A bivariate regression model for matched paired survival data: local influence and residual analysis

The use of bivariate distributions plays a fundamental role in survival and reliability studies. In this paper, we consider a location scale model for bivariate survival times based on the proposal of a copula to model the dependence of bivariate survival data. For the proposed model, we consider inferential procedures based on maximum likelihood. Gains in efficiency from bivariate models are also examined in the censored data setting. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the bivariate regression model for matched paired survival data. Sensitivity analysis methods such as local and total influence are presented and derived under three perturbation schemes. The martingale marginal and the deviance marginal residual measures are used to check the adequacy of the model. Furthermore, we propose a new measure which we call modified deviance component residual. The methodology in the paper is illustrated on a lifetime data set for kidney patients.

Determination of tetramethylthiuram disulfide (thiram) for residual analysis in food using spectrophotometry coupled with a solid-phase reactor (SPR) in a flow system

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Latent residual analysis in binary regression with skewed link

Model diagnostics is an integral part of model determination and an important part of the model diagnostics is residual analysis. We adapt and implement residuals considered in the literature for the probit, logistic and skew-probit links under binary regression. New latent residuals for the skew-probit link are proposed here. We have detected the presence of outliers using the residuals proposed here for different models in a simulated dataset and a real medical dataset.

Validation of a method for the analysis of volatile organic compounds in water

Dissertação de mestrado, Qualidade em Análises, Faculdade de Ciências e Tecnologia, Universidade do Algarve, 2015

The short-term effect of air pollution on cardiovascular mortality in Tianjin, China : comparison of time series and case–crossover analyses

Background: Many studies have illustrated that ambient air pollution negatively impacts on health. However, little evidence is available for the effects of air pollution on cardiovascular mortality (CVM) in Tianjin, China. Also, no study has examined which strata length for the time-stratified case–crossover analysis gives estimates that most closely match the estimates from time series analysis. Objectives: The purpose of this study was to estimate the effects of air pollutants on CVM in Tianjin, China, and compare time-stratified case–crossover and time series analyses. Method: A time-stratified case–crossover and generalized additive model (time series) were applied to examine the impact of air pollution on CVM from 2005 to 2007. Four time-stratified case–crossover analyses were used by varying the stratum length (Calendar month, 28, 21 or 14 days). Jackknifing was used to compare the methods. Residual analysis was used to check whether the models fitted well. Results: Both case–crossover and time series analyses show that air pollutants (PM10, SO2 and NO2) were positively associated with CVM. The estimates from the time-stratified case–crossover varied greatly with changing strata length. The estimates from the time series analyses varied slightly with changing degrees of freedom per year for time. The residuals from the time series analyses had less autocorrelation than those from the case–crossover analyses indicating a better fit. Conclusion: Air pollution was associated with an increased risk of CVM in Tianjin, China. Time series analyses performed better than the time-stratified case–crossover analyses in terms of residual checking.

Sistema computacional para o estudo da estrutura primária e redesenho de genes

Um dos maiores avanços científicos do século XX foi o desenvolvimento de tecnologia que permite a sequenciação de genomas em larga escala. Contudo, a informação produzida pela sequenciação não explica por si só a sua estrutura primária, evolução e seu funcionamento. Para esse fim novas áreas como a biologia molecular, a genética e a bioinformática são usadas para estudar as diversas propriedades e funcionamento dos genomas. Com este trabalho estamos particularmente interessados em perceber detalhadamente a descodificação do genoma efectuada no ribossoma e extrair as regras gerais através da análise da estrutura primária do genoma, nomeadamente o contexto de codões e a distribuição dos codões. Estas regras estão pouco estudadas e entendidas, não se sabendo se poderão ser obtidas através de estatística e ferramentas bioinfomáticas. Os métodos tradicionais para estudar a distribuição dos codões no genoma e seu contexto não providenciam as ferramentas necessárias para estudar estas propriedades à escala genómica. As tabelas de contagens com as distribuições de codões, assim como métricas absolutas, estão actualmente disponíveis em bases de dados. Diversas aplicações para caracterizar as sequências genéticas estão também disponíveis. No entanto, outros tipos de abordagens a nível estatístico e outros métodos de visualização de informação estavam claramente em falta. No presente trabalho foram desenvolvidos métodos matemáticos e computacionais para a análise do contexto de codões e também para identificar zonas onde as repetições de codões ocorrem. Novas formas de visualização de informação foram também desenvolvidas para permitir a interpretação da informação obtida. As ferramentas estatísticas inseridas no modelo, como o clustering, análise residual, índices de adaptação dos codões revelaram-se importantes para caracterizar as sequências codificantes de alguns genomas. O objectivo final é que a informação obtida permita identificar as regras gerais que governam o contexto de codões em qualquer genoma.

