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Treatment, cleansing, moisturizing, and photoprotection are four major components of holistic skin care for dermatological conditions. While treatment (T) is recognized as a key component in the management of dermatological conditions, there is a lack of practical guidance on the adjunctive role of cleansing, moisturizing, and photoprotection ("CMP"). Limited patient knowledge, confusion over product selection, and lack of guidance on how to choose and use CMP skin care products (in conjunction with pharmacological therapy) are the main barriers to establishing a holistic skin care routine for dermatological conditions.This study aimed to review current clinical evidence, identify gaps, and provide practical guidance on conceptualization and implementation of CMP routine in the management of sensitive skin due to underlying acne, atopic dermatitis, or rosacea, including conditions with idiopathic causes referred to as idiopathic sensitive skin syndrome.An expert panel comprising of 10 dermatologists from Australia, China, Hong Kong, Taiwan, India, Indonesia, Philippines, Singapore, South Korea, and Thailand convened to develop consensus statements on holistic skin care in acne, rosacea, atopic dermatitis, and idiopathic sensitive skin syndrome using the Delphi approach.Consensus was defined as ≥80% of panel rating statement as ≥8 or median rating of ≥8. The final statements were collated to develop consensus recommendations on holistic skin care.A dermatologist-guided holistic skin care routine is essential to improve patient confidence and reduce confusion over product selection. The consensus recommendations presented here highlight the importance of cleansing, moisturization, and photoprotection in holistic skin care and how it can be utilized as a communication tool for physicians and patients to achieve overall better patient compliance, satisfaction, and treatment outcomes.

Gut microbiomes are increasingly found to be associated with many health-related characteristics of humans as well as animals. Regression with compositional microbiomes covariates is commonly used to identify important bacterial taxa that are related to various phenotype responses. Often the dimension of microbiome taxa easily exceeds the number of available samples, which creates a serious challenge in the estimation and inference of the model. The sparse log-contrast regression method is useful for such cases as it can yield a model estimate that depends on only a small number of taxa. However, a formal statistical inference procedure for individual regression coefficients has not been properly established yet. We propose a new estimation and inference procedure for linear regression models with extremely low-sample-sized compositional predictors. Under the compositional log-contrast regression framework, the proposed approach consists of two steps. The first step is to screen relevant predictors by fitting a log-contrast model with a sparse penalty. The screened-in variables are used as predictors in the non-sparse log-contrast model in the second step, where each of the regression coefficients is tested using nonparametric, resampling-based methods such as permutation and bootstrap. The performances of the proposed methods are evaluated by a simulation study, which shows they outperform traditional approaches based on normal assumptions or large sample asymptotics. Application to steer microbiome data successfully identifies key bacterial taxa that are related to important cattle quality measures.

Multiblock data, where multiple groups of variables from different sources are observed for a common set of subjects, are routinely collected in many areas of science. Methods for joint factorization of such multiblock data are being developed to explore the potentially joint variation structure of the data. While most of the existing work focuses on delineating joint components, shared across all data blocks, from individual components, which is only relevant to a single data block, we propose to model and estimate partially joint components across some, but not all, data blocks. If covariates, with potential multiblock structures, are available, then the components are further modeled to be driven by the covariate information. To estimate such a covariate-driven, block-structured factor model, we propose an iterative algorithm based on thresholding, by transforming the problem of signal segmentation into a grouped variable selection problem. The proposed factorization provides accurate estimation of individual and (partially) joint structures in multiblock data, as confirmed by simulation studies. In the analysis of a real multiblock genomic dataset from the Cancer Genome Atlas project, we demonstrate that the estimated block structures provide straightforward interpretation and facilitate subsequent analyses.

Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the principal component directions are not consistent, the sample and prediction principal component scores can be useful in revealing the population structure. We further show that these scores are biased, and the bias is asymptotically decomposed into rotation and scaling parts. We propose methods of bias-adjustment that are shown to be consistent and work well in the high dimensional situations with small sample sizes. The potential advantage of bias-adjustment is demonstrated in a classification setting.

