Master of Science / Department of Statistics / Paul I. Nelson / Quantiles are useful in describing distributions of component lifetimes. Data, consisting of the lifetimes of sample units, used to estimate quantiles are often censored. Right censoring, the setting investigated here, occurs, for example, when some test units may still be functioning when the experiment is terminated. This study investigated and compared the performance of parametric and nonparametric estimators of quantiles from right censored data generated from Weibull and Lognormal distributions, models which are commonly used in analyzing lifetime data. Parametric quantile estimators based on these assumed models were compared via simulation to each other and to quantile estimators obtained from the nonparametric Kaplan- Meier Estimator of the survival function. Various combinations of quantiles, censoring proportion, sample size, and distributions were considered. Our simulation show that the larger the sample size and the lower the censoring rate the better the performance of the estimates of the 5th percentile of Weibull data. The lognormal data are very sensitive to the censoring rate and we observed that for higher censoring rates the incorrect parametric estimates perform the best. If you do not know the underlying distribution of the data, it is risky to use parametric estimates of quantiles close to one. A limitation in using the nonparametric estimator of large quantiles is their instability when the censoring rate is high and the largest observations are censored. Key Words: Quantiles, Right Censoring, Kaplan-Meier estimator

Background: Gram-negative resistance is a growing problem worldwide. It is generally believed that rates of resistant bacteria within a hospital are a function of antibiotic use, resistant organisms brought into the hospital, infection control efforts, and underlying severity of patient illness. The relative contribution of each to a particular resistance phenotype is unclear. P. aeruginosa is responsible for many hospital acquired infections and it may become resistant to carbapenems. In addition, newer threats to the future utility of the carbapenems are carbapenemase-producing K. pneumoniae Purpose: To determine if there is an association between the volume and composition of antibiotic use, geography, severity of illness and rates of carbapenem-resistant P. aeruginosa and K. pneumoniae. Methods: This is a retrospective ecological longitudinal investigation within the University HealthSystem Consortium affiliated academic medical centers. Antibiotic use data between January 1, 2006 and December 31, 2009 were obtained from billing records and reported as days of therapy per 1000 patient days (DOT/1000 PD), in addition to hospital characteristics (e.g. geographical location, bed size, case mix index). “Whole house” antibiograms were obtained to determine rates and proportions of carbapenem-resistant P. aeruginosa (CR-PA) and carbapenem resistant K. pneumoniae (CR-KP). Also, CR-KP isolation was generated as a binary outcome. Generalized estimating equations (GEE) were used to model CR-KP and CR-PA. Results: CR-KP rates (1000PDs) increased from 0.07 in 2006 to 0.15 in 2009 (P= 0.0118) and CR-KP proportions increased from 1.3% in 2006 to 3.1% in 2009 (0.0003) within 40 hospitals over 2006-2009. However, CR-PA rates and proportions were stable over the same period. Geographical location, carbapenems use, and antipseudomonal penicillins use were significantly associated with CR-KP isolation. Thus, for every ten DOT/1000 PDs increase in carbapenem use, the odds of CR-KP isolation increased by 42% (P=0.0149). In contrast, for every ten DOT/1000 PDs increase in antipseudomonal penicillin use, the odds of CR-KP isolation decreased by 14%. However, there was no significant model to explain CR-PA rates and proportions. Conclusion: Carbapenems, antipseudomonal penicillins, and geographical location were identified as risk factors associated with CR-KP isolation. These findings emphasize the challenges associated with the treatment of multidrug- gram-negative bacteria.

