Les forces de contact dans un milieu granulaire se répartissent de façon très inhomogène en un réseau de "chaînes de forces" qui supporte la plus grosse partie des contraintes. Il est primordial de bien comprendre l'influence du désordre des forces à l'échelle du grain sur les propriétés d'équilibre mécanique d'un milieu granulaire à l'échelle macroscopique.<br /><br />La mesure de forces dans un milieu granulaire est délicate à cause d'un couplage fondamental entre les déformations du capteur et la mobilisation des forces de friction entre grains ou entre grains et paroi. Cependant, en définissant proprement le protocole de mesure, nous avons pu améliorer de façon très significative la reproductibilité des résultats en comparaison des mesures que l'on trouve dans la littérature.<br /><br />Nous nous sommes intéressé aux liens qui existent entre la structure de l'empilement granulaire et la répartition des contraintes. Sous l'effet d'un cisaillement ou de vibrations, l'équilibre d'une colonne granulaire dans un silo évolue considérablement ainsi que la structure de l'empilement comme le révèlent des mesures de densité moyenne et locale. Sous le sommet d'un tas de sable formé par écoulement des grains en avalanches, j'ai observé très clairement un minimum ou "trou" de pression, alors que la pression est maximum si les grains sont déposés en couches horizontales. Nous avons aussi mesuré les fluctuations résiduelles de la pression en fonction de la taille des grains ou de la hauteur de remplissage du silo et ai observé que leur dépendance avec la taille des grains montrent une régression statistique anormale en comparaison de celle déduite de la distribution des forces à l'échelle du grain.<br /><br />La plupart des observations sont qualitativement et quantitativement bien reproduites par le modèle OSL dans lequel les contraintes se propagent selon deux directions dont l'une s'identifie à la direction moyenne des chaînes de forces. La notion de propagation anisotrope de forces permet de comprendre la distribution de pression sous un tas ou la forme de la courbe de saturation de la pression dans un silo, y compris les oscillations de la pression en présence d'une surcharge.<br /><br />Nous avons proposé en outre un modèle de durcissement d'arches qui permet d'expliquer l'existence d'un mode d'écoulement fragmentaire après renversement d'un tube rempli de grains et met en évidence le rôle non négligeable de l'élasticité des parois.

Long-distance and intercity travel generally make up a small portion of the total number of trips taken by an individual, while representing a large portion of aggregate distance traveled on the transportation system. While some research exists on intercity travel behavior between large metropolitan centers, this thesis addresses a need for more research on travel behavior between non-metropolitan areas and large metropolitan centers. This research specifically considers travel from home locations in northern New England, going to Boston, New York City, Philadelphia, and Washington, DC. These trips are important for quality of life, multimodal planning, and rural economies. This research identifies and quantifies factors that influence people's mode choice (automobile, intercity bus, passenger rail, or commercial air travel) for these trips. The research uses survey questionnaire data, latent factor analysis, and discrete choice modeling methods. Factors include sociodemographic, built environment, latent attitudes, and trip characteristics. The survey, designed by the University of Vermont Transportation Research Center and the New England Transportation Institute, was conducted by Resource Systems Group, Inc. in 2014, with an initial sample size of 2560. Factor analysis was used to prepare 6 latent attitudinal factors, based on 70 attitudinal responses from the survey statements. The survey data were augmented with built environment variables using geographic information systems (GIS) analysis. A set of multinomial logit models, and a set of nested logit models, were estimated for business and non-business trip mode choice. Results indicate that for this type of travel, factors influencing mode choice for both business and non-business trips include trip distance; land use; personal use of technology; and latent attitudes about auto dependence, preference for automobile, and comfort with personal space and safety on public transportation. Gender is a less significant factor. Age is only significant for non-business trips. The results reinforce the importance and viability of modeling long-distance travel from less populated regions to large metropolitan areas, and the significant roles of trip distance, built environment, personal attitudes, and sociodemographic factors in how people choose to make these trips for different purposes. Future research should continue to improve these types of long-distance mode choice models by incorporating mode specific travel time and cost, developing more specific attitudinal statements to expand latent factor analysis, and further exploring built environment variables. Improving these models will promote better planning, engineering, operations, and infrastructure investment decisions in many regions and communities across the United States which have not yet been well studied, possibly impacting levels of service.

