Clustering longitudinal profiles using P-splines and mixed effects models applied to time-course gene expression data

Grouped generalized estimating equations for longitudinal data analysis

Generalized estimating equation (GEE) is widely adopted for regression modeling for longitudinal data, taking account of potential correlations within the same subjects. Although the standard GEE assumes common regression coefficients among all the subjects, such an assumption may not be realistic when there is potential heterogeneity in regression coefficients among subjects. In this paper, we develop a flexible and interpretable approach, called grouped GEE analysis, to modeling longitudinal data with allowing heterogeneity in regression coefficients. The proposed method assumes that the subjects are divided into a finite number of groups and subjects within the same group share the same regression coefficient. We provide a simple algorithm for grouping subjects and estimating the regression coefficients simultaneously, and show the asymptotic properties of the proposed estimator. The number of groups can be determined by the cross validation with averaging method. We demonstrate the proposed method through simulation studies and an application to a real data set.

clusterMLD: An Efficient Hierarchical Clustering Method for Multivariate Longitudinal Data

Longitudinal data clustering is challenging because the grouping has to account for the similarity of individual trajectories in the presence of sparse and irregular times of observation. This paper puts forward a hierarchical agglomerative clustering method based on a dissimilarity metric that quantifies the cost of merging two distinct groups of curves, which are depicted by B-splines for the repeatedly measured data. Extensive simulations show that the proposed method has superior performance in determining the number of clusters, classifying individuals into the correct clusters, and in computational efficiency. Importantly, the method is not only suitable for clustering multivariate longitudinal data with sparse and irregular measurements but also for intensely measured functional data. Towards this end, we provide an R package for the implementation of such analyses. To illustrate the use of the proposed clustering method, two large clinical data sets from real-world clinical studies are analyzed.

Ensemble calibration model of near-infrared spectroscopy based on functional data analysis

As a nondestructive detection technology, near-infrared spectroscopy has been widely applied in various fields. With the wide application of near-infrared spectroscopy, the research on data processing has attracted more attention. Different from the existing discrete data model and based on the functional data analysis method, an ensemble calibration model FDA-EM-PLS (functional data analysis-ensemble learning-partial least squares) of near-infrared spectroscopy is proposed in this paper. Firstly, the near-infrared spectroscopy of each sample is divided into several intervals, and the functional data analysis is carried out on each interval. Then, the samples are clustered according to the generated functions, which can not only reduce the influence of noise, but also provide a theoretical basis for selecting variables. Further, Monte Carlo sampling is used to generate training subsets from clustering samples for ensemble learning, which not only solves the problem of small samples, but also improves the robustness of the model. The relevant experimental results show that the absolute relative error of FDA-EM-PLS for the corn and soil data are both less than 10%.

Boosted-oriented probabilistic smoothing-spline clustering of series

Fuzzy clustering methods allow the objects to belong to several clusters simultaneously, with different degrees of membership. However, a factor that influences the performance of fuzzy algorithms is the value of fuzzifier parameter. In this paper, we propose a fuzzy clustering procedure for data (time) series that does not depend on the definition of a fuzzifier parameter. It comes from two approaches, theoretically motivated for unsupervised and supervised classification cases, respectively. The first is the Probabilistic Distance clustering procedure. The second is the well known Boosting philosophy. Our idea is to adopt a boosting prospective for unsupervised learning problems, in particular we face with non hierarchical clustering problems. The global performance of the proposed method is investigated by various experiments.

Biclustering analysis of functionals via penalized fusion

In biomedical data analysis, clustering is commonly conducted. Biclustering analysis conducts clustering in both the sample and covariate dimensions and can more comprehensively describe data heterogeneity. In most of the existing biclustering analyses, scalar measurements are considered. In this study, motivated by time-course gene expression data and other examples, we take the "natural next step" and consider the biclustering analysis of functionals under which, for each covariate of each sample, a function (to be exact, its values at discrete measurement points) is present. We develop a doubly penalized fusion approach, which includes a smoothness penalty for estimating functionals and, more importantly, a fusion penalty for clustering. Statistical properties are rigorously established, providing the proposed approach a strong ground. We also develop an effective ADMM algorithm and accompanying R code. Numerical analysis, including simulations, comparisons, and the analysis of two time-course gene expression data, demonstrates the practical effectiveness of the proposed approach.

Exploring the longitudinal dynamics of herd BVD antibody test results using model-based clustering

Determining the Bovine Viral Diarrhoea (BVD) infection status of cattle herds is a challenge for control and eradication schemes. Given the changing dynamics of BVD  virus (BVDV) antibody responses in cattle, classifying herds based on longitudinal changes in the results of BVDV antibody tests could offer a novel, complementary approach to categorising herds that is less likely than the present system to result in a herd's status changing from year to year, as it is more likely to capture the true exposure dynamics of the farms. This paper describes the dynamics of BVDV antibody test values (measured as percentage positivity (PP)) obtained from 15,500 bovines between 2007 and 2010 from thirty nine cattle herds located in Scotland and Northern England. It explores approaches of classifying herds based on trend, magnitude and shape of their antibody PP trajectories and investigates the epidemiological similarities between farms within the same cluster. Gaussian mixture models were used for the magnitude and shape clustering. Epidemiologically meaningful clusters were obtained. Farm cluster membership depends on clustering approach used. Moderate concordance was found between the shape and magnitude clusters. These methods hold potential for application to enhance control efforts for BVD and other infectious livestock diseases.

