Short communication: Principal components and factor analytic models for test-day milk yield in Brazilian Holstein cattle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Genetic and environmental heterogeneity of residual variance of weight traits in Nellore beef cattle

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

Short communication: Principal components and factor analytic models for test-day milk yield in Brazilian Holstein cattle

A total of 46,089 individual monthly test-day (TD) milk yields (10 test-days), from 7,331 complete first lactations of Holstein cattle were analyzed. A standard multivariate analysis (MV), reduced rank analyses fitting the first 2, 3, and 4 genetic principal components (PC2, PC3, PC4), and analyses that fitted a factor analytic structure considering 2, 3, and 4 factors (FAS2, FAS3, FAS4), were carried out. The models included the random animal genetic effect and fixed effects of the contemporary groups (herd-year-month of test-day), age of cow (linear and quadratic effects), and days in milk (linear effect). The residual covariance matrix was assumed to have full rank. Moreover, 2 random regression models were applied. Variance components were estimated by restricted maximum likelihood method. The heritability estimates ranged from 0.11 to 0.24. The genetic correlation estimates between TD obtained with the PC2 model were higher than those obtained with the MV model, especially on adjacent test-days at the end of lactation close to unity. The results indicate that for the data considered in this study, only 2 principal components are required to summarize the bulk of genetic variation among the 10 traits.

Longitudinal familial analysis of blood pressure involving parametric (co)variance functions

Abstract Background For analyzing longitudinal familial data we adopted a log-linear form to incorporate heterogeneity in genetic variance components over the time, and additionally a serial correlation term in the genetic effects at different levels of ages. Due to the availability of multiple measures on the same individual, we permitted environmental correlations that may change across time. Results Systolic blood pressure from family members from the first and second cohort was used in the current analysis. Measures of subjects receiving hypertension treatment were set as censored values and they were corrected. An initial check of the variance and covariance functions proposed for analyzing longitudinal familial data, using empirical semi-variogram plots, indicated that the observed trait dispersion pattern follows the assumptions adopted. Conclusion The corrections for censored phenotypes based on ordinary linear models may be an appropriate simple model to correct the data, ensuring that the original variability in the data was retained. In addition, empirical semi-variogram plots are useful for diagnosis of the (co)variance model adopted.

What are the components that contribute to variability in echocardiographic measurements in aortic stenosis?

INTRODUCTION Echocardiography is the standard clinical approach for quantification of the severity of aortic stenosis (AS). A comprehensive examination of its overall reproducibility and the simultaneous estimation of its variance components by multiple operators, readers, probe applications, and beats have not been undertaken. METHOD AND RESULTS Twenty-seven subjects with AS were scanned over 7 months in the echo-department by a median of 3 different operators. From each patient and each operator multiple runs of beats from multiple probe positions were stored for later analysis by multiple readers. The coefficient of variation was 13.3%, 15.9%, 17.6%, and 20.2% for the aortic peak velocity (Vmax), and velocity time integral (VTI), and left ventricular outflow tract (LVOT) Vmax and VTI respectively. The largest individual contributors to the overall variability were the beat-to-beat variability (9.0%, 9.3%, 9.5%, 9.4% respectively) and that of inability of an individual operator to precisely apply the probe to the same position twice (8.3%, 9.4%, 12.9%, 10.7% respectively). The tracing (inter-reader) and reader (inter-reader), and operator (inter-operator) contribution were less important. CONCLUSIONS Reproducibility of measurements in AS is poorer than often reported in the literature. The source of this variability does not appear, as traditionally believed, to result from a lack of training or operator and reader specific factors. Rather the unavoidable beat-to-beat biological variability, and the inherent impossibility of applying the ultrasound probe in exactly the same position each time are the largest contributors. Consequently, guidelines suggesting greater standardisation of procedures and further training for sonographers are unlikely to result in an improvement in precision. Clinicians themselves should be wary of relying on even three-beat averages as their expected coefficient of variance is 10.3% for the peak velocity at the aortic valve.

