<p>Correlated data with complex association structures arise from longitudinal studies and cluster randomized trials. However, some methodological challenges in the design and analysis of such studies or trials have not been overcome. In this thesis, we address three of the challenges: 1) <em>Power analysis for population based longitudinal study investigating gene-environment interaction effects on chronic disease:</em> For longitudinal studies with interest in investigating the gene-environment interaction in disease susceptibility and progression, rigorous statistical power estimation is crucial to ensure that such studies are scientifically useful and cost-effective since human genome epidemiology is expensive. However conventional sample size calculations for longitudinal study can seriously overestimate the statistical power due to overlooking the measurement error, unmeasured etiological determinants, and competing events that can impede the occurrence of the event of interest. 2) <em>Comparing the performance of different multiple imputation strategies for missing binary outcomes in cluster randomized trials</em>: Though researchers have proposed various strategies to handle missing binary outcome in cluster randomized trials (CRTs), comprehensive guidelines on the selection of the most appropriate or optimal strategy are not available in the literature. 3) <em>Comparison of population-averaged and cluster-specific models for the analysis of cluster randomized trials with missing binary outcome</em>: Both population-averaged and cluster-specific models are commonly used for analyzing binary outcomes in CRTs. However, little attention has been paid to their accuracy and efficiency when analyzing data with missing outcomes. The objective of this thesis is to provide researchers recommendations and guidance for future research in handling the above issues.</p> / Doctor of Philosophy (PhD)

Although the research literature supports the notion of language growth trajectories, primarily in monolingual English children, the shape and direction of English-language learners' (ELLs) language growth trajectories are largely unknown. The present study examined the shape of ELLs' language growth trajectories by estimating the initial status and the growth rates of specific oral language skills (mean length of utterance in words (MLUw), number of different words (NDW), and words per minute (WPM)) in each language during the first 3 years of formal schooling. This study was framed from the perspective of language as a dynamic system, composed of linguistic subsystems that change over time. This study utilized secondary data from a larger project, the Bilingual Language Literacy Project (BLLP), which collected narrative retell language samples produced in Spanish and English from ELL children. The final longitudinal dataset used in this study consisted of 12,248 oral narrative language samples (6,516 Spanish; 5,732 English) that were produced by 1,723 ELLs. This study examined the effect of three predictors on language growth: academic semester (metric of time), gender, and schooling. Growth curve model (GCM) testing was used to profile the longitudinal growth of the ELLs' oral language skills in Spanish and English over time. This study had a number of important findings regarding change over time, intra- and inter-individual variability, and the impact of initial status on growth. With regard to change over time: MLUw, NDW, and WPM demonstrated growth over time in Spanish and English; the shapes of Spanish (curvilinear, non-monotonic, and continuous) and English growth (linear, non-monotonic, and discontinuous) were similar within-language; language growth in Spanish was predicted by academic semester and gender; and language growth in English was predicted by academic semester, gender, and schooling. With regard to intra- and inter-individual variability: significant intra-individual differences in the growth of all the oral language measures, across each wave of measurement, were found for both languages; significant intra-individual differences in the initial status of participants for all the oral language measures were found for both languages; significant inter-individual differences in the growth rates were found for WPM-Spanish; and significant inter-individual differences in the growth rates were found for all the oral language measures in English. With regard to the impact of initial status on growth: the growth of MLUw-Spanish was systematically related to initial status (lower performers at initial status may not catch up to higher performers); the growth of NDW- and WPM-Spanish were unrelated to its initial status (lower performers at initial status may, or may not catch up to higher performers); and the growth of MLUw-, NDW-, and WPM-English was systematically related to initial status (lower performers at initial status may catch up to higher performers). With regard to the co-development of interconnected subsystems, qualitative observations (non-empirically tested) based on visual inspection and GCM estimates provided initial insight into the possible co-development occurring within- and across-languages. The present study broke new ground by specifying the shape of growth for MLUw, NDW, and WPM in the Spanish and English of ELLs during their first 3 years of formal schooling. The study had a number of methodological limitations that will guide and motivate future work on the language growth of ELLs. / Communication Sciences

