A clustering procedure for three-way RNA sequencing data using data transformations and matrix-variate Gaussian mixture models

RNA sequencing of time-course experiments results in three-way count data where the dimensions are the genes, the time points and the biological units. Clustering RNA-seq data allows to extract groups of co-expressed genes over time. After standardisation, the normalised counts of individual genes across time points and biological units have similar properties as compositional data. We propose the following procedure to suitably cluster three-way RNA-seq data: (1) pre-process the RNA-seq data by calculating the normalised expression profiles, (2) transform the data using the additive log ratio transform to map the composition in the D-part Aitchison simplex to a D - 1 -dimensional Euclidean vector, (3) cluster the transformed RNA-seq data using matrix-variate Gaussian mixture models and (4) assess the quality of the overall cluster solution and of individual clusters based on cluster separation in the transformed space using density-based silhouette information and on compactness of the cluster in the original space using cluster maps as a suitable visualisation. The proposed procedure is illustrated on RNA-seq data from fission yeast and results are also compared to an analogous two-way approach after flattening out the biological units.

Exploration of model misspecification in latent class methods for longitudinal data: Correlation structure matters

Modeling longitudinal trajectories and identifying latent classes of trajectories is of great interest in biomedical research, and software to identify latent classes of such is readily available for latent class trajectory analysis (LCTA), growth mixture modeling (GMM) and covariance pattern mixture models (CPMM). In biomedical applications, the level of within-person correlation is often non-negligible, which can impact the model choice and interpretation. LCTA does not incorporate this correlation. GMM does so through random effects, while CPMM specifies a model for within-class marginal covariance matrix. Previous work has investigated the impact of constraining covariance structures, both within and across classes, in GMMs-an approach often used to solve convergence problems. Using simulation, we focused specifically on how misspecification of the temporal correlation structure and strength, but correct variances, impacts class enumeration and parameter estimation under LCTA and CPMM. We found (1) even in the presence of weak correlation, LCTA often does not reproduce original classes, (2) CPMM performs well in class enumeration when the correct correlation structure is selected, and (3) regardless of misspecification of the correlation structure, both LCTA and CPMM give unbiased estimates of the class trajectory parameters when the within-individual correlation is weak and the number of classes is correctly specified. However, the bias increases markedly when the correlation is moderate for LCTA and when the incorrect correlation structure is used for CPMM. This work highlights the importance of correlation alone in obtaining appropriate model interpretations and provides insight into model choice.

CO-CLUSTERING OF SPATIALLY RESOLVED TRANSCRIPTOMIC DATA

Spatial transcriptomics is a groundbreaking technology that allows the measurement of the activity of thousands of genes in a tissue sample and maps where the activity occurs. This technology has enabled the study of the spatial variation of the genes across the tissue. Comprehending gene functions and interactions in different areas of the tissue is of great scientific interest, as it might lead to a deeper understanding of several key biological mechanisms, such as cell-cell communication or tumor-microenvironment interaction. To do so, one can group cells of the same type and genes that exhibit similar expression patterns. However, adequate statistical tools that exploit the previously unavailable spatial information to more coherently group cells and genes are still lacking. In this work, we introduce SpaRTaCo, a new statistical model that clusters the spatial expression profiles of the genes according to a partition of the tissue. This is accomplished by performing a co-clustering, i.e., inferring the latent block structure of the data and inducing two types of clustering: of the genes, using their expression across the tissue, and of the image areas, using the gene expression in the spots where the RNA is collected. Our proposed methodology is validated with a series of simulation experiments and its usefulness in responding to specific biological questions is illustrated with an application to a human brain tissue sample processed with the 10X-Visium protocol.

Psychopathological networks: Theory, methods and practice

In recent years, network approaches to psychopathology have sparked much debate and have had a significant impact on how mental disorders are perceived in the field of clinical psychology. However, there are many important challenges in moving from theory to empirical research and clinical practice and vice versa. Therefore, in this article, we bring together different points of view on psychological networks by methodologists and clinicians to give a critical overview on these challenges, and to present an agenda for addressing these challenges. In contrast to previous reviews, we especially focus on methodological issues related to temporal networks. This includes topics such as selecting and assessing the quality of the nodes in the network, distinguishing between- and within-person effects in networks, relating items that are measured at different time scales, and dealing with changes in network structures. These issues are not only important for researchers using network models on empirical data, but also for clinicians, who are increasingly likely to encounter (person-specific) networks in the consulting room.