The generalized linear models (GLM) lately received a lot of attention in modelling the insurance data. However, the violation of assumptions about the independence of underlying data set often causes problems and misinterpretation of achieved results. The need for more exible instruments has been spoken out and consequently various proposals have been made. This thesis deals with GLM based techniques enabling to handle correlated data sets. The usage have been made of generalized linear mixed models (GLMM) and generalized estimating equations (GEE). The main aim of this thesis is to provide a solid statistical background and perform a practical application to demonstrate and compare features of various models. Powered by TCPDF (www.tcpdf.org)

A economia brasileira passa por um momento positivo em sua história, devido principalmente a fatores gerados pela estabilidade econômica advinda com o Plano Real. O conjunto de dados apresentados neste trabalho evidencia uma melhora das condições socioeconômicas de grande parte da população, o que levou a um aumento da renda dos indivíduos e um fortalecimento do poder de consumo dos brasileiros. Nesse contexto, esta tese teve como objetivo a busca de evidências que indicassem uma mudança e possível sofisticação do padrão de consumo dos domicílios brasileiros. Além disso, procurou-se verificar em quais níveis socioeconômicos e em quais regiões as mudanças do padrão de consumo foram mais significativas. Os dados utilizados neste trabalho derivam de um painel de consumidores (Homescan) e foram analisadas informações de dez categorias de produtos de consumo doméstico para os anos de 2007, 2008 e 2009, considerando-se as áreas geográficas auditadas pela Nielsen e os níveis socioeconômicos dos domicílios. Nas análises dos dados, utilizaram-se modelos de equações de estimação generalizadas (EEG), além de análises estatísticas descritivas para avaliar a evolução das variáveis não-contempladas nesses modelos. Além disso, utilizaram-se dados de outra pesquisa (Retail Index) para complementar os resultados obtidos com o painel de consumidores. Os resultados das análises realizadas indicam uma mudança do padrão de consumo, primordialmente, nos domicílios de nível socioeconômico médio (classe C) e baixo (classes D e E) no período analisado. Quanto às áreas geográficas pesquisadas, os destaques foram o Nordeste, o grande Rio de Janeiro e a região Sul. Levando-se em consideração que as categorias analisadas são produtos mais elaborados e de maior valor agregado, o aumento do consumo da grande maioria das categorias nesses níveis socioeconômicos evidencia uma sofisticação do consumo desses domicílios. Esse ambiente de sofisticação dos padrões de consumo, principalmente das classes de renda média e baixa, exigirá das empresas que atuam no mercado de bens e serviços novas estratégias para atender as demandas de consumidores mais conscientes e exigentes. Assim, o grande desafio dessas empresas será decifrar o caminho da expansão e diversificação da cesta de compra desses consumidores. / The Brazilian economy is currently going through a positive time in its history, mainly as a result of factors generated by the economic stability conferred by the Plano Real financial plan. The data presented in this work shows an improvement in the socioeconomic conditions of the vast majority of the population, which has led to an increase in income for individuals, and a strengthening of the consumer power of Brazilians. In this context, this thesis looks for evidence that indicates a change and possible sophistication of consumer patterns in Brazilian households. It also seeks to determine the socioeconomic levels, and the regions in which the changes in consumer patterns are most significant. The data used in this work are derived from a panel of consumers (Homescan), and information from ten categories of domestic consumer goods were analyzed for the years 2007, 2008 and 2009, considering the geographic areas audited by Nielsen and the socioeconomic levels of the households. In the data analyses, generalized estimating equation (GEE) models are used, as well as descriptive statistical analyses, to evaluate the evolution of variables not included in these models. Data are also used from another survey (Retail Index), to complement the results obtained with the panel of consumers. The results of the analyses indicate a change in consumer patterns, particularly in households belonging to the middle (class C) and low (classes D and E) socioeconomic classes, for the period analyzed. In terms of geographical areas researched, the areas highlighted were the Northeast, the greater Rio de Janeiro and the South region. Taking into consideration that the categories analyzed consist of more elaborate products, with higher added value, the increased consumption for the majority of categories at these socioeconomic levels shows that consumption in these households has become more sophisticated. This environment of increasing sophistication of consumer patterns, particularly among the middle and low income classes, will require companies in the goods and services market to implement strategies to meet the requirements of these more aware and demanding consumers. Therefore, the greatest challenge for these companies is to seize the expansion and diversification path of the shopping basket for these consumers.

