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Accelerated life tests (ALT) are appealing to practitioners seeking to maximize information gleaned from reliability studies, while navigating resource constraints due to time and specimen costs. A popular approach to accelerated life testing is to design test regimes such that experimental specimens are exposed to variable stress levels across time. Such ALT experiments allow the practitioner to observe lifetime behavior across various stress levels and infer product life at use conditions using a greater number of failures than would otherwise be observed with a constant stress experiment. The downside to accelerated life tests, however, particularly for those that utilize non-constant stress levels across time on test, is that the corresponding lifetime models are largely dependent upon assumptions pertaining to variant stress. Although these assumptions drive inference at product use conditions, little to no statistical methods exist for assessing their validity. One popular assumption that is prevalent in both literature and practice is the cumulative exposure model which assumes that, at a given time on test, specimen life is solely driven by the integrated stress history and that current lifetime behavior is path independent of the stress trajectory. This dissertation challenges such black box ALT modeling procedures and focuses on the cumulative exposure model in particular. For a simple strep-stress accelerated life test, using two constant stress levels across time on test, we propose a four-parameter Weibull lifetime model that utilizes a threshold parameter to account for the stress transition. To circumvent regularity conditions imposed by maximum likelihood procedures, we use median rank regression to fit and assess our lifetime model. We improve the model fit using a novel incorporation of desirability functions and ultimately evaluate our proposed methods using an extensive simulation study. Finally, we provide an illustrative example to highlight the implementation of our method, comparing it to a corresponding Bayesian analysis. / Ph. D.

In this thesis, we study two methods for inference of parameters in the accelerated failure time model with right censoring data. One is the Wald-type method, which involves parameter estimation. The other one is empirical likelihood method, which is based on the asymptotic distribution of likelihood ratio. We employ a monotone censored data version of Kendall estimating equation, and construct confidence intervals from both methods. In the simulation studies, we compare the empirical likelihood (EL) and the Wald-type procedure in terms of coverage accuracy and average length of confidence intervals. It is concluded that the empirical likelihood method has a better performance. We also compare the EL for Kendall’s rank regression estimator with the EL for other well known estimators and find advantages of the EL for Kendall estimator for small size sample. Finally, a real clinical trial data is used for the purpose of illustration.

Type 2 diabetes (T2DM) is a growing concern worldwide, particularly among Aboriginal Canadians. Diet has been associated with diabetes risk, and dietary pattern analysis (DPA) provides a method in which whole dietary patterns may be explored in relation to disease. Factor analysis (FA) and reduced rank regression (RRR) of data from the Sandy Lake Health and Diabetes Project identified patterns associated with incident T2DM at follow-up. A RRR-derived pattern characterized by tea, hot cereal, and peas, and low intake of high-sugar foods and beef was positively associated with diabetes; however, the relationship was attenuated with adjustment for age and other covariates. A FA-derived pattern characterized by processed foods was positively associated with incident T2DM in a multivariate model (OR=1.38; CIs: 1.02, 1.86 per unit), suggesting intake of processed foods may predict T2DM risk.

The primary objective of this study was to assess the relationship between dietary patterns with diabetes and mortality risk from all-cause and cardiovascular disease while controlling for the confounding effects of fitness. The secondary objective was to examine the combined effects of dietary patterns and fitness on chronic disease and mortality risk. Participants consisted of 13,621 men and women from the Aerobics Center Longitudinal Study who completed a standardized medical examination and 3-day diet record between 1987 and 1999. Reduced rank regression was used to identify dietary patterns that were predictive of unfavorable profiles of cholesterol, white blood cell count, glucose, mean arterial pressure, HDL-cholesterol, uric acid, triglycerides, and body mass index. One primary dietary pattern emerged, which was labeled the “Unhealthy Eating Index”. This pattern was characterized by a large consumption of processed meat, red meat, white potato products, non-whole grains, added fat, and a small consumption of non-citrus fruits. After adjustment for covariates, the odds ratio for diabetes and the hazard ratio for all-cause mortality were 2.55 (95% confidence interval: 1.81-3.58) and 1.40 (1.02-1.91) in the highest quintile of the Unhealthy Eating Index when compared to the lowest quintile, respectively. After controlling for fitness, these risk estimates were reduced by 51.6% and 55.0%. The Unhealthy Eating Index was not a significant predictor of cardiovascular disease mortality before or after controlling for fitness. Examining the combined effects of dietary patterns and fitness revealed that both variables were independent predictors of diabetes (Ptrend <0.0001), while fitness (Ptrend <0.0001) but not unhealthy eating (Ptrend=0.071) significantly predicted all-cause mortality risk. These results suggest that both diet and fitness must be considered when studying disease. / Thesis (Master, Community Health & Epidemiology) -- Queen's University, 2009-07-08 07:11:06.809

