A semiparametric regression model for paired longitudinal outcomes with application in childhood blood pressure development

This research examines the simultaneous influences of height and weight on longitudinally measured systolic and diastolic blood pressure in children. Previous studies have shown that both height and weight are positively associated with blood pressure. In children, however, the concurrent increases of height and weight have made it all but impossible to discern the effect of height from that of weight. To better understand these influences, we propose to examine the joint effect of height and weight on blood pressure. Bivariate thin plate spline surfaces are used to accommodate the potentially nonlinear effects as well as the interaction between height and weight. Moreover, we consider a joint model for paired blood pressure measures, that is, systolic and diastolic blood pressure, to account for the underlying correlation between the two measures within the same individual. The bivariate spline surfaces are allowed to vary across different groups of interest. We have developed related model fitting and inference procedures. The proposed method is used to analyze data from a real clinical investigation.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS567 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Across-country test-day model evaluations for Holstein, Nordic Red Cattle, and Jersey

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Longitudinal modelling of water levels of the Okavango River

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. May 30, 2016.In statistics, a model is as good as the data fed to it. Data about hydrological events continues to grow rapidly over the years, with different variables being recorded on a continuous scale. These variables can be interpreted and used in a different manner among disciplines. Thus, choosing the right variables and interactions among variables is an important statistical step in building a good and accurate model. This dissertation involved the development of a statistical model which can be used to predict weekly water level within the Okavango river in northern Namibia. The parameters of the statistical mixed model were estimated based on two methods for longitudinal data, the Generalised Estimating Equations (GEE) which is a well known method of parameter estimation in longitudinal data analysis when the observed variables are correlated, and the Restricted Maximum Likelihood Estimation (REML) which is a likelihood based approach method, unlike the GEE. Using cross-validation and a simulation study, the GEE method of estimation was found to be less accurate and inconsistent in terms of prediction of parameter estimation of water level while the well known REML was found to predict the water level with a good degree of accuracy, consistency and with lower variance. Parameters from a simulation study have also shown less bias in REML method and predicted the cross-validation test-set with less bias.GR 201

Panel time series analysis : some theory and applications

This thesis offers some theoretical contributions to the literature on large heterogeneous panel data models. It also demonstrates their practical use in empirical research, in the field of housing in macroeconomics, and for the analysis of the determinants of sovereign credit spreads. The first chapter provides the motivation for the research presented in this thesis. In the second chapter, we investigate the causes and the finite-sample consequences of negative definite covariance matrices in Swamy type random coefficient models. Monte Carlo experiments reveal that the negative definiteness problem is less severe when the degree of coefficient dispersion is substantial, and the precision of the regression disturbances is high. The sample size also plays a crucial role. We then evaluate the direct consequences of relying on the asymptotic properties of the estimator of the random coefficient covariance for hypothesis tests. A solution to the aforementioned problem is proposed in the third chapter. In particular, we propose to implement the EM algorithm to compute restricted maximum likelihood estimates of both the average effects and the unit-specific coefficients as well as of the variance components in a wide class of heterogeneous panel data models. Compared to existing methods, our approach leads to unbiased and more efficient estimation of the variance components of the model without running into the problem of negative definite covariance matrices typically encountered in random coefficient models. This in turn leads to more accurate estimated standard errors and hypothesis tests. Monte Carlo simulations reveal that the proposed estimator has relatively good finite sample properties. In evaluating the merits of our estimator, we also provide an overview of the sampling and Bayesian methods commonly used to estimate heterogeneous panel data. A novel approach to investigate heterogeneity of the sensitivity of sovereign spreads to government debt is presented. In a final chapter, we use a structural Bayesian (stochastic search variable selection) vector autoregressive model to investigate the heterogeneous impact of housing demand shocks on the macro-economy and the role of house prices in the monetary policy transmission, across euro area countries. A novel set of identification restrictions, which combines zero and sign restrictions, is proposed. By exploiting the cross-sectional dimension of our data, we explore the differences in the propagation channels of house prices and monetary policy and the challenges they pose in the process of real and nominal convergence in the Eurozone. Among the main results, we find a comparatively stronger housing wealth effect on consumption in Ireland and Spain. We provide new evidence in support of the financial accelerator hypothesis, showing that house prices play an important role in the availability of loans. A significant and highly heterogeneous effect of monetary policy on house price dynamics is also documented

iMap4: An Open Source Toolbox for the Statistical Fixation Mapping of Eye Movement data with Linear Mixed Modeling.

A major challenge in modern eye movement research is to statistically map where observers are looking, by isolating the significant differences between groups and conditions. Compared to signals of contemporary neuroscience measures, such as M/EEG and fMRI, eye movement data are sparser with much larger variations in space across trials and participants. As a result, the implementation of a conventional linear modeling approach on two-dimensional fixation distributions often returns unstable estimations and underpowered results, leaving this statistical problem unresolved (Liversedge, Gilchrist, & Everling. 2011). Here, we present a new version of the iMap toolbox (Caldara and Miellet, 2011) which tackles this issue by implementing a statistical framework comparable to those developped in state-of the- art neuroimaging data processing toolboxes. iMap4 uses univariate, pixel-wise Linear Mixed Models (LMM) on the smoothed fixation data, with the flexibility of coding for multiple between- and within- subject comparisons and performing all the possible linear contrasts for the fixed effects (main effects, interactions, etc.). Importantly, we also introduced novel nonparametric tests based on resampling to assess statistical significance. Finally, we validated this approach by using both experimental and Monte Carlo simulation data. iMap4 is a freely available MATLAB open source toolbox for the statistical fixation mapping of eye movement data, with a user-friendly interface providing straightforward, easy to interpret statistical graphical outputs. iMap4 matches the standards of robust statistical neuroimaging methods and represents an important step in the data-driven processing of eye movement fixation data, an important field of vision sciences