There is substantive literature surrounding the impact of price controls on the research and development (R&D) of new pharmaceutical products. The European Union (EU) and United States (US) are often studied in contrast to examine the influence of price controls as the US has fewer pharmaceutical price controls than the EU. We find moderate evidence that the US spent more on annual domestic pharmaceutical R&D than the EU between 2004 and 2021, on average, before and after adjusting for GDP growth per capita and year. We find strong evidence that the US increased annual domestic R&D spending at a faster rate than the EU between 2004 and 2021, on average, before and after adjusting for GDP growth per capita. Prior studies have asserted that increased US R&D spending leads to the production of more pharmaceutical products. Our study aims to quantify the differences in US and EU orphan drug development. Orphan drugs are pharmaceutical products that treat rare diseases. Both the EU and US aim to stimulate orphan drug production with policies including national grants, tax credits, and extended periods of market exclusivity. Our study gives indication that these policies in the US and EU are effective at spurring rare disease drug creation. We find evidence that orphan drug market authorizations increased annually, on average, in both the US and EU from 2004 to 2021, before and after adjusting for GDP growth rate per capita and the interaction between year and region. We find the same when isolating market authorizations for new orphan drugs. The US awarded more annual orphan drug market authorizations and market authorizations for new orphan drugs than the EU every year from 2004 to 2021, except in 2007. We find evidence that from 2004 to 2021, the US awarded more annual orphan drug market authorizations and market authorizations for new orphan drugs than the EU, on average, before and after adjusting for GDP growth per capita and year. There is also evidence that the US increased the number of these authorizations at a faster rate annually than the EU, on average, before and after adjusting for GDP growth per capita. Our results suggest an association between EU price controls and reduced pharmaceutical innovation. This is seen in the form of less annual R&D spending growth, orphan drug market authorizations, and new orphan drugs compared to the US, on average. However, the benefits of this innovation may not reach patients, as US consumers pay higher pharmaceutical prices due to limited price controls. This may contribute to the expansion of existing health inequities in the US. We are also unsure if the quality of US innovation exceeds that of the EU and if increased innovation is truly the result of lower price controls.

<p dir="ltr">This dissertation addresses three progressively fundamental problems for functional data analysis: (1) To do efficient inference for the functional mean model accounting for within-subject correlation, we propose the refined and bias-corrected empirical likelihood method. (2) To identify functional subjects potentially from different populations, we propose the dominant-set based unsupervised clustering method using the similarity matrix. (3) To learn the similarity matrix from various similarity metrics for functional data clustering, we propose the modularity guided and dominant-set based semi-supervised clustering method.</p><p dir="ltr">In the first problem, the empirical likelihood method is utilized to do inference for the mean function of functional data by constructing the refined and bias-corrected estimating equation. The proposed estimating equation not only improves efficiency but also enables practically feasible empirical likelihood inference by properly incorporating within-subject correlation, which has not been achieved by previous studies.</p><p dir="ltr">In the second problem, the dominant-set based unsupervised clustering method is proposed to maximize the within-cluster similarity and applied to functional data with a flexible choice of similarity measures between curves. The proposed unsupervised clustering method is a hierarchical bipartition procedure under the penalized optimization framework with the tuning parameter selected by maximizing the clustering criterion called modularity of the resulting two clusters, which is inspired by the concept of dominant set in graph theory and solved by replicator dynamics in game theory. The advantage offered by this approach is not only robust to imbalanced sizes of groups but also to outliers, which overcomes the limitation of many existing clustering methods.