3D Simultaneous Inversion for Seismic Structure and Local Hypocenters in Germany under Consideration of Seismic Anisotropy in the Upper Mantel

The main task of this work has been to investigate the effects of anisotropy onto the propagation of seismic waves along the Upper Mantle below Germany and adjacent areas. Refraction- and reflexion seismic experiments proved the existence of Upper Mantle anisotropy and its influence onto the propagation of Pn-waves. By the 3D tomographic investigations that have been done here for the crust and the upper mantle, considering the influence of anisotropy, a gap for the investigations in Europe has been closed. These investigations have been done with the SSH-Inversionprogram of Prof. Dr. M. Koch, which is able to compute simultaneously the seismic structure and hypocenters. For the investigation, a dataset has been available with recordings between the years 1975 to 2003 with a total of 60249 P- and 54212 S-phase records of 10028 seismic events. At the beginning, a precise analysis of the residuals (RES, the difference between calculated and observed arrivaltime) has been done which confirmed the existence of anisotropy for Pn-phases. The recognized sinusoidal distribution has been compensated by an extension of the SSH-program by an ellipse with a slow and rectangular fast axis with azimuth to correct the Pn-velocities. The azimuth of the fast axis has been fixed by the application of the simultaneous inversion at 25° - 27° with a variation of the velocities at +- 2.5 about an average value at 8 km/s. This new value differs from the old one at 35°, recognized in the initial residual analysis. This depends on the new computed hypocenters together with the structure. The application of the elliptical correction has resulted in a better fit of the vertical layered 1D-Model, compared to the results of preceding seismological experiments and 1D and 2D investigations. The optimal result of the 1D-inversion has been used as initial starting model for the 3D-inversions to compute the three dimensional picture of the seismic structure of the Crust and Upper Mantle. The simultaneous inversion has showed an optimization of the relocalization of the hypocenters and the reconstruction of the seismic structure in comparison to the geology and tectonic, as described by other investigations. The investigations for the seismic structure and the relocalization have been confirmed by several different tests. First, synthetic traveltime data are computed with an anisotropic variation and inverted with and without anisotropic correction. Further, tests with randomly disturbed hypocenters and traveltime data have been proceeded to verify the influence of the initial values onto the relocalization accuracy and onto the seismic structure and to test for a further improvement by the application of the anisotropic correction. Finally, the results of the work have been applied onto the Waldkirch earthquake in 2004 to compare the isotropic and the anisotropic relocalization with the initial optimal one to verify whether there is some improvement.

The log-exponentiated Weibull regression model for interval-censored data

In interval-censored survival data, the event of interest is not observed exactly but is only known to occur within some time interval. Such data appear very frequently. In this paper, we are concerned only with parametric forms, and so a location-scale regression model based on the exponentiated Weibull distribution is proposed for modeling interval-censored data. We show that the proposed log-exponentiated Weibull regression model for interval-censored data represents a parametric family of models that include other regression models that are broadly used in lifetime data analysis. Assuming the use of interval-censored data, we employ a frequentist analysis, a jackknife estimator, a parametric bootstrap and a Bayesian analysis for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Furthermore, for different parameter settings, sample sizes and censoring percentages, various simulations are performed; in addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended to a modified deviance residual in log-exponentiated Weibull regression models for interval-censored data. (C) 2009 Elsevier B.V. All rights reserved.

