for a finite representation of functional data. The proposed methodology uses Bernoulli latent variables to assign zero to some of the basis function coefficients with a positive probability. This procedure allows for an adaptive basis selection since it can determine the number of bases and which ones should be selected to represent functional data. Moreover, the proposed procedure measures the uncertainty of the selection process and can be applied to multiple curves simultaneously. The methodology developed can deal with observed curves that may differ due to experimental error and random individual differences between subjects, which one can observe in a real dataset application involving daily numbers of COVID-19 cases in Brazil. Simulation studies show the main properties of the proposed method, such as its accuracy in estimating the coefficients and the strength of the procedure to find the true set of basis functions. Despite having been developed in the context of functional data analysis, we also compared the proposed model via simulation with the well-established LASSO and Bayesian LASSO, which are methods developed for non-functional data.

Alterations in the gut microbiome are associated with the pathogenesis of Alzheimer\'s disease (AD) and can be used as a diagnostic measure. However, longitudinal data of the gut microbiome and knowledge about its prognostic significance for the development and progression of AD are limited. The aim of the present study was to develop a reliable predictive model based on gut microbiome data for AD development. In this longitudinal study, we investigated the intestinal microbiome in 49 mild cognitive impairment (MCI) patients over a mean (SD) follow-up of 3.7 (0.6) years, using shotgun metagenomics. At the end of the 4-year follow-up (4yFU), 27 MCI patients converted to AD dementia and 22 MCI patients remained stable. The best taxonomic model for the discrimination of AD dementia converters from stable MCI patients included 24 genera, yielding an area under the receiver operating characteristic curve (AUROC) of 0.87 at BL, 0.92 at 1yFU and 0.95 at 4yFU. The best models with functional data were obtained via analyzing 25 GO (Gene Ontology) features with an AUROC of 0.87 at BL, 0.85 at 1yFU and 0.81 at 4yFU and 33 KO [Kyoto Encyclopedia of Genes and Genomes (KEGG) ortholog] features with an AUROC of 0.79 at BL, 0.88 at 1yFU and 0.82 at 4yFU. Using ensemble learning for these three models, including a clinical model with the four parameters of age, gender, body mass index (BMI) and Apolipoprotein E (ApoE) genotype, yielded an AUROC of 0.96 at BL, 0.96 at 1yFU and 0.97 at 4yFU. In conclusion, we identified novel and timely stable gut microbiome algorithms that accurately predict progression to AD dementia in individuals with MCI over a 4yFU period.

In this article, we propose a novel estimator of extreme conditional quantiles in partial functional linear regression models with heavy-tailed distributions. The conventional quantile regression estimators are often unstable at the extreme tails due to data sparsity, especially for heavy-tailed distributions. We first estimate the slope function and the partially linear coefficient using a functional quantile regression based on functional principal component analysis, which is a robust alternative to the ordinary least squares regression. The extreme conditional quantiles are then estimated by using a new extrapolation technique from extreme value theory. We establish the asymptotic normality of the proposed estimator and illustrate its finite sample performance by simulation studies and an empirical analysis of diffusion tensor imaging data from a cognitive disorder study.
Dans cet article, un nouvel estimateur de quantiles conditionnels extrêmes est élaboré dans le cadre de modèles de régression linéaire fonctionnelle partielle avec des distributions à queues lourdes. Il est bien connu que la rareté des observations dans les ailes extrêmes de distributions à queues lourdes rend souvent les estimateurs de régression quantile usuels instables. Pour parer à la non robustesse des moindres carrés classiques, les auteurs ont commencé par estimer la fonction de pente et le coefficient partiellement linéaire d’une régression quantile en ayant recours à une approche basée sur l’analyse en composantes principales fonctionnelles. Ensuite, ils ont estimé les quantiles conditionnels extrêmes à l’aide d’une nouvelle technique d’extrapolation issue de la théorie des valeurs extrêmes. En plus d’établir la normalité asymptotique de l’estimateur proposé, les auteurs illustrent ses bonnes performances à distance finie par le biais d’une étude de simulation et une mise en oeuvre pratique sur les données d’imagerie de diffusion par tenseurs provenant d’une étude portant sur des troubles cognitifs.

Modern medical devices are increasingly producing complex data that could offer deeper insights into physiological mechanisms of underlying diseases. One type of complex data that arises frequently in medical imaging studies is functional data, whose sampling unit is a smooth continuous function. In this work, with the goal of establishing the scientific validity of experiments involving modern medical imaging devices, we focus on the problem of evaluating reliability and reproducibility of multiple functional data that are measured on the same subjects by different methods (i.e. different technologies or raters). Specifically, we develop a series of intraclass correlation coefficient and concordance correlation coefficient indices that can assess intra-method, inter-method, and total (intra + inter) agreement based on multivariate multilevel functional data consisting of replicated functional data measurements produced by each of the different methods. For efficient estimation, the proposed indices are expressed using variance components of a multivariate multilevel functional mixed effect model, which can be smoothly estimated by functional principal component analysis. Extensive simulation studies are performed to assess the finite-sample properties of the estimators. The proposed method is applied to evaluate the reliability and reproducibility of renogram curves produced by a high-tech radionuclide image scan used to non-invasively detect kidney obstruction.