This work is motivated by the recent worldwide pandemic of the novel coronavirus disease (COVID-19). When an epidemiological disease is prevalent, estimating the case fatality rate, the proportion of deaths out of the total cases, accurately and quickly is important as the case fatality rate is one of the crucial indicators of the risk of a disease. In this work, we propose an alternative estimator of the case fatality rate that provides more accurate estimate during an outbreak by reducing the downward bias (underestimation) of the naive CFR, the proportion of deaths out of confirmed cases at each time point, which is the most commonly used estimator due to the simplicity. The proposed estimator is designed to achieve the availability of real-time update by using the commonly reported quantities, the numbers of confirmed, cured, deceased cases, in the computation. To enhance the accuracy, the proposed estimator adapts a stratification, that allows the estimator to use information from heterogeneous strata separately. With the COVID-19 cases of China, South Korea and the United States, we numerically show the proposed stratification-based estimator plays a role of providing an early warning about the severity of a epidemiological disease that estimates the final case fatality rate accurately and shows faster convergence to the final case fatality rate.

We investigate geodesic projections of von Mises–Fisher (vMF) distributed directional data. The vMF distribution for random directions on the (p−1)-dimensional unit hypersphere Sp−1⊂Rp plays the role of multivariate normal distribution in directional statistics. For one-dimensional circle S1, the vMF distribution is called von Mises (vM) distribution. Projections onto geodesics are one of main ingredients of modeling and exploring directional data. We show that the projection of vMF distributed random directions onto any geodesic is approximately vM-distributed, albeit not exactly the same. In particular, the distribution of the geodesic-projected score is an infinite scale mixture of vM distributions. Approximations by vM distributions are given along various asymptotic scenarios including large and small concentrations (κ→∞,κ→0), high-dimensions (p→∞), and two important cases of double-asymptotics (p,κ→∞, κ∕p→c or κ∕p→λ), to support our claim: geodesic projections of the vMF are approximately vM. As one of potential applications of the result, we contemplate a projection pursuit exploration of high-dimensional directional data. We show that in a high dimensional model almost all geodesic-projections of directional data are nearly vM, thus measures of non-vM-ness are a viable candidate for projection index.

Set classification aims to classify a set of observations as a whole, as opposed to classifying individual observations separately. To formally understand the unfamiliar concept of binary set classification, we first investigate the optimal decision rule under the normal distribution, which utilizes the empirical covariance of the set to be classified. We show that the number of observations in the set plays a critical role in bounding the Bayes risk. Under this framework, we further propose new methods of set classification. For the case where only a few parameters of the model drive the difference between two classes, we propose a computationally-efficient approach to parameter estimation using linear programming, leading to the Covariance-engaged LInear Programming Set (CLIPS) classifier. Its theoretical properties are investigated for both independent case and various (short-range and long-range dependent) time series structures among observations within each set. The convergence rates of estimation errors and risk of the CLIPS classifier are established to show that having multiple observations in a set leads to faster convergence rates, compared to the standard classification situation in which there is only one observation in the set. The applicable domains in which the CLIPS performs better than competitors are highlighted in a comprehensive simulation study. Finally, we illustrate the usefulness of the proposed methods in classification of real image data in histopathology., 86 pages, 5 figures

Skeletal models that are structurally medial provide effective object representations. This is because they include not only locations but also boundary directions and object widths. We present a skeletal object representation that we call “quasimedial” because geometric properties associated with Blum's [1] medial axis are relaxed to allow the skeleton to have a pre-specified amount of branching and thus to support statistical analysis. We call this form of object representation the s-rep. We explain how such models can be automatically determined from object boundary data in a way that a) avoids boundary noise, b) implies a boundary that closely fits the input boundary, and c) well recognizes shape correspondences across cases. We also explain how to use Riemannian geometry to estimate probability distributions from a sample of s-reps and to find ways to classify s-reps between two categories as trained from s-reps in each class. Finally, we describe various evidence that shows the relative strengths of s-reps vs. other object representations; we also discuss shortcomings of s-reps.