High-throughput genomic datasets obtained from microarray or sequencing studies have revolutionized the field of molecular biology over the last decade. The complexity of these new technologies also poses new challenges to statisticians to separate biological relevant information from technical noise. Two methods are introduced that address important issues with normalization of array comparative genomic hybridization (aCGH) microarrays and the analysis of RNA sequencing (RNA-Seq) studies. Many studies investigating copy number aberrations at the DNA level for cancer and genetic studies use comparative genomic hybridization (CGH) on oligo arrays. However, aCGH data often suffer from low signal to noise ratios resulting in poor resolution of fine features. Bilke et al. showed that the commonly used running average noise reduction strategy performs poorly when errors are dominated by systematic components. A method called pcaCGH is proposed that significantly reduces noise using a non-parametric regression on technical covariates of probes to estimate systematic bias. Then a robust principal components analysis (PCA) estimates any remaining systematic bias not explained by technical covariates used in the preceding regression. The proposed algorithm is demonstrated on two CGH datasets measuring the NCI-60 cell lines utilizing NimbleGen and Agilent microarrays. The method achieves a nominal error variance reduction of 60%-65% as well as an 2-fold increase in signal to noise ratio on average, resulting in more detailed copy number estimates. Furthermore, correlations of signal intensity ratios of NimbleGen and Agilent arrays are increased by 40% on average, indicating a significant improvement in agreement between the technologies. A second algorithm called gamSeq is introduced to test for differential gene expression in RNA sequencing studies. Limitations of existing methods are outlined and the proposed algorithm is compared to these existing algorithms. Simulation studies and real data are used to show that gamSeq improves upon existing methods with regards to type I error control while maintaining similar or better power for a range of sample sizes for RNA-Seq studies. Furthermore, the proposed method is applied to detect differential 3' UTR usage.

This dissertation has multiple aims in studying hierarchical linear models in biomedical data analysis. In Chapter 1, the novel idea of studying the durations of adolescent growth spurts as a predictor of adulthood obesity is defined, established, and illustrated. The concept of contextual effects modeling is introduced in this first section as we study secular trend of adulthood obesity and how this trend is mitigated by the durations of individual adolescent growth spurts and the secular average length of adolescent growth spurts. It is found that individuals with longer periods of fast height growth in adolescence are more prone to having favorable BMI profiles in adulthood. In Chapter 2 we study the estimation of contextual effects in a hierarchical generalized linear model (HGLM). We simulate data and study the effects using the higher level group sample mean as the estimate for the true mean versus using an Empirical Bayes (EB) approach (Shin and Raudenbush 2010). We study this comparison for logistic, probit, log-linear, ordinal and nominal regression models. We find that in general the EB estimate lends a parameter estimate much closer to the true value, except for cases with very small variability in the upper level, where it is a more complicated situation and there is likely no need for contextual effects analysis. In Chapter 3 the HGLM studies are made clearer with large-scale simulations. These large scale simulations are shown for logistic regression and probit regression models for binary outcome data. With repetition we are able to establish coverage percentages of the confidence intervals of the true contextual effect. Coverage percentages show the percentage of simulations that have confidence intervals containing the true parameter values. Results confirm observations from the preliminary simulations in the previous section of this paper, and an accompanying example of adulthood hypertension shows how these results can be used in an application.