Co-clustering of Time-Dependent Data via the Shape Invariant Model

Multivariate time-dependent data, where multiple features are observed over time for a set of individuals, are increasingly widespread in many application domains. To model these data, we need to account for relations among both time instants and variables and, at the same time, for subject heterogeneity. We propose a new co-clustering methodology for grouping individuals and variables simultaneously, designed to handle both functional and longitudinal data. Our approach borrows some concepts from the curve registration framework by embedding the shape invariant model in the latent block model, estimated via a suitable modification of the SEM-Gibbs algorithm. The resulting procedure allows for several user-defined specifications of the notion of cluster that can be chosen on substantive grounds and provides parsimonious summaries of complex time-dependent data by partitioning data matrices into homogeneous blocks. Along with the explicit modelling of time evolution, these aspects allow for an easy interpretation of the clusters, from which also low-dimensional settings may benefit.

Graphical models for mean and covariance of multivariate longitudinal data

Joint mean-covariance modeling of multivariate longitudinal data helps to understand the relative changes among multiple longitudinally measured and correlated outcomes. A key challenge in the analysis of multivariate longitudinal data is the complex covariance structure. This is due to the contemporaneous and cross-temporal associations between multiple longitudinal outcomes. Graphical and data-driven tools that can aid in visualizing the dependence patterns among multiple longitudinal outcomes are not readily available. In this work, we show the role of graphical techniques: profile plots, and multivariate regressograms, in developing mean and covariance models for multivariate longitudinal data. We introduce an R package MLGM (Multivariate Longitudinal Graphical Models) to facilitate visualization and modeling mean and covariance patterns. Through two real studies, microarray data from the T-cell activation study and Mayo Clinic's primary biliary cirrhosis of the liver study, we show the key features of MLGM. We evaluate the finite sample performance of the proposed mean-covariance estimation approach through simulations.

Insight Into Individual Differences in Emotion Dynamics With Clustering

Studying emotion dynamics through time series models is becoming increasingly popular in the social sciences. Across individuals, dynamics can be rather heterogeneous. To enable comparisons and generalizations of dynamics across groups of individuals, one needs sophisticated tools that express the essential similarities and differences. A way to proceed is to identify subgroups of people who are characterized by qualitatively similar emotion dynamics through dynamic clustering. So far, these methods assume equal generating processes for individuals per cluster. To avoid this overly restrictive assumption, we outline a probabilistic clustering approach based on a mixture model that clusters on individuals' vector autoregressive coefficients. We evaluate the performance of the method and compare it with a nonprobabilistic method in a simulation study. The usefulness of the methods is illustrated using 366 ecological momentary assessment time series with external measures of depression and anxiety.

Dynamic latent variable models for the analysis of cognitive abilities in the elderly population

Cognitive functioning is a key indicator of overall individual health. Identifying factors related to cognitive status, especially in later life, is of major importance. We concentrate on the analysis of the temporal evolution of cognitive abilities in the elderly population. We propose to model the individual cognitive functioning as a multidimensional latent process that accounts also for the effects of individual-specific characteristics (gender, age, and years of education). The proposed model is specified within the generalized linear latent variable framework, and its efficient estimation is obtained using a recent approximation technique, called dimensionwise quadrature. It provides a fast and streamlined approximate inference for complex models, with better or no degradation in accuracy compared with standard techniques. The methodology is applied to the cognitive assessment data from the Health and Retirement Study combined with the Asset and Health Dynamic study in the years between 2006 and 2010. We evaluate the temporal relationship between two dimensions of cognitive functioning, that is, episodic memory and general mental status. We find a substantial influence of the former on the evolution of the latter, as well as evidence of severe consequences on both cognitive abilities among less-educated and older individuals.