Clonal raider ant brain transcriptomics identifies candidate molecular mechanisms for reproductive division of labor

BACKGROUND

Division of labor between reproductive queens and workers that perform brood care is a hallmark of insect societies. However, studies of the molecular basis of this fundamental dichotomy are limited by the fact that the caste of an individual cannot typically be experimentally manipulated at the adult stage. Here we take advantage of the unique biology of the clonal raider ant, Ooceraea biroi, to study brain gene expression dynamics during experimentally induced transitions between reproductive and brood care behavior.

RESULTS

Introducing larvae that inhibit reproduction and induce brood care behavior causes much faster changes in adult gene expression than removing larvae. In addition, the general patterns of gene expression differ depending on whether ants transition from reproduction to brood care or vice versa, indicating that gene expression changes between phases are cyclic rather than pendular. Finally, we identify genes that could play upstream roles in regulating reproduction and behavior because they show large and early expression changes in one or both transitions.

CONCLUSIONS

Our analyses reveal that the nature and timing of gene expression changes differ substantially depending on the direction of the transition, and identify a suite of promising candidate molecular regulators of reproductive division of labor that can now be characterized further in both social and solitary animal models. This study contributes to understanding the molecular regulation of reproduction and behavior, as well as the organization and evolution of insect societies.

k-Centres Functional Clustering

In the present paper, we introduce k-centres functional clustering ( k-centres FC), a person-centered method that clusters people with similar patterns of complex, highly nonlinear change over time. We review fundamentals of the methodology and argue how it addresses some of the limitations of the traditional approaches to modeling repeated measures data. The usefulness of k-centres FC is demonstrated by applying the method to weekly measured commitment data from 109 participants who reported psychological contract breach events. The k-centres FC analysis shows two substantively meaningful clusters, the first cluster showing reaction patterns with general growth in commitment after breach and the second cluster showing general decline in commitment after breach. Further, the reaction patterns in the second cluster appear to be the result of a combination of two interesting reaction logics: immediate and delayed reactions. We conclude by outlining how future organizational research can incorporate this methodology.

Assessing variation in life-history tactics within a population using mixture regression models: a practical guide for evolutionary ecologists

Mixed models are now well-established methods in ecology and evolution because they allow accounting for and quantifying within- and between-individual variation. However, the required normal distribution of the random effects can often be violated by the presence of clusters among subjects, which leads to multi-modal distributions. In such cases, using what is known as mixture regression models might offer a more appropriate approach. These models are widely used in psychology, sociology, and medicine to describe the diversity of trajectories occurring within a population over time (e.g. psychological development, growth). In ecology and evolution, however, these models are seldom used even though understanding changes in individual trajectories is an active area of research in life-history studies. Our aim is to demonstrate the value of using mixture models to describe variation in individual life-history tactics within a population, and hence to promote the use of these models by ecologists and evolutionary ecologists. We first ran a set of simulations to determine whether and when a mixture model allows teasing apart latent clustering, and to contrast the precision and accuracy of estimates obtained from mixture models versus mixed models under a wide range of ecological contexts. We then used empirical data from long-term studies of large mammals to illustrate the potential of using mixture models for assessing within-population variation in life-history tactics. Mixture models performed well in most cases, except for variables following a Bernoulli distribution and when sample size was small. The four selection criteria we evaluated [Akaike information criterion (AIC), Bayesian information criterion (BIC), and two bootstrap methods] performed similarly well, selecting the right number of clusters in most ecological situations. We then showed that the normality of random effects implicitly assumed by evolutionary ecologists when using mixed models was often violated in life-history data. Mixed models were quite robust to this violation in the sense that fixed effects were unbiased at the population level. However, fixed effects at the cluster level and random effects were better estimated using mixture models. Our empirical analyses demonstrated that using mixture models facilitates the identification of the diversity of growth and reproductive tactics occurring within a population. Therefore, using this modelling framework allows testing for the presence of clusters and, when clusters occur, provides reliable estimates of fixed and random effects for each cluster of the population. In the presence or expectation of clusters, using mixture models offers a suitable extension of mixed models, particularly when evolutionary ecologists aim at identifying how ecological and evolutionary processes change within a population. Mixture regression models therefore provide a valuable addition to the statistical toolbox of evolutionary ecologists. As these models are complex and have their own limitations, we provide recommendations to guide future users.