Type 2 diabetes (T2DM) is a growing concern worldwide, particularly among Aboriginal Canadians. Diet has been associated with diabetes risk, and dietary pattern analysis (DPA) provides a method in which whole dietary patterns may be explored in relation to disease. Factor analysis (FA) and reduced rank regression (RRR) of data from the Sandy Lake Health and Diabetes Project identified patterns associated with incident T2DM at follow-up. A RRR-derived pattern characterized by tea, hot cereal, and peas, and low intake of high-sugar foods and beef was positively associated with diabetes; however, the relationship was attenuated with adjustment for age and other covariates. A FA-derived pattern characterized by processed foods was positively associated with incident T2DM in a multivariate model (OR=1.38; CIs: 1.02, 1.86 per unit), suggesting intake of processed foods may predict T2DM risk.

In many high dimensional problems, the dependence structure among the variables can be quite complex. An appropriate use of the regularization techniques coupled with other classical statistical methods can often improve estimation and prediction accuracy and facilitate model interpretation, by seeking a parsimonious model representation that involves only the subset of revelent variables. We propose two regularized stochastic regression approaches, for efficiently estimating certain sparse dependence structure in the data. We first consider a multivariate regression setting, in which the large number of responses and predictors may be associated through only a few channels/pathways and each of these associations may only involve a few responses and predictors. We propose a regularized reduced-rank regression approach, in which the model estimation and rank determination are conducted simultaneously and the resulting regularized estimator of the coefficient matrix admits a sparse singular value decomposition (SVD). Secondly, we consider model selection of subset autoregressive moving-average (ARMA) modelling, for which automatic selection methods do not directly apply because the innovation process is latent. We propose to identify the optimal subset ARMA model by fitting a penalized regression, e.g. adaptive Lasso, of the time series on its lags and the lags of the residuals from a long autoregression fitted to the time-series data, where the residuals serve as proxies for the innovations. Computation algorithms and regularization parameter selection methods for both proposed approaches are developed, and their properties are explored both theoretically and by simulation. Under mild regularity conditions, the proposed methods are shown to be selection consistent, asymptotically normal and enjoy the oracle properties. We apply the proposed approaches to several applications across disciplines including cancer genetics, ecology and macroeconomics.

As doenças cardiovasculares (DCV) representam a principal causa de mortalidade e de incapacidade, em ambos os gêneros, no Brasil e no mundo. O padrão de consumo alimentar está tanto positiva como negativamente associado aos principais fatores de risco para DCV, entre eles diabetes, hipertensão, obesidade e hipertrigliceridemia, todos componentes da síndrome metabólica. Este estudo tem como objetivos identificar os padrões alimentares em indivíduos com DCV, considerando a densidade de energia, a gordura saturada, a fibra, o sódio e o potássio consumidos, e investigar sua associação com fatores de risco de DCV e síndrome metabólica. Trata-se de um estudo transversal. Foram utilizados dados do estudo DICA Br. A amostra foi composta de indivíduos com DCV, com idade superior a 45 anos, de todas as regiões brasileiras. O consumo alimentar foi obtido por recordatório alimentar de 24h e os padrões alimentares obtidos pela regressão por posto reduzido (RPR). Para a RPR, utilizaram-se 28 grupos alimentares como preditores e como variáveis respostas componentes dietéticos. O teste de Mann Whitney foi utilizado para testar as diferenças entre as médias dos escores. Foram obtidos dados de 1.047 participantes; 95% apresentavam doença arterial coronariana; em sua maioria, eram idosos, da classe econômica C1 e C2 e estudaram até o ensino médio. A prevalência de síndrome metabólica foi de 58%. Foram extraídos dois padrões alimentares. O primeiro foi marcado pelo maior consumo de fibra alimentar e potássio, composto por arroz e feijão, frutas e sucos naturais com ou sem açúcar, legumes, carne bovina ou processada, verduras, raízes e tubérculos. O segundo padrão caracterizou-se pelo consumo de gordura saturada e maior densidade energética, representado por panificados salgados, gorduras, carne bovina e processada, doces caseiros, pizza, salgadinhos de pacote ou festa, sanduíche e alimento salgado pronto para consumo. Houve associação significativa entre o padrão alimentar 1 com medida da circunferência da cintura e nível de HDL adequados e com o padrão 2 e HDL adequado. A adoção do padrão alimentar 1 pode estar associada à proteção contra alguns dos componentes da síndrome metabólica. / Cardiovascular diseases (CVD) are the leading cause of mortality and disability in both genders in Brazil and worldwide. The dietary pattern is at the same time positive and negatively associated with the main risk factors for CVD, including diabetes, hypertension, obesity and hypertriglyceridemia, all components of the metabolic syndrome. This study aims to identify dietary patterns in individuals with CVD, considering the energy density, and the amount of saturated fatty acid, fiber, sodium and potassium of the diet, and to investigate its association with CVD risk factors and metabolic syndrome. This is a cross-sectional study, data were used from \"DICA Br\" study. The sample consisted of individuals with CVD, over 45 years old, residents from all Brazilian regions. Food consumption was obtained by one 24-hours diet recall and dietary patterns by reduced rank regression (RRR). In the RRR, 28 food groups were included as predictors and dietary components was chosen as the response variable. The Mann-Whitney test was used to test the differences between the factors scores\' means. Data of 1047 participants were analyzed. 95% have coronary artery disease, most are elderly, economical class most observed are C1 and C2. Also, most of them and studied up to high school. The prevalence of metabolic syndrome was 58%. Two dietary patterns were extracted: the first one is higher in dietary fiber and potassium, which is composed by rice, beans, fruits and natural juices with or without sugar, vegetables, beef or processed meat, roots and tubers. The second pattern is higher in saturated fatty acid and energy density, represented by breads, fats, and processed meat, homemade pastries, pizza, snacks or party package, sandwich and salty food ready for consumption. There was a significant association between dietary pattern 1 and low waist circumference and adequate high density cholesterol blood concentration. There was a significant association between dietary pattern 2 and adequate high density cholesterol blood concentration. We suggest that the adoption of the dietary pattern 1 may be associated with protection against some of the components of metabolic syndrome.

