A common goal in medical research is to determine the effect that a treatment has on subjects over time. Unfortunately, the analysis of data from such clinical trials often omits several aspects of the study design, leading to incorrect or misleading conclusions. In this paper, a major objective is to show via case studies that randomized controlled trials with longitudinal designs must account for correlation and clustering among observations in order to make proper statistical inference. Further, the effects of outliers in a multi-center, randomized controlled trial with multiple layers of clustering are examined and strategies for detecting and dealing with outlying observations and clusters are discussed. / McAnulty College and Graduate School of Liberal Arts; / Computational Mathematics / MS; / Thesis;

Robust estimates of forest above-ground biomass (AGB) are needed in order to constrain the uncertainty in regional and global carbon budgets, predictions of global climate change and remote sensing efforts to monitor large scale changes in forest cover and biomass. Estimates of AGB and their associated uncertainty are also essential for international forest-based climate change mitigation strategies such as REDD+. Mangrove forests are widely recognised as globally important carbon stores. Continuing high rates of global mangrove deforestation represent a loss of future carbon sequestration potential and could result in significant release into the atmosphere of the carbon currently being stored within mangroves. The main aims of this thesis are 1) to provide information on the current AGB stocks of mangrove forests in Kenya at spatial scales relevant for climate change research, forest management and REDD+ and 2) to evaluate and constrain the uncertainty associated with these AGB estimates. This thesis adopted both a ground-based statistical approach and a remote sensing based approach to estimating mangrove AGB in Kenya. Allometric equations were developed for Kenyan mangroves using mixed-effects regression analysis and uncertainties were fully propagated (using a Monte Carlo based approach) to estimates of AGB at all spatial scales (tree, plot, region and landscape). In this study, species and site effects accounted for a large proportion (41%) of the total variability in mangrove AGB. The generic biomass equation produced for Kenyan mangroves has the potential for broad application as it can be used to estimate the AGB of new trees where there is no pre-existing knowledge of the specific species-site allometric relationship. The 95% prediction intervals for landscape scale estimates of total AGB suggest that between 5.4 and 7.2 megatonnes (Mt) of AGB is currently held in Kenyan mangrove forests. An in-depth evaluation of the relative contribution of various components of uncertainty (measurement, parameter and residual uncertainty) to the magnitude of the total uncertainty of AGB estimates was carried out. This evaluation was undertaken using both the mixed-effects regression model and a standard ordinary least squares (OLS) regression model. The exclusion of measurement uncertainty during the biomass estimation process had negligible impact on the magnitude of the uncertainty regardless of spatial scale or tree size. Excluding the uncertainty due to species and site effects (from the mixed-effects model) consistently resulted in a large reduction (~ 70%) in the overall uncertainty. Estimates of the uncertainty produced by the OLS model were unrealistically low which is illustrative of the general need to account for group effects in biomass regression models. L-band Synthetic Aperture Radar (SAR) was used to estimate the AGB of Kenyan mangroves. There was an observable relationship (R2 = 0.45) between L-band HH and AGB with HH backscatter found to decrease as a function of increasing AGB. There was no significant relationship found between L-band HV and AGB. The negative relationship between HH and AGB in this study can possibly be attributed to enhanced backscatter at lower AGB due to strong double-bounce and direct surface scattering from short stature/open forests and attenuation of the SAR signal at higher AGB. The SAR-derived estimate of total AGB for Kenyan mangroves was 5.32 Mt ± 18.6%. However, due to the unexpected nature of the HH-AGB relationship found in this study the SAR-derived estimates of mangrove AGB in this study should be considered with caution.

