Estimação clássica e Bayesiana em modelos de sobrevida com fração de cura

In Survival Analysis, long duration models allow for the estimation of the healing fraction, which represents a portion of the population immune to the event of interest. Here we address classical and Bayesian estimation based on mixture models and promotion time models, using different distributions (exponential, Weibull and Pareto) to model failure time. The database used to illustrate the implementations is described in Kersey et al. (1987) and it consists of a group of leukemia patients who underwent a certain type of transplant. The specific implementations used were numeric optimization by BFGS as implemented in R (base::optim), Laplace approximation (own implementation) and Gibbs sampling as implemented in Winbugs. We describe the main features of the models used, the estimation methods and the computational aspects. We also discuss how different prior information can affect the Bayesian estimates

Estudo de simulação de modelos lineares mistos com distribuição normal contaminada no melhoramento genético animal

Objetivou-se com esse trabalho comparar estimativas de componentes de variâncias obtidas por meio de modelos lineares mistos Gaussianos e Robustos, via Amostrador de Gibbs, em dados simulados. Foram simulados 50 arquivos de dados com 1.000 animais cada um, distribuídos em cinco gerações, em dois níveis de efeito fixo e três valores fenotípicos distintos para uma característica hipotética, com diferentes níveis de contaminação. Exceto para os dados sem contaminação, quando os modelos foram iguais, o modelo Robusto apresentou melhores estimativas da variância residual. As estimativas de herdabilidade foram semelhantes em todos os modelos, mas as análises de regressão mostraram que os valores genéticos preditos com uso do modelo Robusto foram mais próximos dos valores genéticos verdadeiros. Esses resultados sugerem que o modelo linear normal contaminado oferece uma alternativa flexível para estimação robusta em melhoramento genético animal.

Inferência bayesiana aplicada à estimação de herdabilidades dos parâmetros da curva de crescimento de fêmeas da raça Nelore

Objetivou-se estimar parâmetros genéticos, utilizando inferência Bayesiana, para as estimativas dos parâmetros individuais de peso à maturidade (Â) e taxa de crescimento, obtidos pela função de crescimento Brody. O arquivo estava constituído de 14.563 registros de pesos e idades referentes a 1.158 fêmeas da raça Nelore, participantes do Programa de Melhoramento Genético da Raça Nelore. Para a análise das estimativas dos parâmetros da curva, via inferência bayesiana, foi proposto um modelo animal unicaráter, que incluiu como fixo o efeito de grupo contemporâneo (animais nascidos no mesmo estado, no mesmo trimestre do ano, mesmo ano e mesmo regime alimentar) e como aleatórios os efeitos genético direto e residual. Nessa análise, foram utilizados dois diferentes tamanhos para as cadeias geradas pelo algoritmo de amostragem de Gibbs, de 550 e 1.100 mil ciclos, com períodos de descarte amostral de 50 e 100 mil ciclos, respectivamente, e amostragens a cada 500 e 1.000 ciclos, respectivamente. As médias posteriores da variância genética aditiva e residual foram próximas, tanto para  quanto para a, mesmo quando implementados diferentes tamanhos para as cadeias geradas pelo algoritmo de amostragem de Gibbs. Os coeficientes de herdabilidade estimados para Â, variaram de 0,44 a 0,46, amplitude semelhante aos 0,46 a 0,48 obtidos para as estimativas de. Essas magnitudes indicam que a seleção pode ser usada como instrumento para alterar a forma da curva de crescimento desses animais. Entretanto, o uso das informações obtidas, visando à alteração da curva de crescimento dos animais, deve ser feito com grande cautela, uma vez que as características a serem trabalhadas na modificação do formato da curva de crescimento, de acordo com resultados da literatura especializada, são negativamente correlacionadas.

Genetic characterization of egg weight, egg production and age at first egg in quails

O objetivo neste estudo foi obter estimativas de parâmetros genéticos para as características peso do ovo, produção de ovos em 189 dias de postura e dia do primeiro ovo em codornas de três linhagens de postura e uma de corte. Os dados foram analisados por meio de procedimentos bayesianos usando amostragem de Gibbs. As estimativas de herdabilidade para peso do ovo, produção de ovos em 189 dias de postura e dia do primeiro ovo foram, respectivamente, para a linhagem amarela, 0,31; 0,84 e 0,53; azul, 0,14; 0,82 e 0,60; vermelha, 0,70; 0,96 e 0,75; e de corte, 0,73; 0,96 e 0,72. As correlações genéticas entre peso do ovo e produção de ovos em 189 dias de postura, peso do ovo e dia do primeiro ovo e, produção de ovos em 189 dias de postura e dia do primeiro ovo foram, para amarela, 0,58; -0,77; e -0,90; azul, 0,09; -0,01; e -0,95; vermelha, 0,09; 0,03; e -0,76; e de corte, -0,18; 0,19 e -0,91. A partir das probabilidades de superposição das distribuições posteriories dos parâmetros, as linhagens dividem-se em dois grupos distintos: um com as linhagens amarela e azul e outro com as linhagens vermelha e de corte.