MODIFIED TEST STATISTICS BY INTER-VOXEL VARIANCE SHRINKAGE WITH AN APPLICATION TO fMRI

Functional Magnetic Resonance Imaging (fMRI) is a non-invasive technique which is commonly used to quantify changes in blood oxygenation and flow coupled to neuronal activation. One of the primary goals of fMRI studies is to identify localized brain regions where neuronal activation levels vary between groups. Single voxel t-tests have been commonly used to determine whether activation related to the protocol differs across groups. Due to the generally limited number of subjects within each study, accurate estimation of variance at each voxel is difficult. Thus, combining information across voxels in the statistical analysis of fMRI data is desirable in order to improve efficiency. Here we construct a hierarchical model and apply an Empirical Bayes framework on the analysis of group fMRI data, employing techniques used in high throughput genomic studies. The key idea is to shrink residual variances by combining information across voxels, and subsequently to construct an improved test statistic in lieu of the classical t-statistic. This hierarchical model results in a shrinkage of voxel-wise residual sample variances towards a common value. The shrunken estimator for voxelspecific variance components on the group analyses outperforms the classical residual error estimator in terms of mean squared error. Moreover, the shrunken test-statistic decreases false positive rate when testing differences in brain contrast maps across a wide range of simulation studies. This methodology was also applied to experimental data regarding a cognitive activation task.

Variância intrapessoal para ajuste da distribuição de nutrientes em estudos epidemiológicos

O objetivo do estudo foi apresentar a fração da variância intrapessoal para ajuste da distribuição de nutrientes de adultos e idosos. Utilizaram-se dados de inquérito populacional com amostra representativa (n = 511) de indivíduos com 19 anos ou mais do município de São Paulo, SP, em 2007. A fração da variância intrapessoal foi obtida pelo método proposto pela Iowa State University. Observaram-se diferenças nas frações das variâncias intrapessoais de nutrientes segundo sexo. Esses valores devem ser utilizados para ajustar a distribuição da ingestão de nutrientes, pois sua não utilização pode resultar em viés na análise e interpretação de dados.

Evaluating gene by sex and age interactions on cardiovascular risk factors in Brazilian families

Background: In family studies, it is important to evaluate the impact of genes and environmental factors on traits of interest. In particular, the relative influences of both genes and the environment may vary in different strata of the population of interest, such as young and old individuals, or males and females. Methods: In this paper, extensions of the variance components model are used to evaluate heterogeneity in the genetic and environmental variance components due to the effects of sex and age (the cutoff between young and old was 43 yrs). The data analyzed were from 81 Brazilian families (1,675 individuals) of the Baependi Family Heart Study. Results: The models allowing for heterogeneity of variance components by sex suggest that genetic and environmental variances are not different in males and females for diastolic blood pressure, LDL-cholesterol, and HDL-cholesterol, independent of the covariates included in the models. However, for systolic blood pressure, fasting glucose and triglycerides, the evidence for heterogeneity was dependent on the covariates in the model. For instance, in the presence of sex and age covariates, heterogeneity in the genetic variance component was suggested for fasting glucose. But, for systolic blood pressure, there was no evidence of heterogeneity in any of the two variance components. Except for the LDL-cholesterol, models allowing for heterogeneity by age provide evidence of heterogeneity in genetic variance for triglycerides and systolic and diastolic blood pressure. There was evidence of heterogeneity in environmental variance in fasting glucose and HDL-cholesterol. Conclusions: Our results suggest that heterogeneity in trait variances should not be ignored in the design and analyses of gene-finding studies involving these traits, as it may generate additional information about gene effects, and allow the investigation of more sophisticated models such as the model including sex-specific oligogenic variance components.

Genetic parameters for pre-weaning traits in Braunvieh cattle

The objective of this study was to estimate genetic parameters for pre-weaning traits of Braunvieh cattle raised under tropical conditions in Brazil. The weight and weight gain parameters were birth weight (BW, N = 9955), weight at 120 days of age (W120, N = 5901), weaning weight at 205 days (WW, N = 6970), weight gain from birth to 205 days (GAIN205, N = 6013), weight gain from birth to 120 days (GAIN120, N = 5135), and weight gain from 120 to 205 days (GAIN85, N = 4482). Variance components were estimated using the animal model with the MTDFREML software. The relationship matrix included 35,188 animals; phenotypic measures were available for 18,688. Direct and maternal heritability increased from birth to weaning, with estimates of 0.23 +/- 0.037, 0.25 +/- 0.050, 0.41 +/- 0.059 for direct heritability for BW, W120 and WW, respectively, 0.08 +/- 0.012, 0.15 +/- 0.032, 0.22 +/- 0.036 for maternal genetic effects, and 0.18, 0.14 and 0.16 for total heritability estimates. For pre-weaning gains, estimates of heritability were 0.36 +/- 0.059, 0.30 +/- 0.059, 0.12 +/- 0.035 for direct genetic effects of the traits GAIN205, GAIN120 and GAIN85, respectively, 0.23 +/- 0.038, 0.17 +/- 0.037, 0.03 +/- 0.029 for estimates of maternal heritability, and 0.12, 0.13, 0.16 for total heritability, respectively. Genetic correlations between weights were greater between measures taken at shorter intervals. This information can be used to optimize the design of programs for genetic improvement of Braunvieh cattle raised under tropical conditions.