Fast and accurate modelling of longitudinal and repeated measures neuroimaging data

Despite the growing importance of longitudinal data in neuroimaging, the standard analysis methods make restrictive or unrealistic assumptions (e.g., assumption of Compound Symmetry—the state of all equal variances and equal correlations—or spatially homogeneous longitudinal correlations). While some new methods have been proposed to more accurately account for such data, these methods are based on iterative algorithms that are slow and failure-prone. In this article, we propose the use of the Sandwich Estimator (SwE) method which first estimates the parameters of interest with a simple Ordinary Least Square model and second estimates variances/covariances with the “so-called” SwE which accounts for the within-subject correlation existing in longitudinal data. Here, we introduce the SwE method in its classic form, and we review and propose several adjustments to improve its behaviour, specifically in small samples. We use intensive Monte Carlo simulations to compare all considered adjustments and isolate the best combination for neuroimaging data. We also compare the SwE method to other popular methods and demonstrate its strengths and weaknesses. Finally, we analyse a highly unbalanced longitudinal dataset from the Alzheimer's Disease Neuroimaging Initiative and demonstrate the flexibility of the SwE method to fit within- and between-subject effects in a single model. Software implementing this SwE method has been made freely available at http://warwick.ac.uk/tenichols/SwE

A Comparison of Procedures to Test for Moderators in Mixed-Effects Meta-Regression Models

Several alternative methods are available when testing for moderators in mixed-effects meta-regression models. A simulation study was carried out to compare different methods in terms of their Type I error and statistical power rates. We included the standard (Wald-type) test, the method proposed by Knapp and Hartung (2003) in 2 different versions, the Huber-White method, the likelihood ratio test, and the permutation test in the simulation study. These methods were combined with 7 estimators for the amount of residual heterogeneity in the effect sizes. Our results show that the standard method, applied in most meta-analyses up to date, does not control the Type I error rate adequately, sometimes leading to overly conservative, but usually to inflated, Type I error rates. Of the different methods evaluated, only the Knapp and Hartung method and the permutation test provide adequate control of the Type I error rate across all conditions. Due to its computational simplicity, the Knapp and Hartung method is recommended as a suitable option for most meta-analyses

Mixed effects modelling for biological systems

En raison des relations complexes entre les variables des systèmes biologiques, l’hétérogénéité des données biologiques pose un défi pour leur modélisation par des modèles mathématiques et statistiques. En réponse, étant conçus pour traiter des données multiniveaux et bruitées, les modèles à effets mixtes deviennent de plus en plus populaires en modélisation quantitative de systèmes biologiques. L'objectif de cette thèse est de présenter l’application de modèles à effets mixtes à différents systèmes biologiques. Le deuxième chapitre de ce mémoire vise à déterminer la relation entre la cote de qualité du sirop d'érable, divers indicateurs de qualité couramment obtenus par les producteurs ainsi qu'un nouvel indicateur, le COLORI, et la concentration en acides aminés (AA). Pour cela, nous avons créé deux modèles à effets mixtes : le premier est un modèle ordinal qui prédit directement la cote de qualité du sirop d'érable en utilisant la transmittance, COLORI et AA ; le deuxième modèle est un modèle non linéaire qui prédit la concentration en AA en utilisant COLORI avec le pH comme approximation temporelle. Nos résultats montrent que la concentration en AA est un bon prédicteur de la qualité du sirop d'érable et que COLORI est un bon prédicteur de la concentration en AA. Le troisième chapitre traite de l’utilisation d’un modèle de la pharmacocinétique de population (PopPK) pour décrire la dynamique de l'estradiol dans un modèle de pharmacologie quantitative des systèmes (QSP) de la différenciation des cellules mammaires en cellules myoépithéliales afin de capturer l'hétérogénéité de la population de patients. Nous avons trouvé que la composante PopPK du modèle QSP n’a pas ajoutée de grande variation dans la dynamique de patients virtuels, ce qui suggère que le modèle QSP inclut intrinsèquement l'hétérogénéité. Dans l'ensemble, ce mémoire démontre l'application de modèles à effets mixtes au systèmes biologiques pour comprendre l'hétérogénéité des données biologiques.Modelling biological systems with mathematical models has been a challenge due to the tendency for biological data to be heavily heterogeneous with complex relationships between the variables. Mixed effects models are an increasingly popular choice as a statistical model for biological systems since it is designed for multilevel data and noisy data. The aim of this thesis is to showcase the range of usage of mixed effects modelling for different biological systems. The second chapter aims to determine the relationship between maple syrup quality rating and various quality indicator commonly obtained by producers as well as a new indicator, COLORI, and amino acid (AA) concentration. For this, we created two mixed effects models: the first is an ordinal model that directly predicts maple syrup quality rating using transmittance, COLORI and AA; the second model is a nonlinear model that predicts AA concentration using COLORI with pH as a time proxy. Our models show that AA concentration is a good predictor for maple syrup quality, and COLORI is a good predictor for AA concentration. The third chapter involves using a population pharmacokinetics (PopPK) model to estimate estradiol dynamics in a quantitative systems pharmacokinetics (QSP) model for mammary cell differentiation into myoepithelial cells in order to capture population heterogeneity among patients. Our results show that the QSP model inherently includes heterogeneity in its structure since the added PopPK estradiol portion of the model does not add large variation in the estimated virtual patients. Overall, this thesis demonstrates the application of mixed effects models in biology as a way to understand heterogeneity in biological data