Assessment of heterogeneity of residual variances using changepoint techniques

Several studies using test-day models show clear heterogeneity of residual variance along lactation. A changepoint technique to account for this heterogeneity is proposed. The data set included 100 744 test-day records of 10 869 Holstein-Friesian cows from northern Spain. A three-stage hierarchical model using the Wood lactation function was employed. Two unknown changepoints at times T₁ and T₂, (0 <T₁ <T₂ <t_max), with continuity of residual variance at these points, were assumed. Also, a nonlinear relationship between residual variance and the number of days of milking t was postulated. The residual variance at a time t() in the lactation phase i was modeled as: for (i = 1, 2, 3), where λ_ι is a phase-specific parameter. A Bayesian analysis using Gibbs sampling and the Metropolis-Hastings algorithm for marginalization was implemented. After a burn-in of 20 000 iterations, 40 000 samples were drawn to estimate posterior features. The posterior modes of T₁, T₂, λ₁, λ₂, λ₃, , , were 53.2 and 248.2 days; 0.575, -0.406, 0.797 and 0.702, 34.63 and 0.0455 kg², respectively. The residual variance predicted using these point estimates were 2.64, 6.88, 3.59 and 4.35 kg² at days of milking 10, 53, 248 and 305, respectively. This technique requires less restrictive assumptions and the model has fewer parameters than other methods proposed to account for the heterogeneity of residual variance during lactation.     

Inhibition of the Transsulfuration Pathway Affects Growth and Feather Follicle Development in Meat-Type Chickens

Cysteine is a nonessential amino acid in poultry nutrition. Poultry diets are deficient in cysteine, but the bird’s cysteine need is met through the transsulfuration pathway (TSP) where homocysteine is converted to cysteine: a process catalyzed by cystathionine β-synthase (CBS) and cystathionine γ-lyase (CTH). Cysteine is also a major component of keratinized protein found in feathers, but the extent to which cysteine is involved in feather and skin development in poultry is unknown. We randomly assigned chicks to control and treatment (control diet plus 100?mg/kg body weight of propargylglycine which is an inhibitor of CTH) diets. The thickness of skin layers, primary feather follicle parameters, growth, and mRNA expression of CBS and CTH were measured. Inhibition of TSP corresponded with the upregulation of liver mRNA of both CBS and CTH and reduction in growth from 35 to 40 days of age. The epidermis thickness, feather follicle length, and diameter were reduced from 10 to 40 days of age. Incorporation of cysteine into keratinized protein may be more sensitive to the level of available cysteine than into nonkeratinized proteins. Thus, disruption of the TSP could affect the thermoregulatory ability of the bird.     

Sample size determination for classifiers based on single-nucleotide polymorphisms

Single-nucleotide polymorphisms (SNPs), believed to determine human differences, are widely used to predict risk of diseases. Typically, clinical samples are limited and/or the sampling cost is high. Thus, it is essential to determine an adequate sample size needed to build a classifier based on SNPs. Such a classifier would facilitate correct classifications, while keeping the sample size to a minimum, thereby making the studies cost-effective. For coded SNP data from 2 classes, an optimal classifier and an approximation to its probability of correct classification (PCC) are derived. A linear classifier is constructed and an approximation to its PCC is also derived. These approximations are validated through a variety of Monte Carlo simulations. A sample size determination algorithm based on the criterion, which ensures that the difference between the 2 approximate PCCs is below a threshold, is given and its effectiveness is illustrated via simulations. For the HapMap data on Chinese and Japanese populations, a linear classifier is built using 51 independent SNPs, and the required total sample sizes are determined using our algorithm, as the threshold varies. For example, when the threshold value is 0.05, our algorithm determines a total sample size of 166 (83 for Chinese and 83 for Japanese) that satisfies the criterion.     

Simulation study for analysis of binary responses in the presence of extreme case problems

Background

Estimates of variance components for binary responses in presence of extreme case problems tend to be biased due to an under-identified likelihood. The bias persists even when a normal prior is used for the fixed effects.

Methods

A simulation study was carried out to investigate methods for the analysis of binary responses with extreme case problems. A linear mixed model that included a fixed effect and random effects of sire and residual on the liability scale was used to generate binary data. Five simulation scenarios were conducted based on varying percentages of extreme case problems, with true values of heritability equal to 0.07 and 0.17. Five replicates of each dataset were generated and analyzed with a generalized prior (g-prior) of varying weight.

Results

Point estimates of sire variance using a normal prior were severely biased when the percentage of extreme case problems was greater than 30%. Depending on the percentage of extreme case problems, the sire variance was overestimated when a normal prior was used by 36 to 102% and 25 to 105% for a heritability of 0.17 and 0.07, respectively. When a g-prior was used, the bias was reduced and even eliminated, depending on the percentage of extreme case problems and the weight assigned to the g-prior. The lowest Pearson correlations between true and estimated fixed effects were obtained when a normal prior was used. When a 15% g-prior was used instead of a normal prior with a heritability equal to 0.17, Pearson correlations between true and fixed effects increased by 11, 20, 23, 27, and 60% for 5, 10, 20, 30 and 75% of extreme case problems, respectively. Conversely, Pearson correlations between true and estimated fixed effects were similar, within datasets of varying percentages of extreme case problems, when a 5, 10, or 15% g-prior was included. Therefore this indicates that a model with a g-prior provides a more adequate estimation of fixed effects.

