A Log-Linear Regression Model for the Beta-Weibull Distribution

We introduce the log-beta Weibull regression model based on the beta Weibull distribution (Famoye et al., 2005; Lee et al., 2007). We derive expansions for the moment generating function which do not depend on complicated functions. The new regression model represents a parametric family of models that includes as sub-models several widely known regression models that can be applied to censored survival data. We employ a frequentist analysis, a jackknife estimator, and a parametric bootstrap 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. Further, for different parameter settings, sample sizes, and censoring percentages, several 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 extended to a modified deviance residual in the proposed regression model applied to censored data. We define martingale and deviance residuals to evaluate the model assumptions. The extended regression model is very useful for the analysis of real data and could give more realistic fits than other special regression models.

Robust integration of real time optimization with linear model predictive control

Here, we study the stable integration of real time optimization (RTO) with model predictive control (MPC) in a three layer structure. The intermediate layer is a quadratic programming whose objective is to compute reachable targets to the MPC layer that lie at the minimum distance to the optimum set points that are produced by the RTO layer. The lower layer is an infinite horizon MPC with guaranteed stability with additional constraints that force the feasibility and convergence of the target calculation layer. It is also considered the case in which there is polytopic uncertainty in the steady state model considered in the target calculation. The dynamic part of the MPC model is also considered unknown but it is assumed to be represented by one of the models of a discrete set of models. The efficiency of the methods presented here is illustrated with the simulation of a low order system. (C) 2010 Elsevier Ltd. All rights reserved.

Double generalized linear model for tissue culture proportion data: a Bayesian perspective

Joint generalized linear models and double generalized linear models (DGLMs) were designed to model outcomes for which the variability can be explained using factors and/or covariates. When such factors operate, the usual normal regression models, which inherently exhibit constant variance, will under-represent variation in the data and hence may lead to erroneous inferences. For count and proportion data, such noise factors can generate a so-called overdispersion effect, and the use of binomial and Poisson models underestimates the variability and, consequently, incorrectly indicate significant effects. In this manuscript, we propose a DGLM from a Bayesian perspective, focusing on the case of proportion data, where the overdispersion can be modeled using a random effect that depends on some noise factors. The posterior joint density function was sampled using Monte Carlo Markov Chain algorithms, allowing inferences over the model parameters. An application to a data set on apple tissue culture is presented, for which it is shown that the Bayesian approach is quite feasible, even when limited prior information is available, thereby generating valuable insight for the researcher about its experimental results.

Chronic obstructive pulmonary disease in Brazil: mortality and hospitalization trends and rates, 1996-2008

SETTING: Chronic obstructive pulmonary disease (COPD) is the third leading cause of death among adults in Brazil. OBJECTIVE: To evaluate the mortality and hospitalisation trends in Brazil caused by COPD during the period 1996-2008. DESIGN: We used the health official statistics system to obtain data about mortality (1996-2008) and morbidity (1998-2008) due to COPD and all respiratory diseases (tuberculosis: codes A15-16; lung cancer: code C34, and all diseases coded from J40 to 47 in the 10th Revision of the International Classification of Diseases) as the underlying cause, in persons aged 45-74 years. We used the Joinpoint Regression Program log-linear model using Poisson regression that creates a Monte Carlo permutation test to identify points where trend lines change significantly in magnitude/direction to verify peaks and trends. RESULTS: The annual per cent change in age-adjusted death rates due to COPD declined by 2.7% in men (95%CI -3.6 to -1.8) and -2.0% (95%CI -2.9 to -1.0) in women; and due to all respiratory causes it declined by -1.7% (95%CI 2.4 to -1.0) in men and -1.1% (95%CI -1.8 to -0.3) in women. Although hospitalisation rates for COPD are declining, the hospital admission fatality rate increased in both sexes. CONCLUSION: COPD is still a leading cause of mortality in Brazil despite the observed decline in the mortality/hospitalisation rates for both sexes.

Comparing diagnostic tests with missing data

When missing data occur in studies designed to compare the accuracy of diagnostic tests, a common, though naive, practice is to base the comparison of sensitivity, specificity, as well as of positive and negative predictive values on some subset of the data that fits into methods implemented in standard statistical packages. Such methods are usually valid only under the strong missing completely at random (MCAR) assumption and may generate biased and less precise estimates. We review some models that use the dependence structure of the completely observed cases to incorporate the information of the partially categorized observations into the analysis and show how they may be fitted via a two-stage hybrid process involving maximum likelihood in the first stage and weighted least squares in the second. We indicate how computational subroutines written in R may be used to fit the proposed models and illustrate the different analysis strategies with observational data collected to compare the accuracy of three distinct non-invasive diagnostic methods for endometriosis. The results indicate that even when the MCAR assumption is plausible, the naive partial analyses should be avoided.