Improving convergence in growth mixture models without covariance structure constraints

Growth mixture models are a popular method to uncover heterogeneity in growth trajectories. Harnessing the power of growth mixture models in applications is difficult given the prevalence of nonconvergence when fitting growth mixture models to empirical data. Growth mixture models are rooted in the random effect tradition, and nonconvergence often leads researchers to modify their intended model with constraints in the random effect covariance structure to facilitate estimation. While practical, doing so has been shown to adversely affect parameter estimates, class assignment, and class enumeration. Instead, we advocate specifying the models with a marginal approach to prevent the widespread practice of sacrificing class-specific covariance structures to appease nonconvergence. A simulation is provided to show the importance of modeling class-specific covariance structures and builds off existing literature showing that applying constraints to the covariance leads to poor performance. These results suggest that retaining class-specific covariance structures should be a top priority and that marginal models like covariance pattern growth mixture models that model the covariance structure without random effects are well-suited for such a purpose, particularly with modest sample sizes and attrition commonly found in applications. An application to PTSD data with such characteristics is provided to demonstrate (a) convergence difficulties with random effect models, (b) how covariance structure constraints improve convergence but to the detriment of performance, and (c) how covariance pattern growth mixture models may provide a path forward that improves convergence without forfeiting class-specific covariance structures.

Inter-Individual Differences in Multivariate Time-Series

Abstract. Theories of emotion regulation posit the existence of individual differences in emotion dynamics. Current multi-subject time-series models account for differences in dynamics across individuals only to a very limited extent. This results in an aggregation that may poorly apply at the individual level. We present the exploratory method of latent class vector-autoregressive modeling (LCVAR), which extends the time-series models to include clustering of individuals with similar dynamic processes. LCVAR can identify individuals with similar emotion dynamics in intensive time-series, which may be of unequal length. The method performs excellently under a range of simulated conditions. The value of identifying clusters in time-series is illustrated using affect measures of 410 individuals, assessed at over 70 time points per individual. LCVAR discerned six clusters of distinct emotion dynamics with regard to diurnal patterns and augmentation and blunting processes between eight emotions.

A theoretical framework for Landsat data modeling based on the matrix variate mean-mixture of normal model

This paper introduces a new family of matrix variate distributions based on the mean-mixture of normal (MMN) models. The properties of the new matrix variate family, namely stochastic representation, moments and characteristic function, linear and quadratic forms as well as marginal and conditional distributions are investigated. Three special cases including the restricted skew-normal, exponentiated MMN and the mixed-Weibull MMN matrix variate distributions are presented and studied. Based on the specific presentation of the proposed model, an EM-type algorithm can be directly implemented for obtaining maximum likelihood estimate of the parameters. The usefulness and practical utility of the proposed methodology are illustrated through two conducted simulation studies and through the Landsat satellite dataset analysis.

Classification with the matrix-variate-t distribution

Matrix-variate distributions can intuitively model the dependence structure of matrix-valued observations that arise in applications with multivariate time series, spatio-temporal or repeated measures. This paper develops an Expectation-Maximization algorithm for discriminant analysis and classification with matrix-variate t-distributions. The methodology shows promise on simulated datasets or when applied to the forensic matching of fractured surfaces or the classification of functional Magnetic Resonance, satellite or hand gestures images.

Risk classification for conversion from mild cognitive impairment to Alzheimer's disease in primary care

There is a pressing need to identify individuals at high risk of conversion from mild cognitive impairment (MCI) to Alzheimer's disease (AD) based on available repeated cognitive measures in primary care. Using data from the Alzheimer's Disease Neuroimaging Initiative (ADNI), we applied a joint latent class mixed model (JLCM) to derive a 3-class solution: low risk (72.65%), medium risk (20.41%) and high risk (6.94%). In the low-risk group, individuals with lower daily activity and ApoEε4 carriers were at greater risk of conversion from MCI to AD. In the medium-risk group, being female, single, and an ApoEε4 carrier increased risk of conversion to AD. In the high-risk group, individuals with lower education level and single individuals were at greater risk of conversion to AD. Individual dynamic prediction for conversion from MCI to AD after 10 years was derived. Accurate identification of conversion from MCI to AD contributes to earlier close monitoring, appropriate management, and targeted interventions. Thereby, it can reduce avoidable hospitalizations for the high-risk MCI population. Moreover, it can avoid expensive follow-up tests that may provoke unnecessary anxiety for low-risk individuals and their families.