Robust linear mixed models with normal/independent distributions and Bayesian MCMC implementation

Linear mixed effects models have been widely used in analysis of data where responses are clustered around some random effects, so it is not reasonable to assume independence between observations in the same cluster. In most biological applications, it is assumed that the distributions of the random effects and of the residuals are Gaussian. This makes inferences vulnerable to the presence of outliers. Here, linear mixed effects models with normal/independent residual distributions for robust inferences are described. Specific distributions examined include univariate and multivariate versions of the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted and Markov chain Monte Carlo is used to carry out the posterior analysis. The procedures are illustrated using birth weight data on rats in a texicological experiment. Results from the Gaussian and robust models are contrasted, and it is shown how the implementation can be used for outlier detection. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process in linear mixed models, and they are easily implemented using data augmentation and MCMC techniques.

A general method to determine sampling windows for nonlinear mixed effects models with an application to population pharmacokinetic studies

Optimal design methods have been proposed to determine the best sampling times when sparse blood sampling is required in clinical pharmacokinetic studies. However, the optimal blood sampling time points may not be feasible in clinical practice. Sampling windows, a time interval for blood sample collection, have been proposed to provide flexibility in blood sampling times while preserving efficient parameter estimation. Because of the complexity of the population pharmacokinetic models, which are generally nonlinear mixed effects models, there is no analytical solution available to determine sampling windows. We propose a method for determination of sampling windows based on MCMC sampling techniques. The proposed method attains a stationary distribution rapidly and provides time-sensitive windows around the optimal design points. The proposed method is applicable to determine sampling windows for any nonlinear mixed effects model although our work focuses on an application to population pharmacokinetic models.

Simulation-based fully Bayesian experimental design for mixed effects models

In this paper, we present fully Bayesian experimental designs for nonlinear mixed effects models, in which we develop simulation-based optimal design methods to search over both continuous and discrete design spaces. Although Bayesian inference has commonly been performed on nonlinear mixed effects models, there is a lack of research into performing Bayesian optimal design for nonlinear mixed effects models that require searches to be performed over several design variables. This is likely due to the fact that it is much more computationally intensive to perform optimal experimental design for nonlinear mixed effects models than it is to perform inference in the Bayesian framework. In this paper, the design problem is to determine the optimal number of subjects and samples per subject, as well as the (near) optimal urine sampling times for a population pharmacokinetic study in horses, so that the population pharmacokinetic parameters can be precisely estimated, subject to cost constraints. The optimal sampling strategies, in terms of the number of subjects and the number of samples per subject, were found to be substantially different between the examples considered in this work, which highlights the fact that the designs are rather problem-dependent and require optimisation using the methods presented in this paper.

The utility and application of mixed-effects models in second language research

Second language acquisition researchers often face particular challenges when attempting to generalize study findings to the wider learner population. For example, language learners constitute a heterogeneous group, and it is not always clear how a study’s findings may generalize to other individuals who may differ in terms of language background and proficiency, among many other factors. In this paper, we provide an overview of how mixed-effects models can be used to help overcome these and other issues in the field of second language acquisition. We provide an overview of the benefits of mixed-effects models and a practical example of how mixed-effects analyses can be conducted. Mixed-effects models provide second language researchers with a powerful statistical tool in the analysis of a variety of different types of data.

A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

A computationally efficient sequential Monte Carlo algorithm is proposed for the sequential design of experiments for the collection of block data described by mixed effects models. The difficulty in applying a sequential Monte Carlo algorithm in such settings is the need to evaluate the observed data likelihood, which is typically intractable for all but linear Gaussian models. To overcome this difficulty, we propose to unbiasedly estimate the likelihood, and perform inference and make decisions based on an exact-approximate algorithm. Two estimates are proposed: using Quasi Monte Carlo methods and using the Laplace approximation with importance sampling. Both of these approaches can be computationally expensive, so we propose exploiting parallel computational architectures to ensure designs can be derived in a timely manner. We also extend our approach to allow for model uncertainty. This research is motivated by important pharmacological studies related to the treatment of critically ill patients.