Ordinal scales are commonly used to measure health status and disease related outcomes in hospital settings as well as in translational medical research. Notable examples include cancer staging, which is a five-category ordinal scale indicating tumor size, node involvement, and likelihood of metastasizing. Glasgow Coma Scale (GCS), which gives a reliable and objective assessment of conscious status of a patient, is an ordinal scaled measure. In addition, repeated measurements are common in clinical practice for tracking and monitoring the progression of complex diseases. Classical ordinal modeling methods based on the likelihood approach have contributed to the analysis of data in which the response categories are ordered and the number of covariates (p) is smaller than the sample size (n). With the emergence of genomic technologies being increasingly applied for obtaining a more accurate diagnosis and prognosis, a novel type of data, known as high-dimensional data where the number of covariates (p) is much larger than the number of samples (n), are generated. However, corresponding statistical methodologies as well as computational software are lacking for analyzing high-dimensional data with an ordinal or a longitudinal ordinal response. In this thesis, we develop a regularization algorithm to build a parsimonious model for predicting an ordinal response. In addition, we utilize the classical ordinal model with longitudinal measurements to incorporate the cutting-edge data mining tool for a comprehensive understanding of the causes of complex disease on both the molecular level and environmental level. Moreover, we develop the corresponding R package for general utilization. The algorithm was applied to several real datasets as well as to simulated data to demonstrate the efficiency in variable selection and precision in prediction and classification. The four real datasets are from: 1) the National Institute of Mental Health Schizophrenia Collaborative Study; 2) the San Diego Health Services Research Example; 3) A gene expression experiment to understand `Decreased Expression of Intelectin 1 in The Human Airway Epithelium of Smokers Compared to Nonsmokers' by Weill Cornell Medical College; and 4) the National Institute of General Medical Sciences Inflammation and the Host Response to Burn Injury Collaborative Study.

O'Brien and Fleming (1979) proposed a straightforward and useful multiple testing procedure (group sequential testing procedure) for comparing two treatments in clinical trials where subject responses are dichotomous (e.g. success and failure). O'Brien and Fleming stated that their group sequential testing procedure has the same Type I error rate and power as that of a fixed one-stage chi-square test, but gives the opportunity to terminate the trial early when one treatment is clearly performing better than the other. We studied and tested the O'Brien and Fleming procedure specifically by correcting the originally proposed critical values. Furthermore, we updated the O’Brien Fleming Group Sequential Testing procedure to make it more flexible via three extensions. The first extension is combining the O’Brien Fleming Group Sequential Testing procedure with the Optimal allocation, where the idea is to allocate more patients to the better treatment after each interim analysis. The second extension is combining the O’Brien Fleming Group Sequential Testing procedure with the Neyman allocation which aims to minimize the variance of the difference in sample proportions. The last extension is that we can allow for different sample weights for different stages, as opposed to equal allocation for different stages. Simulation studies showed that the O’Brien Fleming Group Sequential Testing procedure is relatively robust to the added features.

BACKGROUND: Little is known of the effects of obesity, body size and body composition, and blood pressure (BP) in childhood on hypertension (HBP) and cardiac structure and function in adulthood due to the lack of long-term serial data on these parameters from childhood into adulthood. In the present study, we are poised to analyze these serial data from the Fels Longitudinal Study (FLS) to evaluate the extent to which body size during childhood determines HBP and cardiac structure and function in the same individuals in adulthood through mathematical modeling. METHODS: The data were from 412 males and 403 females in the FLS. Stature and BMI parameters were estimated using the Preeze-Baines model and the third degree polynomial model to describe the timing, velocity and duration of these measure from 2 to 25 years of age. The biological parameters were related to adult BP and echocardiographic (Echo-) measurements using Generalized Linear Models (GLM). RESULTS: The parameters of stature and BMI were compared between male and female to their overall goodness of fit and their capabilities to quantify the timing, rate of increase, and duration of the growth events. For stature parameters, the age at onset and peak velocity was earlier for girls; but the peak velocity was greater in boys; the velocity at onset was about the same for boys and girls; and stature at onset, peak velocity and adult was greater for boys. For BMI parameters, boys tended to have larger BMI values than girls, but the rates of change in BMI were almost the same; there was no sex difference in the timing of BMI rebound, but there was for the age of the peak velocity of BMI and maximum BMI, both of which were earlier in girls than in boys. CONCLUSIONS: Changes in childhood stature and BMI parameters were related to adult BP and Echo-measurements more so in females than males. Also the relationship of the adult BP measurements with corresponding childhood biological parameters was stronger than the relationship for adult Echo-measurements.