Genetic parameters for productive life traits and reproductive efficiency traits at 6 years in Nellore cattle

The objective of the present study was to estimate (co)variance components for length of productive life (LPL) and some alternative reproductive traits of 6-year-old Nellore cattle. The data set contained 57,410 records for age at first calving from Nellore females and was edited to remove animal records with uncertain paternity and cows with just one piece of calving information. Only animals with age at first calving ranging from 23 to 48 months and calving intervals between 11 and 24 months were kept for analysis. LPL and life production ( LP) were used to describe productive life. LPL was defined as the number of months a cow was kept in the herd until she was 6 years old, given that she was alive at first calving and LP was defined as total number of calves in that time. Four traits were used to describe reproductive traits: two breeding efficiencies on original scale were estimated using Wilcox and Tomar functions (BEW and BET, respectively), and two breeding efficiencies transformed (ASBEW and ASBET, respectively), using the function [arcsine (square root (BEi/100))]. Estimates of heritability for measures of LPL and LP were low and ranged from 0.04 to 0.05. Estimates of heritability for breeding efficiencies on original and transformed scales oscillated from 0.18 to 0.32. Estimates of genetic correlations ranged from -0.57 to 0.79 for LPL and other traits and from 0.28 to 0.63 for LP and other traits.

Additive genetic relationship of longevity with fertility and production traits in Nellore cattle based on bivariate models

Survival or longevity is an economically important trait in beef cattle. The main inconvenience for its inclusion in selection criteria is delayed recording of phenotypic data and the high computational demand for including survival in proportional hazard models. Thus, identification of a longevity-correlated trait that could be recorded early in life would be very useful for selection purposes. We estimated the genetic relationship of survival with productive and reproductive traits in Nellore cattle, including weaning weight (WW), post-weaning growth (PWG), muscularity (MUSC), scrotal circumference at 18 months (SC18), and heifer pregnancy (HP). Survival was measured in discrete time intervals and modeled through a sequential threshold model. Five independent bivariate Bayesian analyses were performed, accounting for cow survival and the five productive and reproductive traits. Posterior mean estimates for heritability (standard deviation in parentheses) were 0.55 (0.01) for WW, 0.25 (0.01) for PWG, 0.23 (0.01) for MUSC, and 0.48 (0.01) for SC18. The posterior mean estimates (95% confidence interval in parentheses) for the genetic correlation with survival were 0.16 (0.13-0.19), 0.30 (0.25-0.34), 0.31 (0.25-0.36), 0.07 (0.02-0.12), and 0.82 (0.78-0.86) for WW, PWG, MUSC, SC18, and HP, respectively. Based on the high genetic correlation and heritability (0.54) posterior mean estimates for HP, the expected progeny difference for HP can be used to select bulls for longevity, as well as for post-weaning gain and muscle score.

Genetic parameters for postweaning traits in Braunvieh cattle

Genetic parameters for traits related to postweaning growth in Braunvieh cattle, reared under tropical and sub-tropical conditions in Brazil, were studied. Weight traits were weight at 365 days of age (W365, N = 4055), at 450 days (W450, N = 3453), and at 550 days (W550, N = 1946), while weight gains were gain from weaning to 365 days of age (WGW365, N = 3060), from weaning to 450 days (WGW450, N = 2764), from weaning to 550 days (WGW550, N = 1531), from 365 to 550 days of age (WG365550, N = 1528), from 365 to 450 days (WG365450, N = 2401), and from 450 to 550 days (WG450550, N = 1563). A full animal model was used for estimating the variance components, using the MTDFREML software. The dataset contained 18,688 animals with phenotypic measures and 35,188 animals in the relationship matrix. Heritability estimates for postweaning weights decreased with age. For W365, W450 and W550, respectively, the direct heritability estimates were 0.29 +/- 0.061, 0.25 +/- 0.057, 0.16 +/- 0.060, maternal heritability was 0.20 +/- 0.035, 0.18 +/- 0.035, 0.13 +/- 0.052, and total heritability was 0.30, 0.35, 0.26. In this breed, maternal influence was found to be important up to 550 days of age. The greater genetic correlations between weights were observed for weights measured at shorter intervals. A large environmental effect was observed for weight gain between weaning and 550 days; this effect was greater for the gains between 365 and 550 days.