Analysis of beef cattle longitudinal data applying a nonlinear model

The objective of this work was to evaluate the Nelore beef cattle, growth curve parameters using the Von Bertalanffy function in a nested Bayesian procedure that allowed estimation of the joint posterior distribution of growth curve parameters, their (co)variance components, and the environmental and additive genetic components affecting them. A hierarchical model was applied; each individual had a growth trajectory described by the nonlinear function, and each parameter of this function was considered to be affected by genetic and environmental effects that were described by an animal model. Random samples of the posterior distributions were drawn using Gibbs sampling and Metropolis-Hastings algorithms. The data set consisted of a total of 145,961 BW recorded from 15,386 animals. Even though the curve parameters were estimated for animals with few records, given that the information from related animals and the structure of systematic effects were considered in the curve fitting, all mature BW predicted were suitable. A large additive genetic variance for mature BW was observed. The parameter a of growth curves, which represents asymptotic adult BW, could be used as a selection criterion to control increases in adult BW when selecting for growth rate. The effect of maternal environment on growth was carried through to maturity and should be considered when evaluating adult BW. Other growth curve parameters showed small additive genetic and maternal effects. Mature BW and parameter k, related to the slope of the curve, presented a large, positive genetic correlation. The results indicated that selection for growth rate would increase adult BW without substantially changing the shape of the growth curve. Selection to change the slope of the growth curve without modifying adult BW would be inefficient because their genetic correlation is large. However, adult BW could be considered in a selection index with its corresponding economic weight to improve the overall efficiency of beef cattle production.

Genetic evaluation of performance traits in Brazilian Quarter Horse

The aim of this study was to estimate genetic parameters for racing performance traits in Quarter Horses in Brazil. The data (provided by the Sorocaba Jockey Club) came from 3 Brazilian hippodromes in 1994-2003, with 11875 observations of race time and 7775 of the speed index (Sl), distributed in 2403 and 2169 races, respectively. The variance components were estimated by the MTGSAM program, under animal models including the random additive genetic effect, random permanent environmental effect, and the fixed effects of sex, age and race. Heritabilities for race time and the SI, for the 3 distances studied (301, 365 and 402 in), varied from 0.26 to 0.41 and from 0. 14 to 0. 19, respectively, whereas repeatabilities varied from 0.36 to 0.68 (time) and from 0.27 to 0.42 (SI) and the genetic correlations from 0.90 to 0.97 (time) and from 0.67 to 0.73 (SI).

Robust linear mixed models with normal/independent distributions and Bayesian MCMC implementation

Linear mixed effects models have been widely used in analysis of data where responses are clustered around some random effects, so it is not reasonable to assume independence between observations in the same cluster. In most biological applications, it is assumed that the distributions of the random effects and of the residuals are Gaussian. This makes inferences vulnerable to the presence of outliers. Here, linear mixed effects models with normal/independent residual distributions for robust inferences are described. Specific distributions examined include univariate and multivariate versions of the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted and Markov chain Monte Carlo is used to carry out the posterior analysis. The procedures are illustrated using birth weight data on rats in a texicological experiment. Results from the Gaussian and robust models are contrasted, and it is shown how the implementation can be used for outlier detection. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process in linear mixed models, and they are easily implemented using data augmentation and MCMC techniques.

Correlações entre deslocamento e conformação em eqüinos Mangalarga

The aim of this study was estimate genetic, environmental and phenotypic correlations between movement and conformation traits in Mangalarga horses, in Brazil. The data were provided by Brazilian Association of Mangalarga Horses Breeders, comprised 9865 observations for movement and conformation traits. The data were organized by SAS, and the (co)variance components were estimated by the program MTGSAM. The heritabilities estimates varied from 0.22 (shoulder) to 0.29 (limbs), and the genetic correlations ranged from 0.51 (movement and neck) to 0.31 (movement and limbs).