Generalized log-gamma regression models with cure fraction

In this paper, the generalized log-gamma regression model is modified to allow the possibility that long-term survivors may be present in the data. This modification leads to a generalized log-gamma regression model with a cure rate, encompassing, as special cases, the log-exponential, log-Weibull and log-normal regression models with a cure rate typically used to model such data. The models attempt to simultaneously estimate the effects of explanatory variables on the timing acceleration/deceleration of a given event and the surviving fraction, that is, the proportion of the population for which the event never occurs. The normal curvatures of local influence are derived under some usual perturbation schemes and two martingale-type residuals are proposed to assess departures from the generalized log-gamma error assumption as well as to detect outlying observations. Finally, a data set from the medical area is analyzed.

Log-Burr XII regression models with censored data

In survival analysis applications, the failure rate function may frequently present a unimodal shape. In such case, the log-normal or log-logistic distributions are used. In this paper, we shall be concerned only with parametric forms, so a location-scale regression model based on the Burr XII distribution is proposed for modeling data with a unimodal failure rate function as an alternative to the log-logistic regression model. Assuming censored data, we consider a classic analysis, a Bayesian analysis and a jackknife estimator for the parameters of the proposed model. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the log-logistic and log-Burr XII regression models. Besides, we use sensitivity analysis to detect influential or outlying observations, and residual analysis is used to check the assumptions in the model. Finally, we analyze a real data set under log-Buff XII regression models. (C) 2008 Published by Elsevier B.V.

Deviance residuals in generalised log-gamma regression models with censored observations

In this article, we compare three residuals based on the deviance component in generalised log-gamma regression models with censored observations. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each residual is displayed and compared with the standard normal distribution. For all cases studied, the empirical distributions of the proposed residuals are in general symmetric around zero, but only a martingale-type residual presented negligible kurtosis for the majority of the cases studied. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for the martingale-type residual in generalised log-gamma regression models with censored data. A lifetime data set is analysed under log-gamma regression models and a model checking based on the martingale-type residual is performed.

Diagnostic tools in beta regression with varying dispersion

We consider the issue of performing residual and local influence analyses in beta regression models with varying dispersion, which are useful for modelling random variables that assume values in the standard unit interval. In such models, both the mean and the dispersion depend upon independent variables. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. An application using real data is presented and discussed.

A new class of survival regression models with heavy-tailed errors: robustness and diagnostics

Birnbaum-Saunders models have largely been applied in material fatigue studies and reliability analyses to relate the total time until failure with some type of cumulative damage. In many problems related to the medical field, such as chronic cardiac diseases and different types of cancer, a cumulative damage caused by several risk factors might cause some degradation that leads to a fatigue process. In these cases, BS models can be suitable for describing the propagation lifetime. However, since the cumulative damage is assumed to be normally distributed in the BS distribution, the parameter estimates from this model can be sensitive to outlying observations. In order to attenuate this influence, we present in this paper BS models, in which a Student-t distribution is assumed to explain the cumulative damage. In particular, we show that the maximum likelihood estimates of the Student-t log-BS models attribute smaller weights to outlying observations, which produce robust parameter estimates. Also, some inferential results are presented. In addition, based on local influence and deviance component and martingale-type residuals, a diagnostics analysis is derived. Finally, a motivating example from the medical field is analyzed using log-BS regression models. Since the parameter estimates appear to be very sensitive to outlying and influential observations, the Student-t log-BS regression model should attenuate such influences. The model checking methodologies developed in this paper are used to compare the fitted models.