This thesis deals with univariate and multivariate rank methods in making statistical inference. It is assumed that the underlying distributions belong to the class of elliptical distributions. The class of elliptical distributions is an extension of the normal distribution and includes distributions with both lighter and heavier tails than the normal distribution. In the first part of the thesis the rank covariance matrices defined via the Oja median are considered. The Oja rank covariance matrix has two important properties: it is affine equivariant and it is proportional to the inverse of the regular covariance matrix. We employ these two properties to study the problem of estimating the rank covariance matrices when they have a certain structure. The second part, which is the main part of the thesis, is devoted to rank estimation in linear regression models with symmetric heteroscedastic errors. We are interested in asymptotic properties of rank estimates. Asymptotic uniform linearity of a linear rank statistic in the case of heteroscedastic variables is proved. The asymptotic uniform linearity property enables to study asymptotic behaviour of rank regression estimates and rank tests. Existing results are generalized and it is shown that the Jaeckel estimate is consistent and asymptotically normally distributed also for heteroscedastic symmetric errors.

Many software reliability growth models have beenanalyzed for measuring the growth of software reliability. In this dissertation, regression methods are explored to study software reliability models. First, two parametric linear models are proposed and analyzed, the simple linear regression and transformed linearregression corresponding to a power law process. Some software failure data sets do not follow the linear pattern. Analysis of popular real life data showed that these contain outliers andleverage values. Linear regression methods based on least squares are sensitive to outliers and leverage values. Even though the parametric regression methods give good results in terms of error measurement criteria, these results may not be accurate due to violation of the parametric assumptions. To overcome these difficulties, nonparametric regression methods based on ranks are proposed as alternative techniques to build software reliability models. In particular, monotone regre ssion and rank regression methods are used to evaluate the predictive capability of the models. These models are applied to real life data sets from various projects as well as to diverse simulated data sets. Both the monotone and the rank regression methods are robust procedures that are less sensitive to outliers and leverage values. In particular, the regression approach explains predictive properties of the mean time to failure for modeling the patterns of software failure times.In order to decide on model preference and to asses predictive accuracy of the mean time between failure time estimates for the defined data sets, the following error measurements evaluative criteria are used: the mean square error, mean absolute value difference, mean magnitude of relative error, mean magnitude oferror relative to the estimate, median of the absolute residuals, and a measure of dispersion. The methods proposed in this dissertation, when applied to real software failure data, give lesserror in terms of all the measurement criteria compared to other popular methods from literature. Experimental results show that theregression approach offers a very promising technique in software reliability growth modeling and prediction.