Esta tese tem como objetivo a modelagem da degradação de correias em transportadores utilizados em mineração, como função do tempo e de outras covariáveis independentes que fazem parte do processo de mineração e que influenciam no desgaste das mesmas. Para a realização do trabalho, utilizou-se um método dividido em duas etapas: (i) abordagem qualitativa (estudo teórico do tópico degradação de correias e coleta de dados através da técnica de Grupo Focado – GF), para definição de variáveis influentes no desgaste, e (ii) abordagem quantitativa, para obtenção do modelo de degradação das correias, sendo utilizada, no estudo em questão, uma regressão linear múltipla. Como resultado foi possível identificar através da literatura, assim como via GF, que as variáveis ciclo da correia, comprimento e largura da correia, queda do material, limpador de correias (raspadores), taxa de alimentação, granulometria, composto e velocidade da correia impactariam potencialmente na degradação de correias. Já com o uso da regressão múltipla, constatou-se que as mesmas realmente são significativas e influentes, corroborando os dados obtidos via GF. De posse dos modelos de degradação obtidos para cada correia, foi possível elaborar uma proposta de sistemática de gestão da degradação de correias, baseada na comparação da evolução do desgaste real com o previsto, de modo a se detectar possíveis desvios e permitir a elaboração de ações de correção, visando minimizar a degradação acelerada e maximizar a vida útil das correias. Conseguiu-se estimar um ganho financeiro potencial de cerca de R$ 1.132.000,00 por ano, a partir da comparação entre a vida útil calculada pelos modelos de degradação e a vida estimada pela área de manutenção do complexo. / This thesis aims at modelling of the conveyor’s belt degradation used in mining as a function of time and other independent covariate that are part of the mining process and have influence in their wearing. To carry out the research we implemented a method divided in two stages: (i) a qualitative approach (theoretical study of conveyor belts degradation and data collection through Focused Groups – FG) for definition of factors that are influential in the wearing of belts, and (ii) a quantitative approach for obtaining a belts’ degradation model through multiple linear regression. It was possible to identify in the literature and through FG that variables such as belt cycle, belt length and width, material fall, belt cleaner, feed rate, particle size, compound and belt speed could potentially impact on the degradation of belts. Using multiple regression such variables were found to be statistically significant, corroborating the data obtained from FG. With the degradation models obtained for each conveyor belt it was possible to propose a method for the maintenance management of conveyor belts. The method was based on the comparison of real wear versus predicted wear in order to detect possible deviations and to allow the development of correction actions that aim at minimizing accelerated degradation and maximizing the belt’s lifetime. A potential financial gain of approximately R$ 1.132.000,00 per year was estimated comparing the lifetime obtained using the degradation models and the life estimated by the maintenance area of the complex.

In multilevel MIMIC models, covariates at the between level and at the within level can be modeled simultaneously. Covariates interaction effect occurs when the effect of one covariate on the latent factor varies depending on the level of the other covariate. The two covariates can be both at the between level, both at the within level, and one at the between level and the other one at the within level. And they can create between level covariates interaction, within level covariates interaction, and cross level covariates interaction. Study One purports to examine the performance of multilevel MIMIC models in estimating the covariates interaction described above. Type I error of falsely detecting covariates interaction when there is no covariates interaction effect in the population model, and the power of correctly detecting the covariates interaction effect, bias of the estimate of interaction effect, and RMSE are examined. The design factors include the location of the covariates interaction effect, cluster number, cluster size, intra-class correlation (ICC) level, and magnitude of the interaction effect. The results showed that ML MIMIC performed well in detecting the covariates interaction effect when the covariates interaction effect was at the within level or cross level. However, when the covariates interaction effect was at the between level, the performance of ML MIMIC depended on the magnitude of the interaction effect, ICC, and sample size, especially cluster size. In Study Two, the impact of omitting covariates interaction effect on the estimate of other parameters is investigated when the covariates interaction effect is present in the population model. Parameter estimates of factor loadings, intercepts, main effects of the covariates, and residual variances produced by the correct model in Study One are compared to those produced by the misspecified model to check the impact. Moreover, the sensitivity of fit indices, such as chi-square, CFI, RMSEA, SRMR-B (between), and SRM-W (within) are also examined. Results indicated that none of the fit indices was sensitive to the omission of the covariates interaction effect. The biased parameter estimates included the two covariates main effect and the between-level factor mean.

