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.

Random regression analyses using B-splines functions to model growth from birth to adult age in Canchim cattle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Random regression analyses using B-spline functions to model growth of Nellore cattle

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.

Random regression models using different functions to model test-day milk yield of Brazilian Holstein cows

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

Random regression analyses using B-spline functions to model growth of Nellore cattle

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.

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.

Residuals for log-Burr XII regression models in survival analysis

In this paper, we compare three residuals to assess departures from the error assumptions as well as to detect outlying observations in log-Burr XII regression models with censored observations. These residuals can also be used for the log-logistic regression model, which is a special case of the log-Burr XII regression model. 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. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended to the modified martingale-type residual in log-Burr XII regression models with censored data.

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.

Regression models for grouped survival data: Estimation and sensitivity analysis

In this study, regression models are evaluated for grouped survival data when the effect of censoring time is considered in the model and the regression structure is modeled through four link functions. The methodology for grouped survival data is based on life tables, and the times are grouped in k intervals so that ties are eliminated. Thus, the data modeling is performed by considering the discrete models of lifetime regression. The model parameters are estimated by using the maximum likelihood and jackknife methods. To detect influential observations in the proposed models, diagnostic measures based on case deletion, which are denominated global influence, and influence measures based on small perturbations in the data or in the model, referred to as local influence, are used. In addition to those measures, the local influence and the total influential estimate are also employed. Various simulation studies are performed and compared to the performance of the four link functions of the regression models for grouped survival data for different parameter settings, sample sizes and numbers of intervals. Finally, a data set is analyzed by using the proposed regression models. (C) 2010 Elsevier B.V. All rights reserved.

A Model for comparing reduced impact logging with conventional logging for an Eastern Amazonian Forest

Using data from a logging experiment in the eastern Brazilian Amazon region, we develop a matrix growth and yield model that captures the dynamic effects of harvest system choice on forest structure and composition. Multinomial logistic regression is used to estimate the growth transition parameters for a 10-year time step, while a Poisson regression model is used to estimate recruitment parameters. The model is designed to be easily integrated with an economic model of decisionmaking to perform tropical forest policy analysis. The model is used to compare the long-run structure and composition of a stand arising from the choice of implementing either conventional logging techniques or more carefully planned and executed reduced-impact logging (RIL) techniques, contrasted against a baseline projection of an unlogged forest. Results from log and leave scenarios show that a stand logged according to Brazilian management requirements will require well over 120 years to recover its initial commercial volume, regardless of logging technique employed. Implementing RIL, however, accelerates this recovery. Scenarios imposing a 40-year cutting cycle raise the possibility of sustainable harvest volumes, although at significantly lower levels than is implied by current regulations. Meeting current Brazilian forest policy goals may require an increase in the planned total area of permanent production forest or the widespread adoption of silvicultural practices that increase stand recovery and volume accumulation rates after RIL harvests. Published by Elsevier B.V.

Models involving two inverse Weibull distributions

In this paper, we look at three models (mixture, competing risk and multiplicative) involving two inverse Weibull distributions. We study the shapes of the density and failure-rate functions and discuss graphical methods to determine if a given data set can be modelled by one of these models. (C) 2001 Elsevier Science Ltd. All rights reserved.

Acute Kidney Injury after Pediatric Cardiac Surgery: Risk Factors and Outcomes. Proposal for a Predictive Model

Objectives: To characterize the epidemiology and risk factors for acute kidney injury (AKI) after pediatric cardiac surgery in our center, to determine its association with poor short-term outcomes, and to develop a logistic regression model that will predict the risk of AKI for the study population. Methods: This single-center, retrospective study included consecutive pediatric patients with congenital heart disease who underwent cardiac surgery between January 2010 and December 2012. Exclusion criteria were a history of renal disease, dialysis or renal transplantation. Results: Of the 325 patients included, median age three years (1 day---18 years), AKI occurred in 40 (12.3%) on the first postoperative day. Overall mortality was 13 (4%), nine of whom were in the AKI group. AKI was significantly associated with length of intensive care unit stay, length of mechanical ventilation and in-hospital death (p<0.01). Patients’ age and postoperative serum creatinine, blood urea nitrogen and lactate levels were included in the logistic regression model as predictor variables. The model accurately predicted AKI in this population, with a maximum combined sensitivity of 82.1% and specificity of 75.4%. Conclusions: AKI is common and is associated with poor short-term outcomes in this setting. Younger age and higher postoperative serum creatinine, blood urea nitrogen and lactate levels were powerful predictors of renal injury in this population. The proposed model could be a useful tool for risk stratification of these patients.

Credit default swap (CDS) prediction model & trading strategy

This project focuses on the study of different explanatory models for the behavior of CDS security, such as Fixed-Effect Model, GLS Random-Effect Model, Pooled OLS and Quantile Regression Model. After determining the best fitness model, trading strategies with long and short positions in CDS have been developed. Due to some specifications of CDS, I conclude that the quantile regression is the most efficient model to estimate the data. The P&L and Sharpe Ratio of the strategy are analyzed using a backtesting analogy, where I conclude that, mainly for non-financial companies, the model allows traders to take advantage of and profit from arbitrages.

Association between LDL-C, Non HDL-C, and Apolipoprotein B Levels with Coronary Plaque Regression

Background:Previous reports have inferred a linear relationship between LDL-C and changes in coronary plaque volume (CPV) measured by intravascular ultrasound. However, these publications included a small number of studies and did not explore other lipid markers.Objective:To assess the association between changes in lipid markers and regression of CPV using published data.Methods:We collected data from the control, placebo and intervention arms in studies that compared the effect of lipidlowering treatments on CPV, and from the placebo and control arms in studies that tested drugs that did not affect lipids. Baseline and final measurements of plaque volume, expressed in mm3, were extracted and the percentage changes after the interventions were calculated. Performing three linear regression analyses, we assessed the relationship between percentage and absolute changes in lipid markers and percentage variations in CPV.Results:Twenty-seven studies were selected. Correlations between percentage changes in LDL-C, non-HDL-C, and apolipoprotein B (ApoB) and percentage changes in CPV were moderate (r = 0.48, r = 0.47, and r = 0.44, respectively). Correlations between absolute differences in LDL-C, non‑HDL-C, and ApoB with percentage differences in CPV were stronger (r = 0.57, r = 0.52, and r = 0.79). The linear regression model showed a statistically significant association between a reduction in lipid markers and regression of plaque volume.Conclusion:A significant association between changes in different atherogenic particles and regression of CPV was observed. The absolute reduction in ApoB showed the strongest correlation with coronary plaque regression.

A priori ratemaking using bivariate poisson regression models

In automobile insurance, it is useful to achieve a priori ratemaking by resorting to gene- ralized linear models, and here the Poisson regression model constitutes the most widely accepted basis. However, insurance companies distinguish between claims with or without bodily injuries, or claims with full or partial liability of the insured driver. This paper exa- mines an a priori ratemaking procedure when including two di®erent types of claim. When assuming independence between claim types, the premium can be obtained by summing the premiums for each type of guarantee and is dependent on the rating factors chosen. If the independence assumption is relaxed, then it is unclear as to how the tari® system might be a®ected. In order to answer this question, bivariate Poisson regression models, suitable for paired count data exhibiting correlation, are introduced. It is shown that the usual independence assumption is unrealistic here. These models are applied to an automobile insurance claims database containing 80,994 contracts belonging to a Spanish insurance company. Finally, the consequences for pure and loaded premiums when the independence assumption is relaxed by using a bivariate Poisson regression model are analysed.