Birnbaum-Saunders nonlinear regression models

We introduce, for the first time, a new class of Birnbaum-Saunders nonlinear regression models potentially useful in lifetime data analysis. The class generalizes the regression model described by Rieck and Nedelman [Rieck, J.R., Nedelman, J.R., 1991. A log-linear model for the Birnbaum-Saunders distribution. Technometrics 33, 51-60]. We discuss maximum-likelihood estimation for the parameters of the model, and derive closed-form expressions for the second-order biases of these estimates. Our formulae are easily computed as ordinary linear regressions and are then used to define bias corrected maximum-likelihood estimates. Some simulation results show that the bias correction scheme yields nearly unbiased estimates without increasing the mean squared errors. Two empirical applications are analysed and discussed. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

The generalized log-gamma mixture model with covariates: local influence and residual analysis

In a sample of censored survival times, the presence of an immune proportion of individuals who are not subject to death, failure or relapse, may be indicated by a relatively high number of individuals with large censored survival times. In this paper the generalized log-gamma model is modified for the possibility that long-term survivors may be present in the data. The model attempts to separately estimate the effects of covariates on the surviving fraction, that is, the proportion of the population for which the event never occurs. The logistic function is used for the regression model of the surviving fraction. Inference for the model parameters is considered via maximum likelihood. Some influence methods, such as the local influence and total local influence of an individual are derived, analyzed and discussed. Finally, a data set from the medical area is analyzed under the log-gamma generalized mixture model. A residual analysis is performed in order to select an appropriate model.

The log-bimodal-skew-normal model. A geochemical application

The main objective of this paper is to study a logarithm extension of the bimodal skew normal model introduced by Elal-Olivero et al. [1]. The model can then be seen as an alternative to the log-normal model typically used for fitting positive data. We study some basic properties such as the distribution function and moments, and discuss maximum likelihood for parameter estimation. We report results of an application to a real data set related to nickel concentration in soil samples. Model fitting comparison with several alternative models indicates that the model proposed presents the best fit and so it can be quite useful in real applications for chemical data on substance concentration. Copyright (C) 2011 John Wiley & Sons, Ltd.

Discharge-calcium concentration relationships in streams of the Amazon and Cerrado of Brazil: soil or land use controlled

Stream discharge-concentration relationships are indicators of terrestrial ecosystem function. Throughout the Amazon and Cerrado regions of Brazil rapid changes in land use and land cover may be altering these hydrochemical relationships. The current analysis focuses on factors controlling the discharge-calcium (Ca) concentration relationship since previous research in these regions has demonstrated both positive and negative slopes in linear log(10)discharge-log(10)Ca concentration regressions. The objective of the current study was to evaluate factors controlling stream discharge-Ca concentration relationships including year, season, stream order, vegetation cover, land use, and soil classification. It was hypothesized that land use and soil class are the most critical attributes controlling discharge-Ca concentration relationships. A multilevel, linear regression approach was utilized with data from 28 streams throughout Brazil. These streams come from three distinct regions and varied broadly in watershed size (< 1 to > 10(6) ha) and discharge (10(-5.7)-10(3.2) m(3) s(-1)). Linear regressions of log(10)Ca versus log(10)discharge in 13 streams have a preponderance of negative slopes with only two streams having significant positive slopes. An ANOVA decomposition suggests the effect of discharge on Ca concentration is large but variable. Vegetation cover, which incorporates aspects of land use, explains the largest proportion of the variance in the effect of discharge on Ca followed by season and year. In contrast, stream order, land use, and soil class explain most of the variation in stream Ca concentration. In the current data set, soil class, which is related to lithology, has an important effect on Ca concentration but land use, likely through its effect on runoff concentration and hydrology, has a greater effect on discharge-concentration relationships.

Non-linear boundary element formulation with tangent operator to analyse crack propagation in quasi-brittle materials

This work deals with analysis of cracked structures using BEM. Two formulations to analyse the crack growth process in quasi-brittle materials are discussed. They are based on the dual formulation of BEM where two different integral equations are employed along the opposite sides of the crack surface. The first presented formulation uses the concept of constant operator, in which the corrections of the nonlinear process are made only by applying appropriate tractions along the crack surfaces. The second presented BEM formulation to analyse crack growth problems is an implicit technique based on the use of a consistent tangent operator. This formulation is accurate, stable and always requires much less iterations to reach the equilibrium within a given load increment in comparison with the classical approach. Comparison examples of classical problem of crack growth are shown to illustrate the performance of the two formulations. (C) 2009 Elsevier Ltd. All rights reserved.

PERFORMANCE OF THE MODEL CALLED ACQUANETXL IN THE ALLOCATION OF WATER IN COMPLEX WATER RESOURCE SYSTEMS

This article presents a tool for the allocation analysis of complex systems of water resources, called AcquaNetXL, developed in the form of spreadsheet in which a model of linear optimization and another nonlinear were incorporated. The AcquaNetXL keeps the concepts and attributes of a decision support system. In other words, it straightens out the communication between the user and the computer, facilitates the understanding and the formulation of the problem, the interpretation of the results and it also gives a support in the process of decision making, turning it into a clear and organized process. The performance of the algorithms used for solving the problems of water allocation was satisfactory especially for the linear model.

