Analysis of Melanoma Onset: Assessing Familial Aggregation by Using Estimating Equations and Fitting Variance Components via Bayesian Random Effects Models

We investigate whether relative contributions of genetic and shared environmental factors are associated with an increased risk in melanoma. Data from the Queensland Familial Melanoma Project comprising 15,907 subjects arising from 1912 families were analyzed to estimate the additive genetic, common and unique environmental contributions to variation in the age at onset of melanoma. Two complementary approaches for analyzing correlated time-to-onset family data were considered: the generalized estimating equations (GEE) method in which one can estimate relationship-specific dependence simultaneously with regression coefficients that describe the average population response to changing covariates; and a subject-specific Bayesian mixed model in which heterogeneity in regression parameters is explicitly modeled and the different components of variation may be estimated directly. The proportional hazards and Weibull models were utilized, as both produce natural frameworks for estimating relative risks while adjusting for simultaneous effects of other covariates. A simple Markov Chain Monte Carlo method for covariate imputation of missing data was used and the actual implementation of the Bayesian model was based on Gibbs sampling using the free ware package BUGS. In addition, we also used a Bayesian model to investigate the relative contribution of genetic and environmental effects on the expression of naevi and freckles, which are known risk factors for melanoma.

Multi-level zero-inflated Poisson regression modelling of correlated count data with excess zeros

Count data with excess zeros relative to a Poisson distribution are common in many biomedical applications. A popular approach to the analysis of such data is to use a zero-inflated Poisson (ZIP) regression model. Often, because of the hierarchical Study design or the data collection procedure, zero-inflation and lack of independence may occur simultaneously, which tender the standard ZIP model inadequate. To account for the preponderance of zero counts and the inherent correlation of observations, a class of multi-level ZIP regression model with random effects is presented. Model fitting is facilitated using an expectation-maximization algorithm, whereas variance components are estimated via residual maximum likelihood estimating equations. A score test for zero-inflation is also presented. The multi-level ZIP model is then generalized to cope with a more complex correlation structure. Application to the analysis of correlated count data from a longitudinal infant feeding study illustrates the usefulness of the approach.

Parameterized Link Functions in Generalized Linear Random Effect Models: a Case Study on Breast Cancer Treatment

In non-linear random effects some attention has been very recently devoted to the analysis ofsuitable transformation of the response variables separately (Taylor 1996) or not (Oberg and Davidian 2000) from the transformations of the covariates and, as far as we know, no investigation has been carried out on the choice of link function in such models. In our study we consider the use of a random effect model when a parameterized family of links (Aranda-Ordaz 1981, Prentice 1996, Pregibon 1980, Stukel 1988 and Czado 1997) is introduced. We point out the advantages and the drawbacks associated with the choice of this data-driven kind of modeling. Difficulties in the interpretation of regression parameters, and therefore in understanding the influence of covariates, as well as problems related to loss of efficiency of estimates and overfitting, are discussed. A case study on radiotherapy usage in breast cancer treatment is discussed.

Use of posterior predictive assessments to evaluate model fit in multilevel logistic regression

Assessing the fit of a model is an important final step in any statistical analysis, but this is not straightforward when complex discrete response models are used. Cross validation and posterior predictions have been suggested as methods to aid model criticism. In this paper a comparison is made between four methods of model predictive assessment in the context of a three level logistic regression model for clinical mastitis in dairy cattle; cross validation, a prediction using the full posterior predictive distribution and two “mixed” predictive methods that incorporate higher level random effects simulated from the underlying model distribution. Cross validation is considered a gold standard method but is computationally intensive and thus a comparison is made between posterior predictive assessments and cross validation. The analyses revealed that mixed prediction methods produced results close to cross validation whilst the full posterior predictive assessment gave predictions that were over-optimistic (closer to the observed disease rates) compared with cross validation. A mixed prediction method that simulated random effects from both higher levels was best at identifying the outlying level two (farm-year) units of interest. It is concluded that this mixed prediction method, simulating random effects from both higher levels, is straightforward and may be of value in model criticism of multilevel logistic regression, a technique commonly used for animal health data with a hierarchical structure.