We present a method for individual and integrative analysis of high dimension, low sample size data that capitalizes on the recurring theme in multivariate analysis of projecting higher dimensional data onto a few meaningful directions that are solutions to a generalized eigenvalue problem. We propose a general framework, called SELP (Sparse Estimation with Linear Programming), with which one can obtain a sparse estimate for a solution vector of a generalized eigenvalue problem. We demonstrate the utility of SELP on canonical correlation analysis for an integrative analysis of methylation and gene expression profiles from a breast cancer study, and we identify some genes known to be associated with breast carcinogenesis, which indicates that the proposed method is capable of generating biologically meaningful insights. Simulation studies suggest that the proposed method performs competitive in comparison with some existing methods in identifying true signals in various underlying covariance structures.

We consider the problem of how many components to retain in the application of principal component analysis when the dimension is much higher than the number of observations. To estimate the number of components, we propose to sequentially test skewness of the squared lengths of residual scores that are obtained by removing leading principal components. The residual lengths are asymptotically left-skewed if all principal components with diverging variances are removed, and right-skewed if not. The proposed estimator is shown to be consistent, performs well in high-dimensional simulation studies, and provides reasonable estimates in a number of real data examples.

Jung et al. (2015) introduced a geometric structure on ${\rm Sym}^+(p)$, the set of $p \times p$ symmetric positive-definite matrices, based on eigen-decomposition. Eigenstructure determines both a stratification of ${\rm Sym}^+(p)$, defined by eigenvalue multiplicities, and fibers of the "eigen-composition" map $F:M(p):=SO(p)\times{\rm Diag}^+(p)\to{\rm Sym}^+(p)$. When $M(p)$ is equipped with a suitable Riemannian metric, the fiber structure leads to notions of scaling-rotation distance between $X,Y\in {\rm Sym}^+(p)$, the distance in $M(p)$ between fibers $F^{-1}(X)$ and $F^{-1}(Y)$, and minimal smooth scaling-rotation (MSSR) curves, images in ${\rm Sym}^+(p)$ of minimal-length geodesics connecting two fibers. In this paper we study the geometry of the triple $(M(p),F,{\rm Sym}^+(p))$, focusing on some basic questions: For which $X,Y$ is there a unique MSSR curve from $X$ to $Y$? More generally, what is the set ${\cal M}(X,Y)$ of MSSR curves from $X$ to $Y$? This set is influenced by two potential types of non-uniqueness. We translate the question of whether the second type can occur into a question about the geometry of Grassmannians $G_m({\bf R}^p)$, with $m$ even, that we answer for $p\leq 4$ and $p\geq 11$. Our method of proof also yields an interesting half-angle formula concerning principal angles between subspaces of ${\bf R}^p$ whose dimensions may or may not be equal. The general-$p$ results concerning MSSR curves and scaling-rotation distance that we establish here underpin the explicit $p=3$ results in Groisser et al. (2017). Addressing the uniqueness-related questions requires a thorough understanding of the fiber structure of $M(p)$, which we also provide., arXiv admin note: text overlap with arXiv:1602.01187

A test of modality of rotationally symmetric distributions on hyperspheres is proposed. The test is based on a modified multivariate kurtosis defined for directional data on S d . We first reveal a relationship between the multivariate kurtosis and the types of modality for Euclidean data. In particular, the kurtosis of a rotationally symmetric distribution with decreasing sectional density is greater than the kurtosis of the uniform distribution, while the kurtosis of that with increasing sectional density is less. For directional data, we show an asymptotic normality of the modified spherical kurtosis, based on which a large-sample test is proposed. The proposed test of modality is applied to the problem of preventing overfitting in non-geodesic dimension reduction of directional data. The proposed test is superior than existing options in terms of computation times, accuracy and preventing overfitting. This is highlighted by a simulation study and two real data examples.

We propose a new algorithm for sparse estimation of eigenvectors in generalized eigenvalue problems (GEP). The GEP arises in a number of modern data-analytic situations and statistical methods, including principal component analysis (PCA), multiclass linear discriminant analysis (LDA), canonical correlation analysis (CCA), sufficient dimension reduction (SDR) and invariant co-ordinate selection. We propose to modify the standard generalized orthogonal iteration with a sparsity-inducing penalty for the eigenvectors. To achieve this goal, we generalize the equation-solving step of orthogonal iteration to a penalized convex optimization problem. The resulting algorithm, called penalized orthogonal iteration, provides accurate estimation of the true eigenspace, when it is sparse. Also proposed is a computationally more efficient alternative, which works well for PCA and LDA problems. Numerical studies reveal that the proposed algorithms are competitive, and that our tuning procedure works well. We demonstrate applications of the proposed algorithm to obtain sparse estimates for PCA, multiclass LDA, CCA and SDR. Supplementary materials are available online.