Survival models are used in analysing time-to-event data. This type of data is very common in medical research. The Cox proportional hazard model is commonly used in analysing time-to-event data. However, this model is based on the proportional hazard (PH) assumption. Violation of this assumption often leads to biased results and inferences. Once non-proportionality is established, there is a need to consider time-varying effects of the covariates. Several models have been developed that relax the proportionality assumption making it possible to analyse data with time-varying effects of both baseline and time-updated covariates. I present various approaches for handling time-varying covariates and time-varying effects in time-to-event models. They include the extended Cox model which handles exogenous time-dependent covariates using the counting process formulation introduced by cite{andersen1982cox}. Andersen and Gill accounts for time varying covariates by each individual having multiple observations with the total-at-risk follow up for each individual being further divided into smaller time intervals. The joint models for the longitudinal and time-to-event processes and its extensions (parametrization and multivariate joint models) were used as it handles endogenous time-varying covariates appropriately. Another is the Aalen model, an additive model which accounts for time-varying effects. However, there are situations where all the covariates of interest do not have time-varying effects. Hence, the semi-parametric additive model can be used. In conclusion, comparisons are made on the results of all the fitted models and it shows that choice of a particular model to fit is influenced by the aim and objectives of fitting the model. In 2002, an AntiRetroviral Treatment (ART) service was established in the Cape Town township of Gugulethu, South Africa. These models will be applied to an HIV/AIDS observational dataset obtained from all patients who initiated ART within the programme between September 2002 and June 2007.

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Evaluating the effectiveness of an intervention can pose challenges if there is not an adequate control group. The effects of the intervention can be distorted by observable differences in the characteristics of the control and treatment groups. Propensity score matching can be used to confirm the outcomes of an intervention are due to the treatment and not other characteristics that may also explain the intervention effects. Propensity score matching is an advanced statistical technique that uses background information on the characteristics of the study population to establish matched pairs of treated participants and controls. This technique improves the quality of control groups and allowing for a better evaluation of the true effects of an intervention. The purpose of this study was to implement this technique to derive county-level matches across the southeastern United States for existing counties within a single state where future statewide initiatives are planned. Statistical analysis was performed using SAS 9.4 (Cary, NC, USA). A select set of key county-level socio-demographic measures theoretically relevant for deriving appropriate matches was examined. These include the proportion of African Americans in population, population density, and proportion of the female population below poverty level. To derive the propensity-matched counties, a logistic regression model with the state of primary interest as the outcome was conducted. The baseline covariates of interest were included in the model and used to predict the probability of a county being in the state of primary interest; this acts as the propensity score used to derive matched controls. A caliper of 0.2 was used to ensure the ratio of the variance of the linear propensity score in the control group to the variance of the linear propensity score in the treatment group is close to 1. The balance of covariates before and after the propensity score matching were assessed to determine if significant differences in each respective covariate persisted after the propensity score matching. Before matching, a significant difference was found in the proportion of African Americans in control group (21.08%, n=3,450) and treatment group (36.95%, n=230) using the t-test (P<0.0001). The percent of females below poverty level showed significant difference between control and treatment group (P=0.0264). The t-test of population density also showed significant differences between the groups (P=0.0424). After matching, the mean differences for the treated-control groups were all zero for these three covariates and the characteristics were no longer showing any significant differences between the two groups. This study found that the use of propensity score matching methods improved the accuracy of matched controls. Ensuring that the control and treatment counties have statistically similar characteristics is important for improving the rigor of future studies examining county-level outcomes. Propensity score matching does not account for unobserved differences between the treatment and control groups that may affect the observed outcomes; however, it does ensure that the observable characteristics between the groups are statistically similar.This method reduces the threat to internal validity that observable characteristics pose on interventions by matching for these potentially confounding characteristics.

