Modeling of average growth curve in Santa Ines sheep using random regression models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Comparação de modelos de regressão aleatória para estimação de parâmetros genéticos em caprinos leiteiros

Objetivou-se avaliar a melhor modelagem para as variâncias genética aditiva, de ambiente permanente e residual da produção de leite no dia do controle (PLDC) de caprinos. Utilizaram-se modelos de regressão aleatória sobre polinômios ortogonais de Legendre com diferentes ordens de ajuste e variância residual heterogênea. Consideraram-se como efeitos fixos os efeitos de grupo de contemporâneos, a idade da cabra ao parto (co-variável) e a regressão fixa da PLDC sobre polinômios de Legendre, para modelar a trajetória média da população; e, como efeitos aleatórios, os efeitos genético aditivo e de ambiente permanente. O modelo com quatro classes de variâncias residuais foi o que proporcionou melhor ajuste. Os valores do logaritmo da função de verossimilhança, de AIC e BIC apontaram para seleção de modelos com ordens mais altas (cinco para o efeito genético e sete para o efeito de ambiente permanente). Entretanto, os autovalores associados às matrizes de co-variâncias entre os coeficientes de regressão indicaram a possibilidade de redução da dimensionalidade. As altas ordens de ajuste proporcionaram estimativas de variâncias genéticas e correlações genéticas e de ambiente permanente que não condizem com o fenômeno biológico estudado. O modelo de quinta ordem para a variância genética aditiva e de sétima ordem para o ambiente permanente foi indicado. Entretanto, um modelo mais parcimonioso, de quarta ordem para o efeito genético aditivo e de sexta ordem para o efeito de ambiente permanente, foi suficiente para ajustar as variâncias nos dados.

Modelos de regressão aleatória com diferentes estruturas de variância residual para descrever o tamanho da leitegada

Objetivou-se comparar modelos de regressão aleatória com diferentes estruturas de variância residual, a fim de se buscar a melhor modelagem para a característica tamanho da leitegada ao nascer (TLN). Utilizaram-se 1.701 registros de TLN, que foram analisados por meio de modelo animal, unicaracterística, de regressão aleatória. As regressões fixa e aleatórias foram representadas por funções contínuas sobre a ordem de parto, ajustadas por polinômios ortogonais de Legendre de ordem 3. Para averiguar a melhor modelagem para a variância residual, considerou-se a heterogeneidade de variância por meio de 1 a 7 classes de variância residual. O modelo geral de análise incluiu grupo de contemporâneo como efeito fixo; os coeficientes de regressão fixa para modelar a trajetória média da população; os coeficientes de regressão aleatória do efeito genético aditivo-direto, do comum-de-leitegada e do de ambiente permanente de animal; e o efeito aleatório residual. O teste da razão de verossimilhança, o critério de informação de Akaike e o critério de informação bayesiano de Schwarz apontaram o modelo que considerou homogeneidade de variância como o que proporcionou melhor ajuste aos dados utilizados. As herdabilidades obtidas foram próximas a zero (0,002 a 0,006). O efeito de ambiente permanente foi crescente da 1ª (0,06) à 5ª (0,28) ordem, mas decrescente desse ponto até a 7ª ordem (0,18). O comum-de-leitegada apresentou valores baixos (0,01 a 0,02). A utilização de homogeneidade de variância residual foi mais adequada para modelar as variâncias associadas à característica tamanho da leitegada ao nascer nesse conjunto de dado.

Persistência da lactação e Influência da estrutura de dados sobre a estimação de parâmetros genéticos para a produção de leite de bovinos da raça Holandesa

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Comparison of Multivariate and Univariate Models for Genetic Evaluation of Milk Yield based on Test Day Data

2000 Mathematics Subject Classification: 62H12, 62P99

Fixed and random effects in Classical and Bayesian regression

This paper proposes a common and tractable framework for analyzingdifferent definitions of fixed and random effects in a contant-slopevariable-intercept model. It is shown that, regardless of whethereffects (i) are treated as parameters or as an error term, (ii) areestimated in different stages of a hierarchical model, or whether (iii)correlation between effects and regressors is allowed, when the sameinformation on effects is introduced into all estimation methods, theresulting slope estimator is also the same across methods. If differentmethods produce different results, it is ultimately because differentinformation is being used for each methods.

Measuring fixed costs for firms' use of a free trade agreement : threshold regression approach

In this paper, by employing the threshold regression method, we estimate the average tariff equivalent of fixed costs for the use of a free trade agreement (FTA) among all existing FTAs in the world. It is estimated to be 3.2%. This global estimate serves as a reference rate in the evaluation of each FTA’s fixed costs.