<p>The use of positron emission tomography (PET) in radiation therapy has continued to grow, especially since the development of combined computed tomography (CT) and PET imaging system in the early 1990s. Today, the biggest use of PET-CT is in oncology, where a glucose analog radiotracer is rapidly incorporated into the metabolic pathways of a variety of cancers. Images representing the in-vivo distribution of this radiotracer are used for the staging, delineation and assessment of treatment response of patients undergoing chemotherapy or radiation therapy. While PET offers the ability to provide functional information, the imaging quality of PET is adversely affected by its lower spatial resolution. It also has unfavorable image noise characteristics due to radiation dose concerns and patient compliance. These factors result in PET images having less detail and lower signal-to-noise (SNR) properties compared to images produced by CT. This complicates the use of PET within many areas of radiation oncology, but particularly the delineation of targets for radiation therapy and the assessment of patient response to therapy. The development of segmentation methods that can provide accurate object identification in PET images under a variety of imaging conditions has been a goal of the imaging community for years. The goal of this thesis are to: (1) investigate the effect of filtering on segmentation methods; (2) investigate whether combining individual segmentation methods can improve segmentation accuracy; (3) investigate whether the consensus volumes can be useful in aiding physicians of different experience in defining gross tumor volumes (GTV) for head-and-neck cancer patients; and (4) to investigate whether consensus volumes can be useful in assessing early treatment response in head-and-neck cancer patients.</p><p>For this dissertation work, standard spherical objects of volumes ranging from 1.15 cc to 37 cc and two irregularly shaped objects of volume 16 cc and 32 cc formed by deforming high density plastic bottles were placed in a standardized image quality phantom and imaged at two contrasts (4:1 or 8:1 for spheres, and 4.5:1 and 9:1 for irregular) and three scan durations (1, 2 and 5 minutes). For the work carried out into the comparison of images filters, Gaussian and bilateral filters matched to produce similar image signal to noise (SNR) in background regions were applied to raw unfiltered images. Objects were segmented using thresholding at 40% of the maximum intensity within a region-of-interest (ROI), an adaptive thresholding method which accounts for the signal of the object as well as background, k-means clustering, and a seeded region-growing method adapted from the literature. Quality of the segmentations was assessed using the Dice Similarity Coefficient (DSC) and symmetric mean absolute surface distance (SMASD). Further, models describing how DSC varies with object size, contrast, scan duration, filter choice and segmentation method were fitted using generalized estimating equations (GEEs) and standard regression for comparison. GEEs accounted for the bounded, correlated and heteroscedastic nature of the DSC metric. Our analysis revealed that object size had the largest effect on DSC for spheres, followed by contrast and scan duration. In addition, compared to filtering images with a 5 mm full-width at half maximum (FWHM) Gaussian filter, a 7 mm bilateral filter with moderate pre-smoothing (3 mm Gaussian (G3B7)) produced significant improvements in 3 out of the 4 segmentation methods for spheres. For the irregular objects, time had the biggest effect on DSC values, followed by contrast. </p><p>For the study of applying consensus methods to PET segmentation, an additional gradient based method was included into the collection individual segmentation methods used for the filtering study. Objects in images acquired for 5 minute scan durations were filtered with a 5 mm FWHM Gaussian before being segmented by all individual methods. Two approaches of creating a volume reflecting the agreement between the individual methods were investigated. First, a simple majority voting scheme (MJV), where individual voxels segmented by three or more of the individual methods are included in the consensus volume, and second, the Simultaneous Truth and Performance Level Estimation (STAPLE) method which is a maximum likelihood methodology previously presented in the literature but never applied to PET segmentation. Improvements in accuracy to match or exceed the best performing individual method were observed, and importantly, both consensus methods provided robustness against poorly performing individual methods. In fact, the distributions of DSC and SMASD values for the MJV and STAPLE closely match the distribution that would result if the best individual method result were selected for all objects (the best individual method varies by objects). Given that the best individual method is dependent on object type, size, contrast, and image noise and the best individual method is not able to be known before segmentation, consensus methods offer a marked improvement over the current standard of using just one of the individual segmentation methods used in this dissertation. </p><p>To explore the potential application of consensus volumes to radiation therapy, the MJV consensus method was used to produce GTVs in a population of head and neck cancer patients. This GTV and one created using simple 40% thresholding were then available to be used as a guidance volume for an attending head and neck radiation oncologist and a resident who had completed their head and neck rotation. The task for each physician was to manually delineate GTVs using the CT and PET images. Each patient was contoured three times by each physician- without guidance and with guidance using either the MJV consensus volume or 40% thresholding. Differences in GTV volumes between physicians were not significant, nor were differences between the GTV volumes regardless of the guidance volume available to the physicians. However, on average, 15-20% of the provided guidance volume lay outside the final physician-defined contour.</p><p>In the final study, the MJV and STAPLE consensus volumes were used to extract maximum, peak and mean SUV measurements in two baseline PET scans and one PET scan taken during patients' prescribed radiation therapy treatments. Mean SUV values derived from consensus volumes showed smaller variability compared to maximum SUV values. Baseline and intratreatment variability was assessed using a Bland-Altman analysis which showed that baseline variability in SUV was lower than intratreatment changes in SUV.</p><p>The techniques developed and reported in this thesis demonstrate how filter choice affects segmentation accuracy, how the use of GEEs more appropriately account for the properties of a common segmentation quality metric, and how consensus volumes not only provide an accuracy on par with the single best performing individual method in a given activity distribution, but also exhibit a robustness against variable performance of individual segmentation methods that make up the consensus volume. These properties make the use of consensus volumes appealing for a variety of tasks in radiation oncology.</p> / Dissertation