Conclusions

The results suggest that when analyzing binary data with extreme case problems, bias in the estimation of variance components could be eliminated, or at least significantly reduced by using a g-prior.     

Model for fitting longitudinal traits subject to threshold response applied to genetic evaluation for heat tolerance

A semi-parametric non-linear longitudinal hierarchical model is presented. The model assumes that individual variation exists both in the degree of the linear change of performance (slope) beyond a particular threshold of the independent variable scale and in the magnitude of the threshold itself; these individual variations are attributed to genetic and environmental components. During implementation via a Bayesian MCMC approach, threshold levels were sampled using a Metropolis step because their fully conditional posterior distributions do not have a closed form. The model was tested by simulation following designs similar to previous studies on genetics of heat stress. Posterior means of parameters of interest, under all simulation scenarios, were close to their true values with the latter always being included in the uncertain regions, indicating an absence of bias. The proposed models provide flexible tools for studying genotype by environmental interaction as well as for fitting other longitudinal traits subject to abrupt changes in the performance at particular points on the independent variable scale.     

A simulation study for the analysis of uncertain binary responses: Application to first insemination success in beef cattle

A simulation was carried out to investigate the methods of analyzing uncertain binary responses for success or failure at first insemination. A linear mixed model that included, herd, year, and month of mating as fixed effects; and unrelated service sire, sire and residual as random effects was used to generate binary data. Binary responses were assigned using the difference between days to calving and average gestation length. Females deviating from average gestation length lead to uncertain binary responses. Thus, the methods investigated were the following: (1) a threshold model fitted to certain (no uncertainty) binary data (M1); (2) a threshold model fitted to uncertain binary data ignoring uncertainty (M2); and (3) analysis of uncertain binary data, accounting for uncertainty from day 16 to 26 (M3) or from day 14 to 28 (M4) after introduction of the bull, using a threshold model with fuzzy logic classification. There was virtually no difference between point estimates obtained from M1, M3, and M4 with true values. When uncertain binary data were analyzed ignoring uncertainty (M2), sire variance and heritability were underestimated by 22 and 24%, respectively. Thus, for noisy binary data, a threshold model contemplating uncertainty is needed to avoid bias when estimating genetic parameters.     

Transcriptional profiling of initial differentiation events in human embryonic stem cells

Currently, there are no differentiation strategies for human embryonic stem cells (hESCs) that efficiently produce one specific cell type, possibly because of lack of understanding of the genes that control signaling events prior to overt differentiation. sed HepG2 cell conditioned medium (MEDII), which induces early differentiation in mouse ES cells while retaining pluripotent markers, to query gene expression in hESCs. Treatment of adherent hESCs with 50% MEDII medium effected differentiation to a cell type with gene expression similar to primitive streak stage cells of mouse embryos. MEDII treatment up-regulates TDGF1 (Cripto), a gene essential for anterior-posterior axis and mesoderm formation in mouse embryos and a key component of the TGFB1/NODAL signaling pathway. LEFTYA, an antagonist of NODAL/TDGF1 signaling expressed in anterior visceral endoderm, is down-regulated with MEDII treatment, as is FST, an inhibitor of mesoderm induction via the related INHBE1 pathway. In summary, the TGFB1/NODAL pathway is important for primitive-streak and mesoderm formation and in using MEDII, we present a means for generating an in vitro cell population that maintains pluripotent gene expression (POU5F1, NANOG) and SSEA-4 markers while regulating genes in the TGFB1/NODAL pathway, which may lead to more uniform formation of mesoderm in vitro.     

National evaluation for calving ease,gestation length and birth weight by linear and threshold model methodologies

Data included 393,097 calving ease, 129,520 gestation length, and 412,484 birth weight records on 412,484 Gelbvieh cattle. Additionally, pedigrees were available on 72,123 animals. Included in the models were effects of sex and age of dam, treated as fixed, as well as direct, maternal genetic and permanent environmental effects and effects of contemporary group (herd-year-season), treated as random. In all analyses, birth weight and gestation length were treated as continuous traits. Calving ease (CE) was treated either as a continuous trait in a mixed linear model (LM), or as a categorical trait in linear-threshold models (LTM). Solutions in TM obtained by empirical Bayes (TMEB) and Monte Carlo (TMMC) methodologies were compared with those by LM. Due to the computational cost, only 10,000 samples were obtained for TMMC. For calving ease, correlations between LM and TMEB were 0.86 and 0.78 for direct and maternal genetic effects, respectively. The same correlations but between TMEB and TMMC were 1.00 and 0.98, respectively. The correlations between LM and TMMC were 0.85 and 0.75, respectively. The correlations for the linear traits were above.97 between LM and TMEB but as low as 0.91 between LM and TMMC, suggesting insufficient convergence of TMMC. Computing time required was about 2 hrs, 5 hrs, and 6 days for LM, TMEB and TMMC, respectively, and memory requirements were 169, 171, and 445 megabytes, respectively. Bayesian implementation of threshold model is simple, can be extended to multiple categorical traits, and allows easy calculation of accuracies; however, computing time is prohibitively long for large models.