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.

Multi-trait and random regression mature weight heritability and breeding value estimates in Nelore cattle

Mature weight breeding values were estimated using a multi-trait animal model (MM) and a random regression animal model (RRM). Data consisted of 82 064 weight records from 8 145 animals, recorded from birth to eight years of age. Weights at standard ages were considered in the MM. All models included contemporary groups as fixed effects, and age of dam (linear and quadratic effects) and animal age as covariates. In the RRM, mean trends were modelled through a cubic regression on orthogonal polynomials of animal age and genetic maternal and direct and maternal permanent environmental effects were also included as random. Legendre polynomials of orders 4, 3, 6 and 3 were used for animal and maternal genetic and permanent environmental effects, respectively, considering five classes of residual variances. Mature weight (five years) direct heritability estimates were 0.35 (MM) and 0.38 (RRM). Rank correlation between sires' breeding values estimated by MM and RRM was 0.82. However, selecting the top 2% (12) or 10% (62) of the young sires based on the MM predicted breeding values, respectively 71% and 80% of the same sires would be selected if RRM estimates were used instead. The RRM modelled the changes in the (co) variances with age adequately and larger breeding value accuracies can be expected using this model.

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models

The objective of the present study was to estimate milk yield genetic parameters applying random regression models and parametric correlation functions combined with a variance function to model animal permanent environmental effects. A total of 152,145 test-day milk yields from 7,317 first lactations of Holstein cows belonging to herds located in the southeastern region of Brazil were analyzed. Test-day milk yields were divided into 44 weekly classes of days in milk. Contemporary groups were defined by herd-test-day comprising a total of 2,539 classes. The model included direct additive genetic, permanent environmental, and residual random effects. The following fixed effects were considered: contemporary group, age of cow at calving (linear and quadratic regressions), and the population average lactation curve modeled by fourth-order orthogonal Legendre polynomial. Additive genetic effects were modeled by random regression on orthogonal Legendre polynomials of days in milk, whereas permanent environmental effects were estimated using a stationary or nonstationary parametric correlation function combined with a variance function of different orders. The structure of residual variances was modeled using a step function containing 6 variance classes. The genetic parameter estimates obtained with the model using a stationary correlation function associated with a variance function to model permanent environmental effects were similar to those obtained with models employing orthogonal Legendre polynomials for the same effect. A model using a sixth-order polynomial for additive effects and a stationary parametric correlation function associated with a seventh-order variance function to model permanent environmental effects would be sufficient for data fitting.

Random regression models to estimate test-day milk yield genetic parameters Holstein cows in Southeastern Brazil

A total of 152,145 weekly test-day milk yield records from 7317 first lactations of Holstein cows distributed in 93 herds in southeastern Brazil were analyzed. Test-day milk yields were classified into 44 weekly classes of DIM. The contemporary groups were defined as herd-year-week of test-day. The model included direct additive genetic, permanent environmental and residual effects as random and fixed effects of contemporary group and age of cow at calving as covariable, linear and quadratic effects. Mean trends were modeled by a cubic regression on orthogonal polynomials of DIM. Additive genetic and permanent environmental random effects were estimated by random regression on orthogonal Legendre polynomials. Residual variances were modeled using third to seventh-order variance functions or a step function with 1, 6,13,17 and 44 variance classes. Results from Akaike`s and Schwarz`s Bayesian information criterion suggested that a model considering a 7th-order Legendre polynomial for additive effect, a 12th-order polynomial for permanent environment effect and a step function with 6 classes for residual variances, fitted best. However, a parsimonious model, with a 6th-order Legendre polynomial for additive effects and a 7th-order polynomial for permanent environmental effects, yielded very similar genetic parameter estimates. (C) 2008 Elsevier B.V. All rights reserved.

Multicollinearity and financial constraint in investment decisions: a Bayesian generalized ridge regression

This paper addresses the investment decisions considering the presence of financial constraints of 373 large Brazilian firms from 1997 to 2004, using panel data. A Bayesian econometric model was used considering ridge regression for multicollinearity problems among the variables in the model. Prior distributions are assumed for the parameters, classifying the model into random or fixed effects. We used a Bayesian approach to estimate the parameters, considering normal and Student t distributions for the error and assumed that the initial values for the lagged dependent variable are not fixed, but generated by a random process. The recursive predictive density criterion was used for model comparisons. Twenty models were tested and the results indicated that multicollinearity does influence the value of the estimated parameters. Controlling for capital intensity, financial constraints are found to be more important for capital-intensive firms, probably due to their lower profitability indexes, higher fixed costs and higher degree of property diversification.