Interval censoring arises frequently in life history data, as individuals are often only observed at a sequence of assessment times. This leads to a situation where we do not know when an event of interest occurs, only that it occurred somewhere between two assessment times. Here, the focus will be on methods of estimation for recurrent event data, current status data, and multistate data, subject to interval censoring. With recurrent event data, the focus is often on estimating the rate and mean functions. Nonparametric estimates are readily available, but are not smooth. Methods based on local likelihood and the assumption of a Poisson process are developed to obtain smooth estimates of the rate and mean functions without specifying a parametric form. Covariates and extra-Poisson variation are accommodated by using a pseudo-profile local likelihood. The methods are assessed by simulations and applied to a number of datasets, including data from a psoriatic arthritis clinic. Current status data is an extreme form of interval censoring that occurs when each individual is observed at only one assessment time. If current status data arise in clusters, this must be taken into account in order to obtain valid conclusions. Copulas offer a convenient framework for modelling the association separately from the margins. Estimating equations are developed for estimating marginal parameters as well as association parameters. Efficiency and robustness to the choice of copula are examined for first and second order estimating equations. The methods are applied to data from an orthopedic surgery study as well as data on joint damage in psoriatic arthritis. Multistate models can be used to characterize the progression of a disease as individuals move through different states. Considerable attention is given to a three-state model to characterize the development of a back condition known as spondylitis in psoriatic arthritis, along with the associated risk of mortality. Robust estimates of the state occupancy probabilities are derived based on a difference in distribution functions of the entry times. A five-state model which differentiates between left-side and right-side spondylitis is also considered, which allows us to characterize what effect spondylitis on one side of the body has on the development of spondylitis on the other side. Covariate effects are considered through multiplicative time homogeneous Markov models. The robust state occupancy probabilities are also applied to data on CMV infection in patients with HIV.