The Medical Examiner of Virginia (ME) dataset and the Virginia Department of Forensic Science Driving Under the Influence of Drugs (DUI) datasets were used to determine whether people have the potential to develop tolerances to diphenhydramine, cocaine, oxycodone, hydrocodone, methadone, and morphine. These datasets included the years 2000-2004 and were used to compare the concentrations of these six drugs between people who died from a drug-related cause of death (of the drug of interest) and people who were pulled over for driving under the influence. Three drug pattern groups were created to divide each of the six drug-specific datasets in order to compare concentrations between individuals with the drug alone, the drug and ethanol, or a poly pharmacy of drugs (multiple drugs). An ANOVA model was used to determine if there was an interaction effect between the source dataset (ME or DUI) and the drug pattern groups. For diphenhydramine and cocaine, an interaction was statistically significant, but for the other drugs, it was not significant. The other four drug-specific datasets showed that the DUI and ME were statistically significantly different from each other, and all of those datasets except for methadone showed that there was a statistically significant difference between at least two drug pattern groups. Showing that all of these datasets showed differences between the ME and DUI datasets did not provide sufficient evidence to suggest the development of tolerances to each of the six drugs. One exception was with methadone because there were 14 individuals that had what is defined as a "clinical 'lethal' blood concentration". These individuals provide some evidence for the possibility of developing tolerances.The main outcomes of this study include suggesting changes to make to the ME datasets and the DUI datasets with regard to the way data is kept and collected. Several problems with the fields of these datasets arose before beginning the analysis and had to be corrected. Some of the changes suggested are currently being considered at the Virginia Office of the Chief Medical Examiner as they are beginning to restructure their database.

This dissertation focuses on methodology specific to microarray data analyses that organize the data in preliminary steps and proposes a cluster analysis method which improves the interpretability of the cluster results. Cluster analysis of microarray data allows samples with similar gene expression values to be discovered and may serve as a useful diagnostic tool. Since microarray data is inherently noisy, data preprocessing steps including smoothing and filtering are discussed. Comparing the results of different clustering methods is complicated by the arbitrariness of the cluster labels. Methods for re-labeling clusters to assess the agreement between the results of different clustering techniques are proposed. Microarray data involve large numbers of observations and generally present as arrays of light intensity values reflecting the degree of activity of the genes. These measurements are often two dimensional in nature since each is associated with an individual sample (cell line) and gene. The usual hierarchical clustering techniques do not easily adapt to this type of problem. These techniques allow only one dimension of the data to be clustered at a time and lose information due to the collapsing of the data in the opposite dimension. A novel clustering technique based on normal mixture distribution models is developed. This method clusters observations that arise from the same normal distribution and allows the data to be simultaneously clustered in two dimensions. The model is fitted using the Expectation/Maximization (EM) algorithm. For every cluster, the posterior probability that an observation belongs to that cluster is calculated. These probabilities allow the analyst to control the cluster assignments, including the use of overlapping clusters. A user friendly program, 2-DCluster, was written to support these methods. This program was written for Microsoft Windows 2000 and XP systems and supports one and two dimensional clustering. The program and sample applications are available at http://etd.vcu.edu. An electronic copy of this dissertation is available at the same address.

Response adaptive designs intend to allocate more patients to better treatments without undermining the validity and the integrity of the trial. The immediacy of the primary response (e.g. deaths, remission) determines the efficiency of the response adaptive design, which often requires outcomes to be quickly or immediately observed. This presents difficulties for survival studies, which may require long durations to observe the primary endpoint. Therefore, we introduce auxiliary endpoints to assist the adaptation with the primary endpoint, where an auxiliary endpoint is generally defined as any measurement that is positively associated with the primary endpoint. Our proposed design (referred to as bivariate adaptive design) is based on the classical response adaptive design framework. The connection of auxiliary and primary endpoints is established through Bayesian method. We extend parameter space from one dimension to two dimensions, say primary and auxiliary efficacies, by implementing a conditional weigh function on the loss function of the design. The allocation ratio is updated at each stage by optimization of the loss function subject to the information provided for both the auxiliary and primary outcomes. We demonstrate several methods of joint modeling the auxiliary and primary outcomes. Through simulation studies, we show that the bivariate adaptive design is more effective in assigning patients to better treatments as compared with univariate optimal and balanced designs. As hoped, this joint-approach also reduces the expected number of patient failures and preserves the comparable power as compared with other designs.