Auswahl der wissenschaftlichen Literatur zum Thema „Beta-Binomial Model“

La qualité des données est une préoccupation fondamentale de la recherche clinique. Pour garantir cette qualité, il faut pratiquer un monitorage continu des données. Les organismes internationaux de régulation des médicaments recommandent que ce monitorage soit ciblé, basé sur une analyse des risques. De cette recommandation a germé le concept de « monitoring statistique centralisé » (MSC) qui consiste à détecter des distributions de variables atypiques dans un centre par rapport aux autres centres. Cette thèse recense les méthodes de MSC existants, en propose de nouvelles, et compare les performances des unes et des autres. Dans la première partie, nous rappelons l’intérêt du sujet, dans un contexte marqué par l’accroissement du nombre d’essais cliniques, la nécessité de travailler de plus en plus à distance et le besoin de nouveaux paradigmes de monitorage. Dans la seconde partie, nous recensons les méthodes de MSC existantes, analysons leurs performances rapportées dans la littérature et en tirons deux observations majeurs : (i) le nombre de méthodes est limité; (ii) leurs évaluations par des travaux de simulations et des applications sur données réelles rapportées dans la littérature sont également limitées. Dans la troisième partie nous proposons deux nouvelles méthodes de MSC pour détecter les distributions de variables atypiques dans les essais multicentriques, l’une pour données quantitatives qui utilise une mesure de distance standardisée (méthode de la Distance) et l’autre pour données catégorielles, qui utilise un modèle Bayésien hiérarchique bêta-binomial (HBBB). Nous évaluons les performances de ces méthodes en utilisant des simulations d'essais cliniques, puis les comparons à d’autres méthodes de MSC identifiées dans la littérature. Pour les données quantitatives, la méthode de la Distance a des performances similaires à la méthode proposée par Desmet et al., et supérieures à celles des deux autres méthodes existantes. Pour les données catégorielles, la méthode HBBB a des performances similaires à la seule autre méthode existante, également proposée par Desmet et al. Pour les deux méthodes, Distance et HBBB, la sensibilité est globalement médiocre, mais la spécificité excellente, y compris dans de nombreux scénarios impliquant de petits effectifs. La sensibilité faible suggère que le MSC est un outil supplémentaire pouvant être utilisé en complément des autres procédures de monitoring conventionnelles, mais ne les remplace pas. La spécificité forte et le caractère convivial suggère que ces méthodes peuvent être appliquées en routine dans tous les essais cliniques, car leur utilisation ne prendra pas beaucoup de temps au niveau central et n'engendrera pas de charge de travail inutile dans les centres investigateurs<br>Data quality is a fundamental concern of clinical research. To ensure this quality, continuous data monitoring must be practiced. International drug regulatory bodies recommend that this monitoring be targeted, based on a risk analysis. From this recommendation emerged the concept of “centralized statistical monitoring” (CSM) which consists of detecting atypical distributions of variables in a center compared to other centers. This thesis identifies existing CSM methods, proposes new ones, and compares the performances of each. In the first part, we recall the interest of the subject, in a context marked by the increase in the number of clinical trials, the need to work increasingly remotely and the need for new monitoring paradigms. In the second part, we identify existing CSM methods, analyze their performances reported in the literature and draw two major observations: (i) the number of methods is limited; (ii) their assessments through simulation studies and applications on real data reported in the literature are also limited. In the third part we propose two new CSM methods to detect the distributions of atypical variables in multicenter trials, one for quantitative data which uses a standardized distance measure (Distance method) and the other for categorical data, which uses a hierarchical Bayesian beta-binomial (HBBB) model. We evaluate the performance of these methods using clinical trial simulations and then compare them to other CSM methods identified in the literature. For quantitative data, the Distance method has performances similar to the method proposed by Desmet et al., and superior to those of the two other existing methods. For categorical data, the HBBB method has similar performance to the only other existing method, also proposed by Desmet et al. For both methods, Distance and HBBB, the sensitivity is poor overall, but the specificity is excellent, including in many scenarios involving small sample sizes. The low sensitivity suggests that the CSM is an additional tool that can be used in addition to other conventional monitoring procedures, but does not replace them. The strong specificity and user-friendliness suggest that these methods can be routinely applied in all clinical trials, as their use will not be centrally time consuming and will not create unnecessary workload in investigational centers