Interval censoring arises frequently in life history data, as individuals are often only observed at a sequence of assessment times. This leads to a situation where we do not know when an event of interest occurs, only that it occurred somewhere between two assessment times. Here, the focus will be on methods of estimation for recurrent event data, current status data, and multistate data, subject to interval censoring. With recurrent event data, the focus is often on estimating the rate and mean functions. Nonparametric estimates are readily available, but are not smooth. Methods based on local likelihood and the assumption of a Poisson process are developed to obtain smooth estimates of the rate and mean functions without specifying a parametric form. Covariates and extra-Poisson variation are accommodated by using a pseudo-profile local likelihood. The methods are assessed by simulations and applied to a number of datasets, including data from a psoriatic arthritis clinic. Current status data is an extreme form of interval censoring that occurs when each individual is observed at only one assessment time. If current status data arise in clusters, this must be taken into account in order to obtain valid conclusions. Copulas offer a convenient framework for modelling the association separately from the margins. Estimating equations are developed for estimating marginal parameters as well as association parameters. Efficiency and robustness to the choice of copula are examined for first and second order estimating equations. The methods are applied to data from an orthopedic surgery study as well as data on joint damage in psoriatic arthritis. Multistate models can be used to characterize the progression of a disease as individuals move through different states. Considerable attention is given to a three-state model to characterize the development of a back condition known as spondylitis in psoriatic arthritis, along with the associated risk of mortality. Robust estimates of the state occupancy probabilities are derived based on a difference in distribution functions of the entry times. A five-state model which differentiates between left-side and right-side spondylitis is also considered, which allows us to characterize what effect spondylitis on one side of the body has on the development of spondylitis on the other side. Covariate effects are considered through multiplicative time homogeneous Markov models. The robust state occupancy probabilities are also applied to data on CMV infection in patients with HIV.

In preliminary building energy assessments, it is often desired to estimate a motor's input power. Motor power estimates in this context should be rapid, safe, and noninvasive. Existing methods for motor input power estimation, such as direct measurement (wattmeter), Current Method, and Slip Method were evaluated. If installed equipment displays input power or average current, then using such readings are preferred. If installed equipment does not display input power or current, the application of wattmeters or current clamps is too time-consuming and invasive for the preliminary energy audit. In that case, if a shaft speed measurement is readily available, then the Slip Method is a satisfactory method for estimating motor input power. An analysis of performance data for 459 motors suggests comparable performance for predicting normalized (to the nominal motor input power) motor input power with the Current and Slip Methods: 10.0% and 9.9% RMSE, respectively. Both of these methods may be improved by applying regression on the predicted variable and/or nameplate parameters. For example, the Slip Method could be improved by applying a second-order regression, thereby reducing the predicted load factor residual RMSE of the data set from 9.0% to 8.2%. The Current and Slip Methods were also evaluated on two real motors. The normalized (to the nominal motor input power) predicted input power RMSE for the Current Method was on average 15% for the two motors; for the Slip Method the corresponding average was 17.5%. In some cases, shaft speed measurements may not be available. A temperature-based approach for estimating motor input power was investigated. Other required parameters include ambient temperature, motor efficiency, and a motor thermal constant. The temperature approach offers quick, safe, and non-invasive motor power estimation. However, thermal coefficients may vary significantly across motors and a model to predict the thermal coefficients has yet to be developed. Furthermore, the temperature approach has a very strong dependence on motor efficiency uncertainty. Experiments were performed on two motors to determine their motor thermal constants. If a motor's thermal constants and running efficiency are known, then this method gave motor input power estimates with a RMSE (normalized to the nominal input power) on the order of 4% for the studied motors.

The National health and nutrition examination survey (NHANES) is a respected nation-wide program in charge of assessing the health and nutritional status of adults and children in United States. Recent cal research found that folic acid play an important role in preventing baby birth defects. In this paper, we use the generalized estimating equation (GEE) method to study the generalized linear model (GLM) with compound symmetric correlation matrix for the NHANES data and investigate significant factors to ence the intake of food folic acid.

Kendall and Gehan estimating functions are used to estimate the regression parameter in accelerated failure time (AFT) model with censored observations. The accelerated failure time model is the preferred survival analysis method because it maintains a consistent association between the covariate and the survival time. The jackknife empirical likelihood method is used because it overcomes computation difficulty by circumventing the construction of the nonlinear constraint. Jackknife empirical likelihood turns the statistic of interest into a sample mean based on jackknife pseudo-values. U-statistic approach is used to construct the confidence intervals for the regression parameter. We conduct a simulation study to compare the Wald-type procedure, the empirical likelihood, and the jackknife empirical likelihood in terms of coverage probability and average length of confidence intervals. Jackknife empirical likelihood method has a better performance and overcomes the under-coverage problem of the Wald-type method. A real data is also used to illustrate the proposed methods.