An overview of mixed-effects statistical models for second language researchers

As in any field of scientific inquiry, advancements in the field of second language acquisition (SLA) rely in part on the interpretation and generalizability of study findings using quantitative data analysis and inferential statistics. While statistical techniques such as ANOVA and t-tests are widely used in second language research, this review article provides a review of a class of newer statistical models that have not yet been widely adopted in the field, but have garnered interest in other fields of language research. The class of statistical models called mixed-effects models are introduced, and the potential benefits of these models for the second language researcher are discussed. A simple example of mixed-effects data analysis using the statistical software package R (R Development Core Team, 2011) is provided as an introduction to the use of these statistical techniques, and to exemplify how such analyses can be reported in research articles. It is concluded that mixed-effects models provide the second language researcher with a powerful tool for the analysis of a variety of types of second language acquisition data.

Bayesian longitudinal data analysis with mixed models and thick-tailed distributions using MCMC

Linear mixed effects models are frequently used to analyse longitudinal data, due to their flexibility in modelling the covariance structure between and within observations. Further, it is easy to deal with unbalanced data, either with respect to the number of observations per subject or per time period, and with varying time intervals between observations. In most applications of mixed models to biological sciences, a normal distribution is assumed both for the random effects and for the residuals. This, however, makes inferences vulnerable to the presence of outliers. Here, linear mixed models employing thick-tailed distributions for robust inferences in longitudinal data analysis are described. Specific distributions discussed include the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted, and the Gibbs sampler and the Metropolis-Hastings algorithms are used to carry out the posterior analyses. An example with data on orthodontic distance growth in children is discussed to illustrate the methodology. Analyses based on either the Student-t distribution or on the usual Gaussian assumption are contrasted. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process for modelling distributions of the random effects and of residuals in linear mixed models, and the MCMC implementation allows the computations to be performed in a flexible manner.

Prevalence of mixed neuropathologies in autopsied older adults and associations with clinical disease progression

Thesis (Ph.D.)--University of Washington, 2016-06

Effects of introduced moose (Alces alces) on vegetation composition, nutrient dynamics, and decomposition rates in boreal forest ecosystems in Newfoundland, Canada

Globally, consumers affect ecosystem processes including nutrient dynamics. Herbivores have been known to slow nutrient flow in boreal forest ecosystems. I examined the effects of introduced moose on disturbed forests of Newfoundland, Canada by conducting a field experiment during August - November 2014 in 20 paired moose exclosure-control plots. I tested whether moose browsing directly and indirectly affected forests by measuring plant species composition, litter quality and quantity, soil quality, and decomposition rates in areas moose exclosure-control plots. I analyzed moose effects using linear mixed effects models and found evidence indicating that moose reduce plant height and litter biomass affecting the availability of carbon, nitrogen, and phosphorus. However, plant diversity, soil quality, and litter decomposition did not differ between moose exclosures and controls. Moose in Newfoundland directly influence plant regeneration and litter biomass while indirect effects on soil ecosystems may be limited by time, disturbance, and climate.

Factors affecting distribution of fish within a tidally drained mangrove forest in the Andaman and Nicobar Islands, India

Mangrove forests in meso-tidal areas are completely drained during low tides, forming only temporary habitats for fish. We hypothesised that in such temporary habitats, where stranding risks are high, distance from tidal creeks that provided access to inundated areas during receding tides would be the primary determinant of fish distribution. Factors such as depth, root density and shade were hypothesised to have secondary effects. We tested these hypotheses in a tidally drained mangrove patch in the Andaman Islands, India. Using stake nets, we measured fish abundance and species richness relative to distance from creeks, root density/m(2), shade, water depth and size (total length) of fish. We also predicted that larger fish (including potential predators) would be closer to creeks, as they faced a greater chance of mortality if stranded. Thus we conducted tethering trials to examine if predation would be greater close to the creeks. Generalised linear mixed effects models showed that fish abundance was negatively influenced by increasing creek distance interacting with fish size and positively influenced by depth. Quantile regression analysis showed that species richness was limited by increasing creek distance. Proportion of predation was greatest close to the creeks (0-25 m) and declined with increasing distance. Abundance was also low very close to the creeks, suggesting that close to the creeks predation pressure may be an important determinant of fish abundance. The overall pattern however indicates that access to permanently inundated areas, may be an important determinant of fish distribution in tidally drained mangrove forests.