While a single learned model is adequate for simple prediction problems, it may not be sufficient to represent heterogeneous populations that difficult classification or regression problems often involve. In such scenarios, practitioners often adopt a "divide and conquer" strategy that segments the data into relatively homogeneous groups and then builds a model for each group. This two-step procedure usually results in simpler, more interpretable and actionable models without any loss in accuracy. We consider prediction problems on bi-modal or dyadic data with covariates, e.g., predicting customer behavior across products, where the independent variables can be naturally partitioned along the modes. A pivoting operation can now result in the target variable showing up as entries in a "customer by product" data matrix. We present a model-based co-clustering framework that interleaves partitioning (clustering) along each mode and construction of prediction models to iteratively improve both cluster assignment and fit of the models. This Simultaneous CO-clustering And Learning (SCOAL) framework generalizes co-clustering and collaborative filtering to model-based co-clustering, and is shown to be better than independently clustering the data first and then building models. Our framework applies to a wide range of bi-modal and multi-modal data, and can be easily specialized to address classification and regression problems in domains like recommender systems, fraud detection and marketing. Further, we note that in several datasets not all the data is useful for the learning problem and ignoring outliers and non-informative values may lead to better models. We explore extensions of SCOAL to automatically identify and discard irrelevant data points and features while modeling, in order to improve prediction accuracy. Next, we leverage the multiple models provided by the SCOAL technique to address two prediction problems on dyadic data, (i) ranking predictions based on their reliability, and (ii) active learning. We also extend SCOAL to predictive modeling of multi-modal data, where one of the modes is implicitly ordered, e.g., time series data. Finally, we illustrate our implementation of a parallel version of SCOAL based on the Google Map-Reduce framework and developed on the open source Hadoop platform. We demonstrate the effectiveness of specific instances of the SCOAL framework on prediction problems through experimentation on real and synthetic data. / text

Using data from the Chicago Homicide Dataset for years 1988-1992 and the Chicago Community Area Demographics, multiple regression and mediation analysis are used to examine various community level factors’ impact on Intimate Partner Homicide (IPH) rates per Chicago community area. The relationship between the percentage of non-white and IPH rate per Chicago community area is significant and positive, but disappears once economic strain is taken into account, as well as when family disruption is included in the model. There is a weak, but positive relationship between population density and IPH rates, but neither economic strain nor family disruption mediates the relationship between population density and IPH rates. Economic deprivation is positively related to IPH rates, but economic strain and family disruption partially mediate the relationship between economic deprivation and IPH rates. Finally, the relationship between the percentage of males aged 30-59 and IPH rates per community area in Chicago is moderately negative, but this relationship disappears once economic strain is accounted for in the model. However, family disruption does not mediate the relationship between the percentage of males aged 30-59 and IPH rates. These results indicate that some structural covariates impact IPH rates and that some relationships are mediated by economic strain and family disruption. These results also lend support to a modified approach to general strain theory (GST). More research is necessary to validate these results.

Em estudos cujo interesse é avaliar o efeito de fatores prognósticos sobre a sobrevida ou algum outro evento de interesse, é comum o uso de modelos de regressão que relacionam tempos de sobrevivência e covariáveis. Quando covariáveis que apresentam dados omissos são incluídas nos modelos de regressão, os programas estatísticos usuais automaticamente excluem aqueles indivíduos que apresentam omissão em pelo menos uma das covariáveis. Com isso, muitos pesquisadores utilizam apenas as observações completas, descartando grande parte da informação disponível. Está comprovado que a análise baseada apenas nos dados completos pode levar a estimadores altamente viesados e ineficientes. Para lidar com este problema, alguns métodos foram propostos na literatura. O objetivo deste trabalho é estender métodos que lidam com dados de sobrevivência e omissão nas covariáveis para a situação em que existe uma proporção de pacientes na população que não são suscetíveis ao evento de interesse. A idéia principal é utilizar modelos com fração de cura incluindo ponderações para compensar possíveis desproporcionalidades na subamostra de casos completos, levando-se em conta uma possível relação entre omissão e pior prognóstico. Foi considerado um modelo de mistura no qual os tempos de falha foram modelados através da família Weibull ou do modelo semiparamétrico de Cox e as probabilidade de cura foram especificadas por um modelo logístico. Os métodos propostos foram aplicados a dados reais, em que a omissão foi simulada em 10\\%, 30\\% e 50\\% das observações. / Survival regression models are considered to evaluate the effect of prognostic factors for survival or some other event of interest. The standard statistical packages automatically exclude cases with at least one missing covariate value. Thus, many researchers use only the complete cases, discarding substantial part of the available information. It is known that this complete case analysis provides biased and inefficient estimates. The aim of this work is to extend survival models with missing covariate values to situations where some individuals are not susceptible to the event of interest. The main idea is to use cure rate models introducing individual weights to incorporate possible bias in the sample with complete cases, taking a possible relation between missingness and worse prognosis into account. Mixture models in which Weibull and Cox models are used to represent the failure times and logistic models to model the cure probabilities are considered. The performance of the procedure was evaluated via a simulation study. The proposed methods were applied to real data where the missingness was simulated in 10\\%, 30\\% and 50\\% of the observations.