Estilo de vida individual de universitários jovens com excesso de peso da Universidade Católica de Murcia-Espanha

Individual lifestyle includes health and risk behaviors that can altar health status. Excess weight is a public health problem of modern civilization and there is an estimated mean prevalence of 45% in European countries. In Spain, the Murcia Region is an area of high morbidity and mortality from cardiovascular disorders. In this study we assess the differences in health and risk behaviors in ove/weight and normal weight undergraduates at the Universidad Católica San Antonio de Murcia (UCAM). Methods: Transversal design of parallel groups (overweight - cases and normal weight - control) , formed using the anthropometric technique. A questionnaire applied to a sample of 471 undergraduates of either sex, between the ages of 18 and 29 years, enrolled in 4 bachelor degree courses (ADE, CA, PER, PUB) at UCAM. We performed a standardized measurement of body mass (weight in kg), height (in meters) using a Seca® scale with calibrated stadiometer, waist and hip circumferences (in cm) with an inelastic tape and skinfolds thickness (triceps and subscapular in mm) with a Holtain® caliper, to calculate body mass index (BMI), waist-to-hip ratio (WHR) and the sum of skinfolds (SSF). We applied a lifestyle questionnaire about alcohol and tobacco consumption, knowledge and behaviors related to health indicators (arterial pressure and cholesterol), diet and physical activity. The information was collected in April and May, 2001 at the UCAM laboratory of Applied Nutrition. Statistical analysis: analysis of independent groups, contingency tables that reveal which qualitativa variables show differences and associations between the groups, Pearson's chi-square,and a significance levei of p < 0.05 followed by a residual analysis (1.96). Descriptive statistics (mean and standard deviation) were used to establish the two groups: case and contrai with 65 men and 26 women each who had BMI < 25 kg/m2. Results: A total of 65 of the men assessed (14%) and 26 (6%) of the women were overweight. Mean body mass index of the case group was 27. 78 ±: 2.83 kg/m2 in the men and 26.26 ± 1.37 kg/m2 in the women, while contrai group men had mean BMI of 22.36 ± 1.72 kg/m2, while for the women it was 20.76 ±: 2.13 kg/m2. The self-declared values of weight and height were underestimated, but with high accuracy, sensitivity and specificity. Thus, these can be used to calculate the BMI of overweight Spanish undergraduates. Regular vigorous physical activity was observed only in normal weight men. The analysis showed the following significant differences for the qualitativa variables of the two groups. The contrai group was interested in arterial hypertension, believed that they were not overweight, that they had no abdominal fat, and had not considered controlling 'fatty food consumption. Those who thought of controlling it sometimes, did so without professional help. However, part of the overweight group believed that they were overweight and had abdominal fat between average and considerable, had often or always considered controlling fatty foods and had often or always tried to control consumption with the help of professionals. They had always thought of engaging in physical activities, unlike the normal weight individuals. Nearly all (95%) of the overweight undergraduates and most (75%) of the normal weight group reported that they sometimes or always controlled fatty food ingestion. Mean physical activity was nearly twice as high in the summer than in the winter. Conclusions: The overweight undergraduates in this sample displayed a lifestyle with a greater number of healthy behaviors when compared to normal weight individuals

Estimativa da área foliar de Ageratum conyzoides usando dimensões lineares do limbo foliar

The aim of this research was to obtain a mathematical equation to estimate the leaf area of Ageratum conyzoides based on linear measures of its leaf blade. Correlation studies were done using real leaf area (Sf), leaf length (C) and the maximum leaf width (L), in about 200 leaf blades. The evaluated statistic models were: linear Y = a + bx; simple linear Y = bx; geometric Y = ax(b); and exponential Y = ab(x). The evaluated linear, exponential and geometric models can be used in the billygoat weed leaf area estimation. In the practical sense, the simple linear regression model is suggested using the C*L multiplication product and taking the linear coefficient equal to zero, because it showed weak-alteration on sum of squares error and satisfactory residual analysis. Thus, an estimate of A conyzoides leaf area can be obtained using the equation Sf = 0.6789*(C*L), with a determination coefficient of 0.8630.