Statistical learning of random probability measures

The study of random probability measures is a lively research topic that has attracted interest from different fields in recent years. In this thesis, we consider random probability measures in the context of Bayesian nonparametrics, where the law of a random probability measure is used as prior distribution, and in the context of distributional data analysis, where the goal is to perform inference given avsample from the law of a random probability measure. The contributions contained in this thesis can be subdivided according to three different topics: (i) the use of almost surely discrete repulsive random measures (i.e., whose support points are well separated) for Bayesian model-based clustering, (ii) the proposal of new laws for collections of random probability measures for Bayesian density estimation of partially exchangeable data subdivided into different groups, and (iii) the study of principal component analysis and regression models for probability distributions seen as elements of the 2-Wasserstein space. Specifically, for point (i) above we propose an efficient Markov chain Monte Carlo algorithm for posterior inference, which sidesteps the need of split-merge reversible jump moves typically associated with poor performance, we propose a model for clustering high-dimensional data by introducing a novel class of anisotropic determinantal point processes, and study the distributional properties of the repulsive measures, shedding light on important theoretical results which enable more principled prior elicitation and more efficient posterior simulation algorithms. For point (ii) above, we consider several models suitable for clustering homogeneous populations, inducing spatial dependence across groups of data, extracting the characteristic traits common to all the data-groups, and propose a novel vector autoregressive model to study of growth curves of Singaporean kids. Finally, for point (iii), we propose a novel class of projected statistical methods for distributional data analysis for measures on the real line and on the unit-circle.

On the effect of confounding in linear regression models: an approach based on the theory of quadratic forms

The main topic of this thesis is confounding in linear regression models. It arises when a relationship between an observed process, the covariate, and an outcome process, the response, is influenced by an unmeasured process, the confounder, associated with both. Consequently, the estimators for the regression coefficients of the measured covariates might be severely biased, less efficient and characterized by misleading interpretations. Confounding is an issue when the primary target of the work is the estimation of the regression parameters. The central point of the dissertation is the evaluation of the sampling properties of parameter estimators. This work aims to extend the spatial confounding framework to general structured settings and to understand the behaviour of confounding as a function of the data generating process structure parameters in several scenarios focusing on the joint covariate-confounder structure. In line with the spatial statistics literature, our purpose is to quantify the sampling properties of the regression coefficient estimators and, in turn, to identify the most prominent quantities depending on the generative mechanism impacting confounding. Once the sampling properties of the estimator conditionally on the covariate process are derived as ratios of dependent quadratic forms in Gaussian random variables, we provide an analytic expression of the marginal sampling properties of the estimator using Carlson’s R function. Additionally, we propose a representative quantity for the magnitude of confounding as a proxy of the bias, its first-order Laplace approximation. To conclude, we work under several frameworks considering spatial and temporal data with specific assumptions regarding the covariance and cross-covariance functions used to generate the processes involved. This study allows us to claim that the variability of the confounder-covariate interaction and of the covariate plays the most relevant role in determining the principal marker of the magnitude of confounding.

Seemingly unrelated linear regression for contaminated data based on Gaussian mixtures

In this thesis, new classes of models for multivariate linear regression defined by finite mixtures of seemingly unrelated contaminated normal regression models and seemingly unrelated contaminated normal cluster-weighted models are illustrated. The main difference between such families is that the covariates are treated as fixed in the former class of models and as random in the latter. Thus, in cluster-weighted models the assignment of the data points to the unknown groups of observations depends also by the covariates. These classes provide an extension to mixture-based regression analysis for modelling multivariate and correlated responses in the presence of mild outliers that allows to specify a different vector of regressors for the prediction of each response. Expectation-conditional maximisation algorithms for the calculation of the maximum likelihood estimate of the model parameters have been derived. As the number of free parameters incresases quadratically with the number of responses and the covariates, analyses based on the proposed models can become unfeasible in practical applications. These problems have been overcome by introducing constraints on the elements of the covariance matrices according to an approach based on the eigen-decomposition of the covariance matrices. The performances of the new models have been studied by simulations and using real datasets in comparison with other models. In order to gain additional flexibility, mixtures of seemingly unrelated contaminated normal regressions models have also been specified so as to allow mixing proportions to be expressed as functions of concomitant covariates. An illustration of the new models with concomitant variables and a study on housing tension in the municipalities of the Emilia-Romagna region based on different types of multivariate linear regression models have been performed.