Recent Next Generation Sequencing methods provide a count of RNA molecules in the form of short reads, yielding discrete, often highly non-normally distributed gene expression measurements. Due to this feature of RNA sequencing (RNA-seq) data, appropriate statistical inference methods are required. Although Negative Binomial (NB) regression has been generally accepted in the analysis of RNA-seq data, its appropriateness in the application to genetic studies has not been exhaustively evaluated. Additionally, adjusting for covariates that have an unknown relationship with expression of a gene has not been extensively evaluated in RNA-seq studies using the NB framework. Finally, the dependent structures in RNA-Seq data may violate the assumptions of some multiple testing correction methods. In this dissertation, we suggest an alternative regression method, evaluate the effect of covariates, and compare various multiple testing correction methods. We conduct simulation studies and apply these methods to a real data set. First, we suggest Firth’s logistic regression for detecting differentially expressed genes in RNA-seq data. We also recommend the data adaptive method that estimates a recalibrated distribution of test statistics. Firth’ logistic regression exhibits an appropriately controlled Type-I error rate using the data adaptive method and shows comparable power to NB regression in simulation studies. Next, we evaluate the effect of disease-associated covariates where the relationship between the covariate and gene expression is unknown. Although the power of NB and Firth’s logistic regression is decreased as disease-associated covariates are added in a model, Type-I error rates are well controlled in Firth’ logistic regression if the relationship between a covariate and disease is not strong. Finally, we compare multiple testing correction methods that control family-wise error rates and impose false discovery rates. The evaluation reveals that an understanding of study designs, RNA-seq data, and the consequences of applying specific regression and multiple testing correction methods are very important factors to control family-wise error rates or false discovery rates. We believe our statistical investigations will enrich gene expression studies and influence related statistical methods.

O desenvolvimento de métodos para o tratamento de omissões nos dados é recente na estatística e tem sido alvo de muitas pesquisas. A presença de omissões em covariáveis é um problema comum na análise estatística e, em particular nos modelos de análise de sobrevivência, ocorrendo com freqüência em pesquisas clínicas, epidemiológicas e ambientais. Este trabalho apresenta propostas bayesianas para a análise de dados de sobrevivência com omissões nas covariáveis considerando modelos paramétricos da família Weibull e o modelo semi-paramétrico de Cox. Os métodos estudados foram avaliados tanto sob o enfoque paramétrico quanto o semiparamétrico considerando um conjunto de dados de portadores de insuficiência cardíaca. Além disso, é desenvolvido um estudo para avaliar o impacto de diferentes proporções de omissão. / The development of methods dealing with missing data is recent in Statistics and is the target of many researchers. The presence of missing values in the covariates is very common in statistical analysis and, in particular, in clinical, epidemiological and enviromental studies for survival data. This work considers a bayesian approach to analise data with missing covariates for parametric models in the Weibull family and for the Cox semiparametric model. The studied methods are evaluated for the parametric and semiparametric approaches considering a dataset of patients with heart insufficiency. Also, the impact of different omission proportions is assessed.