Propomos um modelo Beta-Binomial/Poisson para dados provenientes de um estudo com doentes de Parkinson, que consistiu em contar durante um minuto quantas tarefas foram realizadas e destas, quantas de maneira correta, antes e depois de um treinamento. O objetivo era verificar se o treinamento aumentava o número de tentativas e a porcentagem de acerto, o que destaca o aspecto bivariado do problema. Esse modelo considera tal aspecto, usa uma distribuição mais adequada a dados de contagem e ainda suporta a sobredispersão presente nos dados. Obtemos estimadores de máxima verossimilhança dos parâmetros utilizando um algoritmo de Newton-Raphson. Ilustramos a aplicação da metodologia desenvolvida aos dados do estudo.<br>We propose a Beta-Binomial/Poisson model to the data from a study with Parkinson disease patients, which consisted in counting for one minute how many trials were attempted and how many of them were successful, before and after a training period. The main goal was to check if training increased the number of trials and success probability, which emphasizes the bivariate aspect of the problem. This model takes this aspect into account, uses a distribution which is usually more adequate to count data and supports the overdispersion present in the data. We obtain the maximum likelihood estimators using a Newton-Raphson algorithm. For illustration, the methodology is applied to the data from study.

Em Lora e Singer (Statistics in Medicine, 2008), propusemos um modelo Beta- Binomial/Poisson p-variado para análise dos dados provenientes de um estudo que consistiu em contar o número de tentativas e acertos de um exercício manual com duração de um minuto realizado por doentes de Parkinson, antes e depois de um treinamento. O objetivo era verificar se o treinamento aumentava o número de tentativas e a porcentagem de acerto, o que destaca o aspecto bivariado do problema. Esse modelo leva tais características em consideração, usa uma distribuição adequada para dados de contagem e ainda acomoda a sobredispersão presente na contagem dos acertos. Como generalização, inicialmente, propomos um modelo Beta-Binomial/Poisson-Gama que acomoda sobredispersão também para as contagens dos totais de tentativas, além incluir covariâncias possivelmente diferentes entre as contagens em diversos instantes de avaliação. Neste novo modelo, introduzimos um parâmetro que relaciona o total de tentativas com a probabilidade de acerto, tornando-o ainda mais geral. Obtemos estimadores de máxima verossimilhança dos parâmetros utilizando um algoritmo de Newton-Raphson. Consideramos um outro conjunto de dados provenientes do mesmo estudo para ilustração da metodologia proposta.<br>In Lora and Singer (Statistics in Medicine, 2008), we proposed a Beta-Binomial/Poisson p-variate model to analyze data from a study which consists in counting the number of trials and successes of a manual exercise in one minute periods, done by Parkinsons disease patients, before and after a training. The purpose was to verify if the training improves the number of trials and the percentage of success, which emphasizes the bivariate aspect of the problem. This model considers these characteristics, uses an adequate distribution to count data and settles the overdispersion suggested in the number os successes. As a generalization, initially, we propose a Beta-Binomial/Poisson-Gama model which also settles the overdispersion suggested by the total number of trials, besides includes possible different covariances between total trial counts in different evaluation instants. In this new model, we introduce a parameter that links the total trials with the success probability, making it even more general. We obtain maximum likelihood estimators for the parameters using an Newton-Raphson algorithm. We consider another data from the same study to illustrate the proposal methodology.