Censored Linear Regression Models For Irregularly Observed Longitudinal Data Using The Multivariate-t Distribution.

In acquired immunodeficiency syndrome (AIDS) studies it is quite common to observe viral load measurements collected irregularly over time. Moreover, these measurements can be subjected to some upper and/or lower detection limits depending on the quantification assays. A complication arises when these continuous repeated measures have a heavy-tailed behavior. For such data structures, we propose a robust structure for a censored linear model based on the multivariate Student's t-distribution. To compensate for the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is employed. An efficient expectation maximization type algorithm is developed for computing the maximum likelihood estimates, obtaining as a by-product the standard errors of the fixed effects and the log-likelihood function. The proposed algorithm uses closed-form expressions at the E-step that rely on formulas for the mean and variance of a truncated multivariate Student's t-distribution. The methodology is illustrated through an application to an Human Immunodeficiency Virus-AIDS (HIV-AIDS) study and several simulation studies.

Biased Random-key Genetic Algorithms For The Winner Determination Problem In Combinatorial Auctions.

Abstract In this paper, we address the problem of picking a subset of bids in a general combinatorial auction so as to maximize the overall profit using the first-price model. This winner determination problem assumes that a single bidding round is held to determine both the winners and prices to be paid. We introduce six variants of biased random-key genetic algorithms for this problem. Three of them use a novel initialization technique that makes use of solutions of intermediate linear programming relaxations of an exact mixed integer-linear programming model as initial chromosomes of the population. An experimental evaluation compares the effectiveness of the proposed algorithms with the standard mixed linear integer programming formulation, a specialized exact algorithm, and the best-performing heuristics proposed for this problem. The proposed algorithms are competitive and offer strong results, mainly for large-scale auctions.

Comparing Near-infrared Conventional Diffuse Reflectance Spectroscopy And Hyperspectral Imaging For Determination Of The Bulk Properties Of Solid Samples By Multivariate Regression: Determination Of Mooney Viscosity And Plasticity Indices Of Natural Rubber.

Conventional reflectance spectroscopy (NIRS) and hyperspectral imaging (HI) in the near-infrared region (1000-2500 nm) are evaluated and compared, using, as the case study, the determination of relevant properties related to the quality of natural rubber. Mooney viscosity (MV) and plasticity indices (PI) (PI0 - original plasticity, PI30 - plasticity after accelerated aging, and PRI - the plasticity retention index after accelerated aging) of rubber were determined using multivariate regression models. Two hundred and eighty six samples of rubber were measured using conventional and hyperspectral near-infrared imaging reflectance instruments in the range of 1000-2500 nm. The sample set was split into regression (n = 191) and external validation (n = 95) sub-sets. Three instruments were employed for data acquisition: a line scanning hyperspectral camera and two conventional FT-NIR spectrometers. Sample heterogeneity was evaluated using hyperspectral images obtained with a resolution of 150 × 150 μm and principal component analysis. The probed sample area (5 cm(2); 24,000 pixels) to achieve representativeness was found to be equivalent to the average of 6 spectra for a 1 cm diameter probing circular window of one FT-NIR instrument. The other spectrophotometer can probe the whole sample in only one measurement. The results show that the rubber properties can be determined with very similar accuracy and precision by Partial Least Square (PLS) regression models regardless of whether HI-NIR or conventional FT-NIR produce the spectral datasets. The best Root Mean Square Errors of Prediction (RMSEPs) of external validation for MV, PI0, PI30, and PRI were 4.3, 1.8, 3.4, and 5.3%, respectively. Though the quantitative results provided by the three instruments can be considered equivalent, the hyperspectral imaging instrument presents a number of advantages, being about 6 times faster than conventional bulk spectrometers, producing robust spectral data by ensuring sample representativeness, and minimizing the effect of the presence of contaminants.