</p><p dir="ltr">In the third problem, the metric-based semi-supervised clustering method is proposed with similarity metric learned by modularity maximization and followed by the above proposed dominant-set based clustering procedure. Under semi-supervised setting where some clustering memberships are known, the goal is to determine the best linear combination of candidate similarity metrics as the final metric to enhance the clustering performance. Besides the global metric-based algorithm, another algorithm is also proposed to learn individual metrics for each cluster, which permits overlapping membership for the clustering. This is innovatively different from many existing methods. This method is superiorly applicable to functional data with various similarity metrics between functional curves, while also exhibiting robustness to imbalanced sizes of groups, which are intrinsic to the dominant-set based clustering approach.</p><p dir="ltr">In all three problems, the advantages of the proposed methods are demonstrated through extensive empirical investigations using simulations as well as real data applications.</p>

Wiederholte Messungen mehrerer Individuen sind von entscheidender Bedeutung für die Psychologie. Beispiele sind längsschnittliche Paneldaten und Elektroenzephalografie-Daten (EEG-Daten). In dieser Arbeit entwickle ich für jede dieser beiden Datenarten neue Analyseansätze, denen Methoden des maschinellen Lernens zu Grunde liegen. Für Paneldaten entwickle ich Gauß-Prozess-Panelmodellierung (GPPM), die auf der flexiblen Bayesschen Methode der Gauß-Prozess-Regression basiert. Der Vergleich von GPPM mit längsschnittlicher Strukturgleichungsmodellierung (lSEM), welche die meisten herkömmlichen Panelmodellierungsmethoden als Sonderfälle enthält, zeigt, dass lSEM wiederum als Sonderfall von GPPM aufgefasst werden kann. Im Gegensatz zu lSEM eignet sich GPPM gut zur zeitkontinuierlichen Modellierung, kann eine größere Menge von Modellen beschreiben, und beinhaltet einen einfachen Ansatz zur Generierung personenspezifischer Vorhersagen. Ich zeige, dass die implementierte GPPM-Darstellung gegenüber bestehender SEM Software eine bis zu neunfach beschleunigte Parameterschätzung erlaubt. Für EEG-Daten entwickle ich einen personenspezifischen Modellierungsansatz zur Identifizierung und Quantifizierung von Unterschieden zwischen Personen, die in konventionellen EEG-Analyseverfahren ignoriert werden. Im Rahmen dieses Ansatzes wird aus einer großen Menge hypothetischer Kandidatenmodelle das beste Modell für jede Person ausgewählt. Zur Modellauswahl wird ein Verfahren aus dem Bereich des maschinellen Lernens genutzt. Ich zeig ich, wie die Modelle sowohl auf der Personen- als auch auf der Gruppenebene interpretiert werden können. Ich validiere den vorgeschlagenen Ansatz anhand von Daten zur Arbeitsgedächtnisleistung. Die Ergebnisse verdeutlichen, dass die erhaltenen personenspezifischen Modelle eine genauere Beschreibung des Zusammenhangs von Verhalten und Hirnaktivität ermöglichen als konventionelle, nicht personenspezifische EEG-Analyseverfahren. / Repeated measures obtained from multiple individuals are of crucial importance for developmental research. Examples of repeated measures obtained from multiple individuals include longitudinal panel and electroencephalography (EEG) data. In this thesis, I develop a novel analysis approach based on machine learning methods for each of these two data modalities. For longitudinal panel data, I develop Gaussian process panel modeling (GPPM), which is based on the flexible Bayesian approach of Gaussian process regression. The comparison of GPPM with longitudinal structural equation modeling (SEM), which contains most conventional panel modeling approaches as special cases, reveals that GPPM in turn encompasses longitudinal SEM as a special case. In contrast to longitudinal SEM, GPPM is well suited for continuous-time modeling, can express a larger set of models, and includes a straightforward approach to obtain person-specific predictions. The comparison between the developed GPPM toolbox and existing SEM software reveals that the GPPM representation of popular longitudinal SEMs decreases the amount of time needed for parameter estimation up to ninefold. For EEG data, I develop an approach to derive person-specific models for the identification and quantification of between-person differences in EEG responses that are ignored by conventional EEG analysis methods. The approach relies on a framework that selects the best model for each person based on a large set of hypothesized candidate models using a model selection approach from machine learning. I show how the obtained models can be interpreted on the individual as well as on the group level. I validate the proposed approach on a working memory data set. The results demonstrate that the obtained person-specific models provide a more accurate description of the link between behavior and EEG data than the conventional nonspecific EEG analysis approach.