In 2005 and 2010, high sea surface temperatures caused widespread coral bleaching on Jamaica’s north coast reefs. Three shallow (9m) reef sites were surveyed during each event to quantify the prevalence and intensity of coral bleaching. In October 2005, 29-57% of the colonies surveyed were bleached. By April 2006, 10% of the corals remained pale/partially bleached. Similarly, in October 2010, 23-51% of corals surveyed at the same sites were bleached. By April 2011, 12% of the colonies remained pale/partially bleached. Follow-up surveys revealed low coral mortality following both events, with an overall mean of 4% partial colony mortality across all species and sites observed in April 2006, and 2% in April 2011. Mixed effects models were used to quantify the relationship between colony size and (a) bleaching intensity, and (b) bleaching related mortality among coral species. The bleaching intensity model explained 51% of the variance in the bleaching response observed during the two events. Of this 51%, fixed effects accounted for ~26% of the variance, 17% of which was attributed to species-specific susceptibility to bleaching , 5% to colony size, <1% colony morphology and 4% to the difference in bleaching intensity between the two events. The random factor (site) accounted for the remaining ~25% of the variance. The mortality model explained 16% of the variance in post bleaching mortality with fixed effects, including colony size, morphology and species explaining ~11% of the variance, and the random effect (site) explaining 5%. On average, there was a twofold difference in bleaching intensity between the smallest and the largest size classes. Modelling the relationship between colony level characteristics and site-specific environmental factors on coral species’ susceptibility to thermal stress can shed light on community level responses to future disturbances.

In 2005 and 2010, high sea surface temperatures caused widespread coral bleaching on Jamaica’s north coast reefs. Three shallow (9m) reef sites were surveyed during each event to quantify the prevalence and intensity of coral bleaching. In October 2005, 29-57% of the colonies surveyed were bleached. By April 2006, 10% of the corals remained pale/partially bleached. Similarly, in October 2010, 23-51% of corals surveyed at the same sites were bleached. By April 2011, 12% of the colonies remained pale/partially bleached. Follow-up surveys revealed low coral mortality following both events, with an overall mean of 4% partial colony mortality across all species and sites observed in April 2006, and 2% in April 2011. Mixed effects models were used to quantify the relationship between colony size and (a) bleaching intensity, and (b) bleaching related mortality among coral species. The bleaching intensity model explained 51% of the variance in the bleaching response observed during the two events. Of this 51%, fixed effects accounted for ~26% of the variance, 17% of which was attributed to species-specific susceptibility to bleaching , 5% to colony size, <1% colony morphology and 4% to the difference in bleaching intensity between the two events. The random factor (site) accounted for the remaining ~25% of the variance. The mortality model explained 16% of the variance in post bleaching mortality with fixed effects, including colony size, morphology and species explaining ~11% of the variance, and the random effect (site) explaining 5%. On average, there was a twofold difference in bleaching intensity between the smallest and the largest size classes. Modelling the relationship between colony level characteristics and site-specific environmental factors on coral species’ susceptibility to thermal stress can shed light on community level responses to future disturbances.

Diseases vectored by mosquitoes cause millions of deaths each year. In modern times Florida*s disease risk has been reduced due to efforts to lessen the prevalence of mosquitoes through habitat modification of non-adults. With emerging diseases (i.e. Dengue and Chikunguya) encroaching into Florida from the Caribbean, this traditional approach may not be enough. Alternatively, we can better understand the ecology of how disease works in an ecosystem. One possible way is through the Dilution Effect, which states that the more species that are in a system the lower the chance for zoonosis. This project models mosquito diversity across regions, land use, and vegetation height in South-Central Florida, for the purpose of identifying predictors that indicate a higher disease risk using information theory (AICc). The plains and coastal regions as well as the developed areas have a relatively higher risk of disease. Florida is a fire maintained habitat, but has been fire suppressed for the last century. Archbold Biological Station (ABS) has used prescribed fires since the early 1980s to try and restore a more natural system. This has created a mosaic of different fire histories. Fire affects the structures that mosquitoes rest under during the day (they are vulnerable to desiccation during the day and hide in darker/shady places), therefore there is a high likelihood that fire will have some effect on mosquito assemblages. This project used model selection to determine the most plausible set of predictors that describe the effect of fire on mosquito assemblages at ABS, using information theory (AICc). In general, time of season accounted for the largest proportion of the variation in the data and TSF had negligible effect on adult mosquito assemblages measured as abundance, speices richness, and Jost D.