Modelling the Distribution of Ischaemic Stroke-Specific Survival Time Using an EM-based Mixture Approach with Random Effects Adjustment

A two-component survival mixture model is proposed to analyse a set of ischaemic stroke-specific mortality data. The survival experience of stroke patients after index stroke may be described by a subpopulation of patients in the acute condition and another subpopulation of patients in the chronic phase. To adjust for the inherent correlation of observations due to random hospital effects, a mixture model of two survival functions with random effects is formulated. Assuming a Weibull hazard in both components, an EM algorithm is developed for the estimation of fixed effect parameters and variance components. A simulation study is conducted to assess the performance of the two-component survival mixture model estimators. Simulation results confirm the applicability of the proposed model in a small sample setting. Copyright (C) 2004 John Wiley Sons, Ltd.

Comparison of different nonlinear functions to describe Nelore cattle growth

This work aims to compare different nonlinear functions for describing the growth curves of Nelore females. The growth curve parameters, their (co) variance components, and environmental and genetic effects were estimated jointly through a Bayesian hierarchical model. In the first stage of the hierarchy, 4 nonlinear functions were compared: Brody, Von Bertalanffy, Gompertz, and logistic. The analyses were carried out using 3 different data sets to check goodness of fit while having animals with few records. Three different assumptions about SD of fitting errors were considered: constancy throughout the trajectory, linear increasing until 3 yr of age and constancy thereafter, and variation following the nonlinear function applied in the first stage of the hierarchy. Comparisons of the overall goodness of fit were based on Akaike information criterion, the Bayesian information criterion, and the deviance information criterion. Goodness of fit at different points of the growth curve was compared applying the Gelfand`s check function. The posterior means of adult BW ranged from 531.78 to 586.89 kg. Greater estimates of adult BW were observed when the fitting error variance was considered constant along the trajectory. The models were not suitable to describe the SD of fitting errors at the beginning of the growth curve. All functions provided less accurate predictions at the beginning of growth, and predictions were more accurate after 48 mo of age. The prediction of adult BW using nonlinear functions can be accurate when growth curve parameters and their (co) variance components are estimated jointly. The hierarchical model used in the present study can be applied to the prediction of mature BW in herds in which a portion of the animals are culled before adult age. Gompertz, Von Bertalanffy, and Brody functions were adequate to establish mean growth patterns and to predict the adult BW of Nelore females. The Brody model was more accurate in predicting the birth weight of these animals and presented the best overall goodness of fit.

Models for genetic evaluation of Nelore cattle mature body weight

Records of 18,770 Nelore animals, born from 1975 to 2002, in 8 herds participating in the Nelore Cattle Breeding Program, were analyzed to estimate genetic parameters for mature BW. The mature BW were analyzed as a single BW taken closest to 4.5 yr of age for each cow in the data file, considering BW starting from 2 (W2Y_S), 3 (W3Y_S), or 4 (W4Y_S) yr of age or as repeated records, including all BW starting from 2 (W2Y_R), 3 (W3Y_R), or 4 (W4Y_R) yr of age. The variance components were estimated by restricted maximum likelihood, fitting univariate and bivariate animal models, including weaning weight. The heritability estimates were 0.29, 0.34, 0.36, 0.41, 0.44, and 0.46 for W2Y_S, W3Y_S, W4Y_S, W2Y_R, W3Y_R, and W4Y_R, respectively. The repeatability estimates for W2Y_R, W3Y_R, and W4Y_R were 0.59, 0.64, and 0.72, respectively. Larger accuracy values associated with the EBV were obtained in the repeated records models. The results indicated the bivariate repeated records model as the most appropriate for analyzing mature BW.