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近幾年來，國人自殺死亡率不斷提高，且自殺死亡從1997年起已連續多年列於國人十大死亡原因之一，所以自殺防治工作刻不容緩。本研究採用自殺防治中心在桃園縣六家居家服務單位(龍祥、中國、仁愛、紅十字、家輔及寬福)所做之問卷調查資料，目的在於找出何種特性者，BSRS5 (The Five-Item Brief Symptom Rating Scale)分數及自殺意念分數可能較高。本研究屬於時序性追蹤資料，自民國96年5月份起，由居服人員針對受測對象進行訪談，大約每隔兩週收集一次，總共進行四次。 針對問卷進行基本敘述性統計、單項排名分析以及交叉分析後發現，在人口特質方面，男女性比例相當，年齡層主要皆在65~84歲，教育程度以不識字及國小為主；在BSRS5五題排名方面，以第一題「睡眠困難(難以入睡或早醒)」的平均分數最高，第四題「覺得比不上別人」平均分數最低；由交叉分析的結果發現身體狀況為一個重要的變數，身體狀況差的人BSRS5總分6分以上或自殺意念2分以上明顯較多。 對資料配適廣義估計方程式及Alternating Logistic Regressions的結果，發現在反應變數為BSRS5總分時，女性、身體狀況差及曾經看過精神科者BSRS5分數達到6分以上的可能性較高。若反應變數為自殺意念時，無論是利用廣義估計方程式或Alternating Logistic Regressions，從模型配適的結果發現只有BSRS5的效應顯著。不管利用BSRS5總分或是各題分開來看，BSRS5對自殺意念是一個相當有效的檢測工具，BSRS5分數愈高則自殺意念2分以上的機會也愈高。此外利用多層結構分析方法配適廣義估計方程式，針對BSRS5與受測次數間的關聯性分析，發現與配適傳統unstructured相關性矩陣的估計結果差異不大，但是可以減少許多參數估計，並且在電腦計算時間上是較快速的。 / In Taiwan, suicide has been among the top ten causes of death since 1997, and suicide prevention has thus attracted much attention since. Using the data provided by Taiwan Suicide Prevention Center (TSPC), this study is aimed to find out possible personal characteristics that might have some impacts on the BSRS5 (the Five-Item Brief Symptom Rating Scale) and suicide ideation scores The data come from a longitudinal study in which subjects from six elderly home service centers in Taoyuan County, Taiwan were visited four times between May and July, 2007, about two weeks between each visit. The total number of subjects is 1981. The proportions of male and female are nearly the same, the age range is from 65 to 84, and most of them have only an elementary school degree. Preliminary analyses indicate that among the five items in BSRS5, insomnia (the first item) is ranked the highest, and inferiority (the fourth item) is the lowest. In addition, health status is highly correlated to the BSRS5 and suicide ideation scores, the worse the health status, the higher the BSRS5 and suicide ideation scores. Fitting the data with Generalized Estimating Equation (GEE) and Alternating Logistic Regressions models with respect to the BSRS5 score, we further find that female, those who have bad health status, and those who have ever consulted a psychiatrist have higher probability that the BSRS5 score is greater than 6. As far as the suicide ideation score is concerned, the BSRS5 score is the only covariate that is statistically significant, an indication that BSRS5 is a useful tool for screening subjects at risk of committing suicide. While the conclusions stay the same whether the data are analyzed through GEE with commonly used unstructured correlation structure or newly developed multiblock and multilayer correlation structure, the latter approach reduces the computer time significantly.