This article discusses a novel framework to analyze rotational deformations of real three-dimensional objects. The rotational deformations such as twisting or bending have been observed as the major variation in some medical applications, where the features of the deformed three-dimensional objects are directional data. We propose modeling and estimation of the global deformations in terms of generalized rotations of directions. The proposed method can be cast as a generalized small circle fitting on the unit sphere. We also discuss the estimation of descriptors for more complex deformations composed of two simple deformations. The proposed method can be used for a number of different three-dimensional object models. Two analyses of three-dimensional object data are presented in detail: one using skeletal representations in medical image analysis and the other from biomechanical gait analysis of the knee joint. Supplementary materials for this article are available online.

PurposeRespiratory motion prediction using an artificial neural network (ANN) was integrated with pseudocontinuous arterial spin labeling (pCASL) MRI to allow free-breathing perfusion measurements in the kidney. In this study, we evaluated the performance of the ANN to accurately predict the location of the kidneys during image acquisition.MethodsA pencil-beam navigator was integrated with a pCASL sequence to measure lung/diaphragm motion during ANN training and the pCASL transit delay. The ANN algorithm ran concurrently in the background to predict organ location during the 0.7-s 15-slice acquisition based on the navigator data. The predictions were supplied to the pulse sequence to prospectively adjust the axial slice acquisition to match the predicted organ location. Additional navigators were acquired immediately after the multislice acquisition to assess the performance and accuracy of the ANN. The technique was tested in eight healthy volunteers.ResultsThe root-mean-square error (RMSE) and mean absolute error (MAE) for the eight volunteers were 1.91±0.17mm and 1.43±0.17mm, respectively, for the ANN. The RMSE increased with transit delay. The MAE typically increased from the first to last prediction in the image acquisition. The overshoot was 23.58%±3.05% using the target prediction accuracy of±1mm.ConclusionRespiratory motion prediction with prospective motion correction was successfully demonstrated for free-breathing perfusion MRI of the kidney. The method serves as an alternative to multiple breathholds and requires minimal effort from the patient.

We investigate a geometric computational framework, called the "scaling-rotation framework", on ${\rm Sym}^+(p)$, the set of $p \times p$ symmetric positive-definite (SPD) matrices. The purpose of our study is to lay geometric foundations for statistical analysis of SPD matrices, in situations in which eigenstructure is of fundamental importance, for example diffusion-tensor imaging (DTI). Eigen-decomposition, upon which the scaling-rotation framework is based, determines both a stratification of ${\rm Sym}^+(p)$, defined by eigenvalue multiplicities, and fibers of the "eigen-composition" map $SO(p)\times{\rm Diag}^+(p)\to{\rm Sym}^+(p)$. This leads to the notion of scaling-rotation distance [Jung et al. (2015)], a measure of the minimal amount of scaling and rotation needed to transform an SPD matrix, $X,$ into another, $Y,$ by a smooth curve in ${\rm Sym}^+(p)$. Our main goal in this paper is the systematic characterization and analysis of minimal smooth scaling-rotation (MSSR) curves, images in ${\rm Sym}^+(p)$ of minimal-length geodesics connecting two fibers in the "upstairs" space $SO(p)\times{\rm Diag}^+(p)$. The length of such a geodesic connecting the fibers over $X$ and $Y$ is what we define to be the scaling-rotation distance from $X$ to $Y.$ For the important low-dimensional case $p = 3$ (the home of DTI), we find new explicit formulas for MSSR curves and for the scaling-rotation distance, and identify ${\cal M}(X,Y)$ in all "nontrivial" cases. The quaternionic representation of $SO(3)$ is used in these computations. We also provide closed-form expressions for scaling-rotation distance and MSSR curves for the case $p = 2$., 15 figures