The renewable energy sources (RES) are intermittent in their nature and their integration in electric power grid has introduced the mismatch between supply and demand. This mismatch can be leveled by using the flexibilities from the supply and the demand side. The demand side in a power system has key importance in the evolving context of the energy systems. Electrical load patterns that represent the consumption level are affected by different types of uncertainties associated with customer’s behavior and with keeping acceptable comfort level. The resulting aggregated load pattern indicates the system response that may be more or less flexible in different periods of time. The distribution system operator in a microgrid is responsible for its secure and economic operation. Enhancing the knowledge on the aggregated behavior of these customers is particularly important for the distribution system operator, also with the aim of determining the potential flexibility of the demand and setting up the economic terms of the electricity provision to the customers. Extra charges due to high energy demand and contract violation penalties can be avoided using demand side flexibility. Demand side flexibility has many benefits in normal as well as emergency conditions like less cost and quick response. The study of aggregate residential demand for flexibility measures is important due to the diverse energy usage behavior of individual residents and conceptually, its availability all around the year for load management. Exploitation of possible flexibilities of the group of residential customer’s behavior is considered as an important option to promote demand response programs and to achieve greater energy savings. As far as the residential sector is concerned, a reasonable work can be found in the literature to assess the flexibility for the individual appliances, the aggregation of selected appliances. However, little work is found on the aggregation of residential units. Also, despite of many discussions about the concept of flexibility, the few mathematical definitions of flexibility available do not address the variation in time of the overall demand aggregation. There is a need to develop a methodology to extract flexibility information from aggregate electricity consumption behavior of the residents and develop useful flexibility indices for the aggregate residential loads. For this purpose, the first action required is to augment availability of information about the characteristics of aggregate electricity demand. The analysis of aggregate demand patterns is carried out by considering the demand pattern data representing the average power determined from the energy referring to a given time step duration. This thesis contains a comprehensive statistical analysis to investigate the effect of time step duration and aggregation level on load variation profile. Then the customer behavior about the change is demand is modeled using the binomial probability distribution. This model has led towards some novel definitions of flexibility indices. A new method based on the Beta probability distribution has been developed to generate the time coupled aggregate residential demand patterns, whose evolution depends on the uncertainties associated with the customer’s behavior. The outcome of this research work has also led towards defining the role of customers in microgrid application. For this purpose, a structure of the business model for a smart (mini) grid is proposed. The data sets used for all kind of analysis are generated for the different aggregations of the extra-urban residential customers using a bottom-up approach. The tools presented in this research work can be helpful for a system operator or an aggregator to assess demand side flexibilities, manage resources and efficiently use demand response programs. The findings of this work are also supportive to determine the metering structure for a microgrid application in which, by using current ICT technologies, it is possible to decide a compromise solution between the aggregation level and time step duration for smart metering. On the other hand, the research findings also led to the conclusion that the flexibility level for the individual residential customers is not so high to give economic benefits that make it attractive to participate in DR programs. From the studies, it seems that the problem is not with the technical aspects but with the current business model of the smart grids. For the future extension of this work, a framework of a new smart business model for smart (mini) grids, centric to customers, is presented. It is expected that the developments using the proposed background of the business model can lead towards a different era in the development of the power systems with the new wave of research; as new tools are required to embed economic and social considerations in planning the proposed architecture.

Master of Science<br>Department of Statistics<br>Leigh Murray<br>This case study was motivated by the need for effective statistical analysis for a series of poultry feeding experiments conducted in 2006 by Kansas State University researchers in the department of Animal Science. Some of these experiments involved an automated auger feed line system commonly used in commercial broiler houses and continuous, proportion response data. Two of the feed line experiments are considered in this case study to determine if a statistical model using a non-normal response offers a better fit for this data than a model utilizing a normal approximation. The two experiments involve fixed as well as multiple random effects. In this case study, the data from these experiments is analyzed using a linear mixed model and Generalized Linear Mixed Models (GLMM’s) with the SAS Glimmix procedure. Comparisons are made between a linear mixed model and GLMM’s using the beta and binomial responses. Since the response data is not count data a quasi-binomial approximation to the binomial is used to convert continuous proportions to the ratio of successes over total number of trials, N, for a variety of possible N values. Results from these analyses are compared on the basis of point estimates, confidence intervals and confidence interval widths, as well as p-values for tests of fixed effects. The investigation concludes that a GLMM may offer a better fit than models using a normal approximation for this data when sample sizes are small or response values are close to zero. This investigation discovers that these same instances can cause GLMM’s utilizing the beta response to behave poorly in the Glimmix procedure because lack of convergence issues prevent the obtainment of valid results. In such a case, a GLMM using a quasi-binomial response distribution with a high value of N can offer a reasonable and well behaved alternative to the beta distribution.

COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>Inferência ecológica reúne o conjunto de procedimentos estatísticos para se prever dados desagregados quando só estão disponíveis dados agregados. Duas novas metodologias propostas recentemente vêm motivando novos desenvolvimentos na área: o modelo baseado na normal bivariada truncada (MNBT) e o modelo hierárquico binomial-beta (MHBB). A tese reavalia estas metodologias e explora implementações computacionais mais eficientes através do Algoritmo EM e uma de suas extensões, o Algoritmo ECM. Comparando-se com métodos de quase-Newton, uma versão estável, porém mais lenta, é obtida para implementação do MNBT e uma versão estável e mais rápida é obtida para o MHBB. Adicionalmente, as metodologias são comparadas em termos de suas capacidades preditivas através de um extenso experimento de Monte Carlo e da aplicação sobre bases de dados reais selecionadas. A superioridade do MNBT se evidencia na maioria dos casos. Problemas de modelagem do MHBB são corrigidos e é apontada uma limitação assintótica das previsões produzidas por este último.<br>Ecological inference comprises the set of statistical procedures for the prediction of disaggegate data when data are available only in aggregate form. Two recently proposed approaches have motivated new developments in the field: the model based on a truncated bivariate normal (MNBT) and the hierchical binomial-beta model (MHBB). The thesis reevaluates these approaches and explores more efficient computational implementations via the EM Algorithm and one of its extensions, the ECM Algorithm. As compared to quasi-Newton algorithms, a stable yet slower version is obtained for the implementation of the MNBT, and a stable and faster version is obtained for the MHBB. The methodologies are compared in predictive terms by means of an extensive Monte Carlo experiment and of the application to real datasets. The superiority of the MNBT is evident in the majority of cases. Modeling mistakes of the MHBB are corrected and an asymptotic restriction of the predictions made with this model is pointed.<br>La inferencia ecológica reúne un conjunto de procedimentos estatísticos para prever datos desagregados cuando solo están disponibles datos agregados. Dos nuevas metodologías propuestas recientemente han motivando nuevos desarrollos en el área: el modelo que tiene como base la normal bivariada truncada (MNBT) y el modelo jerárquico binomial- beta (MHBB). La tesis reevalúa estas metodologías y explora implementaciones computacionales más eficientes a través del Algoritmo EM y una de sus extensiones, el Algoritmo ECM. Estos métodos se comparan con métodos de quase- Newton. Se obtiene una versión estable aunque más lenta, para la implementación de MNBT y una versión estable y más rápida para el MHBB. Adicionalmente, se comparan las metodologías en función de sus capacidades predictivas a través de un extenso experimento de Monte Carlo. Em la mayor parte de los casos se observa superioridad del MHNBT. Se corrigen problemas de modelaje del MHBB apuntadando uma limitación asintótica de las previsiones producidas por este último.

This study develops and tests a new multivariate distribution model for the estimation of advertising vehicle exposure. The new multivariate distribution model is developed as three versions (i.e., one which doesn't adjust negative probabilities, and the others which adjust negative probabilities in unvariate distributions). In addition, eight other media exposure models are evaluated against a database of 440 tabulated schedules constructed from 2003 comScore network data. The types of models tested include: three univariate models -- the Binomial Distribution Model (BIN), the Beta Binomial Distribution Model (BBD), and the Hofmans Beta Binomial Distribution Model (HBBD); three multivariate models -- the Dirichlet Multinomial Distribution Model (DMD), the Canonical Expansion Model (CANEX), and the Conditional Beta Distribution Model (CBD); and one aggregation model -- the Morgensztern Sequential Aggregation Model (MSAD). All of the models tested are based on probability distributions. Some models are a combination of probability distributions and ad hoc methods. In addition, the approximation model of the MBD called the Hyper Beta Distribution Model (HBD), is described and tested. The accuracy of the eleven models is assessed via two evaluation criteria of model performance -- the Average Percentage Error in Reach (AER) and the Average Percentage Error in Exposure Distribution (APE). All models are compared according to their relative overall accuracy as assessed by the two error measures. The proposed new multivariate model -- the Multivariate Beta Binomial Distribution Model (MBD) -- was generally more accurate than the other models for the estimation of reach. For the estimation of the exposure distribution, the model proved more accurate than the Binomial Distribution Model (BIN), the Beta Binomial Distribution Model (BBD), the Hofmans Beta Binomial Distribution Model (HBBD), and the Dirichlet Multinomial Distribution Model (DMD), but less accurate than the Canonical Expansion Model (CANEX), the Conditional Beta Distribution Model (CBD), the Morgensztern Sequential Aggregation Model (MSAD), and Hyper Beta Distribution Model (HBD). This study provides the foundation for further improvement of the model, along with recommendations for further investigation, since the theoretical potential for the performance of the model is high.<br>text

acase@tulane.edu<br>The Beta-binomial distribution is often employed as a model for count data in cases where the observed dispersion is greater than would be expected for the standard binomial distribution. Parameter estimation in this setting is typically performed using a Bayesian approach, which requires specifying appropriate prior distributions for parameters. In the context of many applications, incorporating estimates from previous analyses can offer advantages over naive or diffuse priors. An example of this is in the food security setting, where baseline consumption surveys can inform parameter estimation in crisis situations during which data must be collected hastily on smaller samples of individuals. We have developed an approach for Bayesian updating in the beta-binomial model that incorporates adjustable prior weights and enables inference using a bivariate normal approximation for the mode of the posterior distribution. Our methods, which are implemented in the R programming environment, include tools for the estimation of statistical power to detect changes in parameter values.<br>1<br>Aleksandra Gorzycka