Linear models are the dominant means of extracting summaries of events in fMRI for feature vector based machine learning. While they are both useful and robust, they are limited by the assumptions made in modeling. In this work, we examine a number of feature extraction techniques adjacent to linear models that account for or allow wider variation. Primarily, we construct mixed effects models able to account for variation between stimuli of the same class and perform empirical tests on the resulting feature extraction – classifier system. We extend this analysis to spatial temporal models as well as summary models. We find that mixed effects models increase classifier performance at the cost of increased uncertainty in prediction estimates. In addition, these models identify similar regions of interest in separating classes. While they currently require knowledge hidden during testing, we present these results as an optimum to be reached in additional works. / Doctor of Philosophy / Machine learning is a popular tool for extracting useful information from functional MR images. One approach is classification using feature vectors derived from observations. In this work, we examine new strategies for extracting feature vectors time varying data and explore the effect these feature vectors have on the results of machine learning analysis. In a set of simulations and real data, we compare a range of standard methods for feature extraction to new methods developed for this work. We find the most effective approach for successful classification is feature extraction through the use of mixed effects models. We also find that these models preserve the selection of feature sets that are maximally important to classification. We then explore the range of considerations required to use any of the methods examined in this work for a range of cases. We hope this provides solid ground for both future expansion of feature extraction methods and helpful advice for future users of these methods.

Mixed-effects models are commonly used to model longitudinal data as they can appropriately account for within and between subject sources of variability. Univariate mixed effect modeling strategies are well developed for a single outcome (response) variable that may be continuous (e.g. Gaussian) or categorical (e.g. binary, Poisson) in nature. Only recently have extensions been discussed for jointly modeling multiple outcome variables measures longitudinally. Many diseases processes are a function of several factors that are correlated. For example, the metabolic syndrome, a constellation of cardiovascular risk factors associated with an increased risk of cardiovascular disease and type 2 diabetes, is often defined as having three of the following: elevated blood pressure, high waist circumference, elevated glucose, elevated triglycerides, and decreased HDL. Clearly these multiple measures within a subject are not independent. A model that could jointly model two or more of these risk factors and appropriately account for between subjects sources of variability as well as within subject sources of variability due to the longitudinal and multivariate nature of the data would be more useful than several univariate models. In fact, the univariate mixed-effects model can be extended in a relatively straightforward fashion to define a multivariate mixed-effects model for longitudinal data by appropriately defining the variance-covariance structure for the random-effects. Existing software such as the PROC MIXED in SAS can be used to fit the multivariate mixed-effects model. The Fels Longitudinal Study data were used to illustrate both univariate and multivariate mixed-effects modeling strategies. Specifically, jointly modeled longitudinal measures of systolic (SBP) and diastolic (DBP) blood pressure during childhood (ages two to eighteen) were compared between participants who were diagnosed with at least three of the metabolic syndrome risk factors in adulthood (ages thirty to fifty-five) and those who were never diagnosed with any risk factors. By identifying differences in risk factors, such as blood pressure, early in childhood between those who go on to develop the metabolic syndrome in adulthood and those who do not, earlier interventions could be used to prevent the development cardiovascular disease and type 2 diabetes. As demonstrated by these analyses, the multivariate model is able to not only answer the same questions addressed as the univariate model, it is also able to answer additional important questions about the association in the evolutions of the responses as well as the evolution of the associations. Furthermore, the additional information gained by incorporating information about the correlations between the responses was able to reduce the variability (standard errors) in both the fixed-effects estimates (e.g. differences in groups, effects of covariates) as well as the random-effects estimates (e.g. variability).