Determinação da velolcidade critica como referencia do limiar anaerobio para o nado costas

Universidade Estadual de Campinas . Faculdade de Educação Física

Comparação entre protocolos de determinação do limiar anaerobio e suas correlações com o desempenho aerobio em nadadores adolescentes

Universidade Estadual de Campinas . Faculdade de Educação Física

O risco espacial e fatores associados ao edentulismo em idosos em município do Sudeste do Brasil

Objetivou-se identificar fatores associados ao edentulismo e o seu risco espacial em idosos. Foi realizado um estudo transversal em uma amostra de 372 indivíduos de 60 anos e mais, no Município de Botucatu, São Paulo, Brasil, em 2005. Razões de prevalência brutas e ajustadas foram estimadas por meio de regressão de Poisson, com estimativa robusta da variância e procedimentos de modelagem hierárquica. A análise espacial foi realizada por estimativas de densidade de Kernel. A prevalência de edentulismo foi de 63,17%. Os fatores sociodemográficos associados ao edentulismo foram a baixa escolaridade, o aumento do número de pessoas por cômodo, não possuir automóvel e idade mais avançada, presença de comorbidades, ausência de um cirurgião-dentista regular e ter realizado a última consulta há três anos ou mais. A análise espacial mostrou maior risco nas áreas periféricas. Obteve-se uma melhor compreensão da perda dentária entre os idosos, subsidiando o planejamento de ações em saúde coletiva.

Allometric models for estimating the phytomass of a secondary Atlantic Forest area of southeastern Brazil

The purpose of this study was to develop and validate equations to estimate the aboveground phytomass of a 30 years old plot of Atlantic Forest. In two plots of 100 m², a total of 82 trees were cut down at ground level. For each tree, height and diameter were measured. Leaves and woody material were separated in order to determine their fresh weights in field conditions. Samples of each fraction were oven dried at 80 °C to constant weight to determine their dry weight. Tree data were divided into two random samples. One sample was used for the development of the regression equations, and the other for validation. The models were developed using single linear regression analysis, where the dependent variable was the dry mass, and the independent variables were height (h), diameter (d) and d²h. The validation was carried out using Pearson correlation coefficient, paired t-Student test and standard error of estimation. The best equations to estimate aboveground phytomass were: lnDW = -3.068+2.522lnd (r² = 0.91; s y/x = 0.67) and lnDW = -3.676+0.951ln d²h (r² = 0.94; s y/x = 0.56).

Reproductive behavior, development and eye regression in the cave armored catfish, Ancistrus cryptophthalmus Reis, 1987 (Siluriformes: Loricariidae), breed in laboratory

The troglobitic armored catfish, Ancistrus cryptophthalmus (Loricariidae, Ancistrinae) is known from four caves in the São Domingos karst area, upper rio Tocantins basin, Central Brazil. These populations differ in general body shape and degree of reduction of eyes and of pigmentation. The small Passa Três population (around 1,000 individuals) presents the most reduced eyes, which are not externally visible in adults. A small group of Passa Três catfish, one male and three females, reproduced spontaneously thrice in laboratory, at the end of summertime in 2000, 2003 and 2004. Herein we describe the reproductive behavior during the 2003 event, as well as the early development of the 2003 and 2004 offsprings, with focus on body growth and ontogenetic regression of eyes. The parental care by the male, which includes defense of the rock shelter where the egg clutch is laid, cleaning and oxygenation of eggs, is typical of many loricariids. On the other hand, the slow development, including delayed eye degeneration, low body growth rates and high estimated longevity (15 years or more) are characteristic of precocial, or K-selected, life cycles. In the absence of comparable data for close epigean relatives (Ancistrus spp.), it is not possible to establish whether these features are an autapomorphic specialization of the troglobitic A. cryptophthalmus or a plesiomorphic trait already present in the epigean ancestor, possibly favoring the adoption of the life in the food-poor cave environment. We briefly discuss the current hypotheses on eye regression in troglobitic vertebrates.