Bias-corrected Pearson estimating functions for Taylor`s power law applied to benthic macrofauna data

Estimation of Taylor`s power law for species abundance data may be performed by linear regression of the log empirical variances on the log means, but this method suffers from a problem of bias for sparse data. We show that the bias may be reduced by using a bias-corrected Pearson estimating function. Furthermore, we investigate a more general regression model allowing for site-specific covariates. This method may be efficiently implemented using a Newton scoring algorithm, with standard errors calculated from the inverse Godambe information matrix. The method is applied to a set of biomass data for benthic macrofauna from two Danish estuaries. (C) 2011 Elsevier B.V. All rights reserved.

Model-Predicted Performance of Second-Trimester Down Syndrome Screening With Sonographic Prenasal Thickness

Objective. The purpose of this study was to estimate the Down syndrome detection and false-positive rates for second-trimester sonographic prenasal thickness (PT) measurement alone and in combination with other markers. Methods. Multivariate log Gaussian modeling was performed using numerical integration. Parameters for the PT distribution, in multiples of the normal gestation-specific median (MoM), were derived from 105 Down syndrome and 1385 unaffected pregnancies scanned at 14 to 27 weeks. The data included a new series of 25 cases and 535 controls combined with 4 previously published series. The means were estimated by the median and the SDs by the 10th to 90th range divided by 2.563. Parameters for other markers were obtained from the literature. Results. A log Gaussian model fitted the distribution of PT values well in Down syndrome and unaffected pregnancies. The distribution parameters were as follows: Down syndrome, mean, 1.334 MoM; log(10) SD, 0.0772; unaffected pregnancies, 0.995 and 0.0752, respectively. The model-predicted detection rates for 1%, 3%, and 5% false-positive rates for PT alone were 35%, 51%, and 60%, respectively. The addition of PT to a 4 serum marker protocol increased detection by 14% to 18% compared with serum alone. The simultaneous sonographic measurement of PT and nasal bone length increased detection by 19% to 26%, and with a third sonographic marker, nuchal skin fold, performance was comparable with first-trimester protocols. Conclusions. Second-trimester screening with sonographic PT and serum markers is predicted to have a high detection rate, and further sonographic markers could perform comparably with first-trimester screening protocols.

COMPARISON BETWEEN LINEAR AND DAILY UNDULATING PERIODIZED RESISTANCE TRAINING TO INCREASE STRENGTH

Prestes, J, Frollini, AB, De Lima, C, Donatto, FF, Foschini, D, de Marqueti, RC, Figueira Jr, A, and Fleck, SJ. Comparison between linear and daily undulating periodized resistance training to increase strength. J Strength Cond Res 23(9): 2437-2442, 2009-To determine the most effective periodization model for strength and hypertrophy is an important step for strength and conditioning professionals. The aim of this study was to compare the effects of linear (LP) and daily undulating periodized (DUP) resistance training on body composition and maximal strength levels. Forty men aged 21.5 +/- 8.3 and with a minimum 1-year strength training experience were assigned to an LP (n = 20) or DUP group (n = 20). Subjects were tested for maximal strength in bench press, leg press 45 degrees, and arm curl (1 repetition maximum [RM]) at baseline (T1), after 8 weeks (T2), and after 12 weeks of training (T3). Increases of 18.2 and 25.08% in bench press 1 RM were observed for LP and DUP groups in T3 compared with T1, respectively (p <= 0.05). In leg press 45 degrees, LP group exhibited an increase of 24.71% and DUP of 40.61% at T3 compared with T1. Additionally, DUP showed an increase of 12.23% at T2 compared with T1 and 25.48% at T3 compared with T2. For the arm curl exercise, LP group increased 14.15% and DUP 23.53% at T3 when compared with T1. An increase of 20% was also found at T2 when compared with T1, for DUP. Although the DUP group increased strength the most in all exercises, no statistical differences were found between groups. In conclusion, undulating periodized strength training induced higher increases in maximal strength than the linear model in strength-trained men. For maximizing strength increases, daily intensity and volume variations were more effective than weekly variations.

Transformed generalized linear models

The estimation of data transformation is very useful to yield response variables satisfying closely a normal linear model, Generalized linear models enable the fitting of models to a wide range of data types. These models are based on exponential dispersion models. We propose a new class of transformed generalized linear models to extend the Box and Cox models and the generalized linear models. We use the generalized linear model framework to fit these models and discuss maximum likelihood estimation and inference. We give a simple formula to estimate the parameter that index the transformation of the response variable for a subclass of models. We also give a simple formula to estimate the rth moment of the original dependent variable. We explore the possibility of using these models to time series data to extend the generalized autoregressive moving average models discussed by Benjamin er al. [Generalized autoregressive moving average models. J. Amer. Statist. Assoc. 98, 214-223]. The usefulness of these models is illustrated in a Simulation study and in applications to three real data sets. (C) 2009 Elsevier B.V. All rights reserved.