Este trabalho tem como objetivo aplicar a teoria de modelos mistos ao estudo do teor de nitrogênio e carbono no solo, em diversas profundidades. Devido a grande quantidade de matéria orgânica no solo, o teor de nitrogênio e carbono apresentam alta variabilidade nas primeiras profundidades, além de apresentar um comportamento não linear. Assim, fez-se necessário utilizar a abordagem de modelos não lineares mistos a dados longitudinais. A utilização desta abordagem proporciona um modelo que permite modelar dados não lineares, com heterogeneidade de variâncias, fornecendo uma curva para cada amostra. / This paper has as an objective to apply the theory of mixed models to the content of nitrogen and carbon in the soil at various depths. Due to the large amount of organic material in the soil, the content of nitrogen and carbon present high variability in the depths of soil surface, and present a nonlinear behavior. Thus, it was necessary to use the approach of nonlinear mixed models to longitudinal data analysis. The use of this approach provides a model that allows to model nonlinear data with heterogeneity of variances by providing a curve for each sample.

With societies aging all around the world, the global burden of degenerative diseases is expected to increase exponentially. From the perspective drug development, degenerative diseases represent an especially challenging class. Clinical trials, in this context often termed disease progression studies, are long, costly, require many individuals, and have low success rates. Therefore, it is crucial to use informative study designs and to analyze efficiently the obtained trial data. The development of novel approaches intended towards facilitating both the design and the analysis of disease progression studies was the aim of this thesis. This aim was pursued in three stages (i) the characterization and extension of pharmacometric software, (ii) the development of new methodology around statistical power, and (iii) the demonstration of application benefits. The optimal design software PopED was extended to simplify the application of optimal design methodology when planning a disease progression study. The performance of non-linear mixed effect estimation algorithms for trial data analysis was evaluated in terms of bias, precision, robustness with respect to initial estimates, and runtime. A novel statistic allowing for explicit optimization of study design for statistical power was derived and found to perform superior to existing methods. Monte-Carlo power studies were accelerated through application of parametric power estimation, delivering full power versus sample size curves from a few hundred Monte-Carlo samples. Optimal design and an explicit optimization for statistical power were applied to the planning of a study in Alzheimer's disease, resulting in a 30% smaller study size when targeting 80% power. The analysis of ADAS-cog score data was improved through application of item response theory, yielding a more exact description of the assessment score, an increased statistical power and an enhanced insight in the assessment properties. In conclusion, this thesis presents novel pharmacometric methods that can help addressing the challenges of designing and planning disease progression studies.

The cost of releasing a new drug on the market has increased rapidly in the last decade. The reasons for this increase vary with the drug, but the need to make correct decisions earlier in the drug development process and to maximize the information gained throughout the process is evident. Optimal experimental design (OD) describes the procedure of maximizing relevant information in drug development and drug treatment processes. While various optimization criteria can be considered in OD, the most common is to optimize the unknown model parameters for an upcoming study. To date, OD has mainly been used to optimize the independent variables, e.g. sample times, but it can be used for any design variable in a study. This thesis addresses the OD of multiple continuous or discrete design variables for nonlinear mixed effects models. The methodology for optimizing and the optimization of different types of models with either continuous or discrete data are presented and the benefits of OD for such models are shown. A software tool for optimizing these models in parallel is developed and three OD examples are demonstrated: 1) optimization of an intravenous glucose tolerance test resulting in a reduction in the number of samples by a third, 2) optimization of drug compound screening experiments resulting in the estimation of nonlinear kinetics and 3) an individual dose-finding study for the treatment of children with ciclosporin before kidney transplantation resulting in a reduction in the number of blood samples to ~27% of the original number and an 83% reduction in the study duration. This thesis uses examples and methodology to show that studies in drug development and drug treatment can be optimized using nonlinear mixed effects OD. This provides a tool than can lower the cost and increase the overall efficiency of drug development and drug treatment.