Optimisation de l’administration des médicaments chez les enfants transplantés grâce à la pharmacocinétique de population

Ce travail de thèse porte sur l’application de la pharmacocinétique de population dans le but d’optimiser l’utilisation de certains médicaments chez les enfants immunosupprimés et subissant une greffe. Parmi les différents médicaments utilisés chez les enfants immunosupprimés, l’utilisation du busulfan, du tacrolimus et du voriconazole reste problématique, notamment à cause d’une très grande variabilité interindividuelle de leur pharmacocinétique rendant nécessaire l’individualisation des doses par le suivi thérapeutique pharmacologique. De plus, ces médicaments n’ont pas fait l’objet d’études chez les enfants et les doses sont adaptées à partir des adultes. Cette dernière pratique ne prend pas en compte les particularités pharmacologiques qui caractérisent l’enfant tout au long de son développement et rend illusoire l’extrapolation aux enfants des données acquises chez les adultes. Les travaux effectués dans le cadre de cette thèse ont étudié successivement la pharmacocinétique du busulfan, du voriconazole et du tacrolimus par une approche de population en une étape (modèles non-linéaires à effets mixtes). Ces modèles ont permis d’identifier les principales sources de variabilités interindividuelles sur les paramètres pharmacocinétiques. Les covariables identifiées sont la surface corporelle et le poids. Ces résultats confirment l’importance de tenir en compte l’effet de la croissance en pédiatrie. Ces paramètres ont été inclus de façon allométrique dans les modèles. Cette approche permet de séparer l’effet de la mesure anthropométrique d’autres covariables et permet la comparaison des paramètres pharmacocinétiques en pédiatrie avec ceux des adultes. La prise en compte de ces covariables explicatives devrait permettre d’améliorer la prise en charge a priori des patients. Ces modèles développés ont été évalués pour confirmer leur stabilité, leur performance de simulation et leur capacité à répondre aux objectifs initiaux de la modélisation. Dans le cas du busulfan, le modèle validé a été utilisé pour proposer par simulation une posologie qui améliorerait l’atteinte de l’exposition cible, diminuerait l’échec thérapeutique et les risques de toxicité. Le modèle développé pour le voriconazole, a permis de confirmer la grande variabilité interindividuelle dans sa pharmacocinétique chez les enfants immunosupprimés. Le nombre limité de patients n’a pas permis d’identifier des covariables expliquant cette variabilité. Sur la base du modèle de pharmacocinétique de population du tacrolimus, un estimateur Bayesien a été mis au point, qui est le premier dans cette population de transplantés hépatiques pédiatriques. Cet estimateur permet de prédire les paramètres pharmacocinétiques et l’exposition individuelle au tacrolimus sur la base d’un nombre limité de prélèvements. En conclusion, les travaux de cette thèse ont permis d’appliquer la pharmacocinétique de population en pédiatrie pour explorer les caractéristiques propres à cette population, de décrire la variabilité pharmacocinétique des médicaments utilisés chez les enfants immunosupprimés, en vue de l’individualisation du traitement. Les outils pharmacocinétiques développés s’inscrivent dans une démarche visant à diminuer le taux d'échec thérapeutique et l’incidence des effets indésirables ou toxiques chez les enfants immunosupprimés suite à une transplantation.

How well do regional or national Breeding Bird Survey data predict songbird population trends at an intact boreal site?

A study to monitor boreal songbird trends was initiated in 1998 in a relatively undisturbed and remote part of the boreal forest in the Northwest Territories, Canada. Eight years of point count data were collected over the 14 years of the study, 1998-2011. Trends were estimated for 50 bird species using generalized linear mixed-effects models, with random effects to account for temporal (repeat sampling within years) and spatial (stations within stands) autocorrelation and variability associated with multiple observers. We tested whether regional and national Breeding Bird Survey (BBS) trends could, on average, predict trends in our study area. Significant increases in our study area outnumbered decreases by 12 species to 6, an opposite pattern compared to Alberta (6 versus 15, respectively) and Canada (9 versus 20). Twenty-two species with relatively precise trend estimates (precision to detect > 30% decline in 10 years; observed SE ≤ 3.7%/year) showed nonsignificant trends, similar to Alberta (24) and Canada (20). Precision-weighted trends for a sample of 19 species with both reliable trends at our site and small portions of their range covered by BBS in Canada were, on average, more negative for Alberta (1.34% per year lower) and for Canada (1.15% per year lower) relative to Fort Liard, though 95% credible intervals still contained zero. We suggest that part of the differences could be attributable to local resource pulses (insect outbreak). However, we also suggest that the tendency for BBS route coverage to disproportionately sample more southerly, developed areas in the boreal forest could result in BBS trends that are not representative of range-wide trends for species whose range is centred farther north.