Os modelos mistos são apropriados na análise de dados longitudinais, agrupados e hierárquicos, permitindo descrever e comparar os perfis médios de respostas, levando em conta a variabilidade e a correlação entre as unidades experimentais de um mesmo grupo e entre os valores observados na mesma unidade experimental ao longo do tempo, assim como a heterogeneidade das variâncias. Esses modelos possibilitam a análise de dados desbalanceados, incompletos ou irregulares com relação ao tempo. Neste trabalho, buscou-se mostrar a flexibilidade dos modelos lineares mistos e a sua importância na análise de dados toxicológicos longitudinais. Os modelos lineares mistos foram utilizados para analisar os efeitos de dose no ganho de peso de ratos adultos machos e fêmeas, em teste de toxicidade por doses repetidas e também os efeitos de fase de gestação e dose nos perfis de pesos de filhotes de ratas tratadas. Foram comparados os modelos lineares mistos de regressão polinomial de grau 3, spline e de regressão por partes, ambos com um único ponto de mudança na idade média de abertura dos olhos dos filhotes, buscando o mais apropriado para descrever o crescimento dos mesmos ao longo do período de amamentação. São apresentados os códigos escritos no SAS/STAT para a análise exploratória dos dados, ajuste, comparação e validação dos modelos. Espera-se que o detalhamento da teoria e das aplicações apresentado contribua para a compreensão, interesse e uso desta metodologia por estatísticos e pesquisadores da área. / Mixed models are appropriate in the analysis of longitudinal, grouped and hierarchical data, allowing describe and compare the average response profiles, taking into account the variability and correlation among the experimental units of the same group and among the values observed over the time in the same experimental unit, as well as the heterogeneity of variances. These models allow the analysis of unbalanced, incomplete or irregular data with respect to time. This work aimed to show the flexibility of linear mixed models and its importance in the analysis of longitudinal toxicological data. Linear mixed models were used to evaluate the effects of doses in the body weight gain of adult male and female Wistar rats, in repeated doses toxicity test and also the effects of pregnancy period and dose in the pups growth of treated dams. It were compared the linear mixed models of third degree polynomial regression, spline and piecewise regression, both with a single point of change in the average time of pups eyes opening, searching for the most appropriate one to describe their growth along the lactation period. The SAS/STAT codes used for exploratory data analysis, comparison and validation of fitted models are presented. It is expected that the detailing of the theory and of the applications presented contribute with the understanding, interest and use of this methodology by statisticians and researchers in the area.

Nous considérions des modèles à espace d'état où les observations sont multicatégorielles et longitudinales, et l'état est décrit par des modèles du type CHARN. Nous estimons l'état au moyen des récursivités de Kalman généralisées. Celles-ci reposent sur l'application d'une variété de filtres particulaires et de l’algorithme EM. Nos résultats sont appliqués à l'estimation du trait latent en qualité de vie. Ce qui fournit une alternative et une généralisation des méthodes existantes dans la littérature. Ces résultats sont illustrés par des simulations numériques et une application aux données réelles sur la qualité de vie des femmes ayant subi une opération pour cause de cancer du sein / We consider state space models where the observations are multicategorical and longitudinal, and the state is described by CHARN models. We estimate the state by generalized Kalman recursions, which rely on a variety of particle filters and EM algorithm. Our results are applied to estimating the latent trait in quality of life, and this furnishes an alternative and a generalization of existing methods. These results are illustrated by numerical simulations and an application to real data in the quality of life of patients surged for breast cancer

Diversos delineamentos experimentais que são aplicados correntemente tomam como base experimentos agronômicos. Esses dados experimentais são, geralmente, analisados usando-se modelos que consideram uma variância residual constante (ou homogênea), como pressuposto inicial. Entretanto, esta pressuposição mostra-se relativamente forte quando se está diante de situações para as quais fatores ambientais ou externos exercem considerável influência nas medidas experimentais. Neste trabalho, são estudados modelos para a média e a variância, simultaneamente, com a variância estruturada de duas formas: (i) por meio de um preditor linear, que permite incorporar variáveis externas e fatores de ruído e (ii) por meio de efeitos aleatórios, que permitem acomodar tanto o efeito longitudinal quanto o efeito de superdispersão, no caso de medidas binárias repetidas no tempo. A classe de modelos lineares generalizados duplos (MLGD) foi aplicada a um estudo observacional que consistiu em medir a mortalidade de frangos de corte no fim da condição de espera pré-abate. Nesse problema, é forte a evidência de que alguns fatores influenciam a variabilidade, e consequentemente, diminuem a precisão das análises inferenciais. Outro problema agronômico relevante, associado à horticultura, são os experimentos de cultura de tecidos vegetais, em que o número de explantes que regeneram são contados. Como esse tipo de experimento apresenta um grande número de parâmetros a serem estimados, comparado ao tamanho da amostra, os modelos existente podem gerar estimativas questionáveis ou até levar a conclusões erroneas, uma vez esse que são baseados em grandes amostras para se fazer inferência estatística. Foi proposto um modelo linear generalizados duplo, para os dados de proporções, de uma perspectiva Bayesiana, visando a análise estatística sob pequenas amostras e a incorporação do conhecimento especialista no processo de estimação dos parâmetros. Um problema clínico, que envolve dados binários medidos repetidamente no tempo é apresentado e são propostos dois modelos que acomodam o efeito da superdispersão e a dependência longitudinal das medidas, utilizandos-se efeitos aleatórios. Foram obtidos resultados satisfatórios nos três problemas estudados. Os MLGD permitiram identificar os fatores associados à mortalidade das aves de corte, o que permitirá minimizar perdas e habilitar os processos de manejo, transporte e abate aos critérios de bem-estar animal e exigências da comunidade européia. O MLGD Bayesiano permitiu identificar o genótipo associado ao efeito de superdispersão, aumentando a precisão da inferência de seleção de variedades. Dois modelos combinados foram propostos logit-normal-Bernoulli-beta e o probit-normal-Bernoulli-beta, que acomodaram satisfatoriamente a superdispersão e a dependência longitudinal das medidas binárias. Esses resultados reforçam a importância de se modelar a média e a variância conjuntamente, o que aumenta a precisão na pesquisa agronômica, tanto em estudos experimentais quanto em estudos observacionais. / Several experimental designs that are currently applied are based on agricultural experiments. These experimental data are, usually, analised with statistical models that assume constant residual variance (or homogeneous), as basic assumption. However, this assumption shows hard to stand for, when environmental or external factors exert strong influence over the measurements. In this work, we study the joint modelling for the mean and the variance, the latter being structured on two ways: (i) through a linear predictor, which allows the incorporation of external variables and/or noise factors and (ii) by the use of random effects, that accommodate jointly the possible overdispersion effect and the dependence of longitudinal data in the case of binary measusurements taken over time. The class of double generalized linear models (DGLM) was applied to an observational study where the poultry mortality was measured in the preslaughter operations. With this situation, it can be observed that there is a strong influence from some environmental factors over the variability observed, and consequently, this reduces the precision of the inferential analysis. Another relevant agricultural problem, related to horticulture, is the tissue culture experiments, where the number of regenerated explants is counted. Usually, this kind of experiment use a large number of parameters to be estimated, when compared with the sample size. The current frequentist models are based on large samples for statistical inference and, under this experimental condition, can generate unreliable estimates or even lead to erroneous conclusions. A double generalized linear model was proposed to analyse proportion data, under the Bayesian perspective, which can be applied to small samples and can incorporate expert knowledge into the parameter estimation process. One clinical research, that measured binary data repeatedly through the time is presented and two models are proposed to fit the overdispersion effect and the dependence of longitudinal measurements, using random effects. It was obtained satisfactory results under these three problems studied. the DGLM allowed to identify factors associated with the poultry mortality, that will allow to minimize loss and improve the process, since the catching until lairage on slaughterhouse, agreeing with animal welfare criteria and the European community rules. The Bayesian DGLM allowed to identify the genotype associated with the overdispersion effect, increasing the precision on the inference about varieties selection. Two combined models were proposed, a logit-normal- Bernoulli-beta and a probit-normal-Bernoulli-beta, which have both addressed the overdispersion effect and the longitudinal dependence of the binary measurements. These results reinforce the importance to modelling mean and dispersion jointly, as a way to increase the precision of agricultural experimentation, be it on experimental studies or observational studies.