Weighted Kernel regression

In the fixed design regression model, additional weights areconsidered for the Nadaraya--Watson and Gasser--M\"uller kernel estimators.We study their asymptotic behavior and the relationships between new andclassical estimators. For a simple family of weights, and considering theIMSE as global loss criterion, we show some possible theoretical advantages.An empirical study illustrates the performance of the weighted estimatorsin finite samples.

Test of four colon cancer risk-scores in formalin fixed paraffin embedded microarray gene expression data.

BACKGROUND: Prognosis prediction for resected primary colon cancer is based on the T-stage Node Metastasis (TNM) staging system. We investigated if four well-documented gene expression risk scores can improve patient stratification. METHODS: Microarray-based versions of risk-scores were applied to a large independent cohort of 688 stage II/III tumors from the PETACC-3 trial. Prognostic value for relapse-free survival (RFS), survival after relapse (SAR), and overall survival (OS) was assessed by regression analysis. To assess improvement over a reference, prognostic model was assessed with the area under curve (AUC) of receiver operating characteristic (ROC) curves. All statistical tests were two-sided, except the AUC increase. RESULTS: All four risk scores (RSs) showed a statistically significant association (single-test, P < .0167) with OS or RFS in univariate models, but with HRs below 1.38 per interquartile range. Three scores were predictors of shorter RFS, one of shorter SAR. Each RS could only marginally improve an RFS or OS model with the known factors T-stage, N-stage, and microsatellite instability (MSI) status (AUC gains < 0.025 units). The pairwise interscore discordance was never high (maximal Spearman correlation = 0.563) A combined score showed a trend to higher prognostic value and higher AUC increase for OS (HR = 1.74, 95% confidence interval [CI] = 1.44 to 2.10, P < .001, AUC from 0.6918 to 0.7321) and RFS (HR = 1.56, 95% CI = 1.33 to 1.84, P < .001, AUC from 0.6723 to 0.6945) than any single score. CONCLUSIONS: The four tested gene expression-based risk scores provide prognostic information but contribute only marginally to improving models based on established risk factors. A combination of the risk scores might provide more robust information. Predictors of RFS and SAR might need to be different.

Routine delivery of artemisinin-based combination treatment at fixed health facilities reduces malaria prevalence in Tanzania: an observational study.

BACKGROUND: Artemisinin-based combination therapy (ACT) has been promoted as a means to reduce malaria transmission due to their ability to kill both asexual blood stages of malaria parasites, which sustain infections over long periods and the immature derived sexual stages responsible for infecting mosquitoes and onward transmission. Early studies reported a temporal association between ACT introduction and reduced malaria transmission in a number of ecological settings. However, these reports have come from areas with low to moderate malaria transmission, been confounded by the presence of other interventions or environmental changes that may have reduced malaria transmission, and have not included a comparison group without ACT. This report presents results from the first large-scale observational study to assess the impact of case management with ACT on population-level measures of malaria endemicity in an area with intense transmission where the benefits of effective infection clearance might be compromised by frequent and repeated re-infection. METHODS: A pre-post observational study with a non-randomized comparison group was conducted at two sites in Tanzania. Both sites used sulphadoxine-pyrimethamine (SP) monotherapy as a first-line anti-malarial from mid-2001 through 2002. In 2003, the ACT, artesunate (AS) co-administered with SP (AS + SP), was introduced in all fixed health facilities in the intervention site, including both public and registered non-governmental facilities. Population-level prevalence of Plasmodium falciparum asexual parasitaemia and gametocytaemia were assessed using light microscopy from samples collected during representative household surveys in 2001, 2002, 2004, 2005 and 2006. FINDINGS: Among 37,309 observations included in the analysis, annual asexual parasitaemia prevalence in persons of all ages ranged from 11% to 28% and gametocytaemia prevalence ranged from <1% to 2% between the two sites and across the five survey years. A multivariable logistic regression model was fitted to adjust for age, socioeconomic status, bed net use and rainfall. In the presence of consistently high coverage and efficacy of SP monotherapy and AS + SP in the comparison and intervention areas, the introduction of ACT in the intervention site was associated with a modest reduction in the adjusted asexual parasitaemia prevalence of 5 percentage-points or 23% (p < 0.0001) relative to the comparison site. Gametocytaemia prevalence did not differ significantly (p = 0.30). INTERPRETATION: The introduction of ACT at fixed health facilities only modestly reduced asexual parasitaemia prevalence. ACT is effective for treatment of uncomplicated malaria and should have substantial public health impact on morbidity and mortality, but is unlikely to reduce malaria transmission substantially in much of sub-Saharan Africa where individuals are rapidly re-infected.