Inferência bayesiana na predição de valores genéticos do peso aos 365 dias de bovinos de corte

Data from purebred Simmental, Nellore and Canchim cattle breeds obtained from the respective Brazilian Associations of Breeders were used to estimate variance components and to predict genetic values for 365 days weight. The results obtained by Bayesian inference were compared to those from Restricted Maximum Likelihood (REML) and Best Linear Unbiased Prediction (BLUP), which are the most commonly used methods of estimation and prediction in animal breeding. The two methods presented similar point estimates but the study of the marginal posterior distributions in the Bayesian approach yields more detailed information about the parameters and other unknowns in the model.

Genetic variability for temperament indicators of Nellore cattle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Multiple-trait random regression models for the estimation of genetic parameters for milk, fat, and protein yield in buffaloes

In this study, genetic parameters for test-day milk, fat, and protein yield were estimated for the first lactation. The data analyzed consisted of 1,433 first lactations of Murrah buffaloes, daughters of 113 sires from 12 herds in the state of São Paulo, Brazil, with calvings from 1985 to 2007. Ten-month classes of lactation days were considered for the test-day yields. The (co)variance components for the 3 traits were estimated using the regression analyses by Bayesian inference applying an animal model by Gibbs sampling. The contemporary groups were defined as herd-year-month of the test day. In the model, the random effects were additive genetic, permanent environment, and residual. The fixed effects were contemporary group and number of milkings (1 or 2), the linear and quadratic effects of the covariable age of the buffalo at calving, as well as the mean lactation curve of the population, which was modeled by orthogonal Legendre polynomials of fourth order. The random effects for the traits studied were modeled by Legendre polynomials of third and fourth order for additive genetic and permanent environment, respectively, the residual variances were modeled considering 4 residual classes. The heritability estimates for the traits were moderate (from 0.21-0.38), with higher estimates in the intermediate lactation phase. The genetic correlation estimates within and among the traits varied from 0.05 to 0.99. The results indicate that the selection for any trait test day will result in an indirect genetic gain for milk, fat, and protein yield in all periods of the lactation curve. The accuracy associated with estimated breeding values obtained using multi-trait random regression was slightly higher (around 8%) compared with single-trait random regression. This difference may be because to the greater amount of information available per animal. © 2013 American Dairy Science Association.

Genetic parameters for scrotal circumference, breeding soundness examination and sperm defects in young Nellore bulls

A total of 51,161 records of scrotal circumference measurements at 18 mo of age (SCI 8) and 17,648 records of sperm defects and breeding soundness of Nellore bulls (mean age of 22.5 mo), raised under extensive conditions, were analyzed to estimate coefficients of heritability and genetic correlations of morphological semen traits by Bayesian inference. The observed semen traits were classified as minor (MID). major (MAD), and total sperm defects (TD). The animals were classified according to breeding soundness as satisfactory and unsatisfactory potential breeders. The (co)variance components and breeding values were estimated by Gibbs sampling using the GIBBS2F90 program under an animal model that included contemporary group as fixed effect, age of animal as linear covariate, and direct additive genetic effects as random effects. Heritabilities of 0.40 ± 0.02, 0.16 ± 0.02, 0.04 ± 0.01, 0.15 ± 0.01, and 0.10 ± 0.01 were obtained for SCI8, MID, MAD, TD, and breeding soundness, respectively. The SC18 showed a positive and moderate correlation with breeding soundness (0.56 ± 0.04) and a negative and low correlation with MID (-0.23 ± 0.03), MAD (-0.16 ± 0.02), and TD (-0.24 ± 0.02). In conclusion, scrotal circumference showed the best response to selection among the traits studied and was favorably correlated with breeding soundness and sperm morphology in young Nellore bulls. © 2013 American Society of Animal Science. All rights reserved.

Parâmetros genéticos para rentabilidade monetária em cavalos de corrida da raça Quarto de Milha

Pós-graduação em Genética e Melhoramento Animal - FCAV

Análise bayesiana do modelo fatorial dinâmico para um vetor de séries temporais utilizando a distribuição t multivariada

The multivariate t models are symmetric and with heavier tail than the normal distribution, important feature in financial data. In this theses is presented the Bayesian estimation of a dynamic factor model, where the factors follow a multivariate autoregressive model, using multivariate t distribution. Since the multivariate t distribution is complex, it was represented in this work as a mix between a multivariate normal distribution and a square root of a chi-square distribution. This method allowed to define the posteriors. The inference on the parameters was made taking a sample of the posterior distribution, through the Gibbs Sampler. The convergence was verified through graphical analysis and the convergence tests Geweke (1992) and Raftery & Lewis (1992a). The method was applied in simulated data and in the indexes of the major stock exchanges in the world.

Métodos para avaliação do temperamento de bovinos: estimação de parâmetros genéticos e relações com o desempenho

Pós-graduação em Genética e Melhoramento Animal - FCAV