Degree of multicollinearity and variables involved in linear dependence in additive-dominant models

The objective of this work was to assess the degree of multicollinearity and to identify the variables involved in linear dependence relations in additive-dominant models. Data of birth weight (n=141,567), yearling weight (n=58,124), and scrotal circumference (n=20,371) of Montana Tropical composite cattle were used. Diagnosis of multicollinearity was based on the variance inflation factor (VIF) and on the evaluation of the condition indexes and eigenvalues from the correlation matrix among explanatory variables. The first model studied (RM) included the fixed effect of dam age class at calving and the covariates associated to the direct and maternal additive and non-additive effects. The second model (R) included all the effects of the RM model except the maternal additive effects. Multicollinearity was detected in both models for all traits considered, with VIF values of 1.03 - 70.20 for RM and 1.03 - 60.70 for R. Collinearity increased with the increase of variables in the model and the decrease in the number of observations, and it was classified as weak, with condition index values between 10.00 and 26.77. In general, the variables associated with additive and non-additive effects were involved in multicollinearity, partially due to the natural connection between these covariables as fractions of the biological types in breed composition.

The presence of anti-citrullinated protein antibodies (ACPA) and rheumatoid factor on patients with rheumatoid arthritis (RA) does not interfere with the chance of clinical remission in a follow-up of 3 years

Autoantibodies in early rheumatoid arthritis (RA) have important diagnostic value. The association between the presence of autoantibodies against cyclic citrullinated peptide and the response to treatment is controversial. To prospectively evaluate a cohort of patients with early rheumatoid arthritis (< 12 months of symptoms) in order to determine the association between serological markers (rheumatoid factor (RF), anti-citrullinated protein antibodies) such as anti-cyclic citrullinated peptide antibodies (anti-CCP) and citrullinated anti-vimentin (anti-Sa) with the occurrence of clinical remission, forty patients diagnosed with early RA at the time of diagnosis were evaluated and followed for 3 years, in use of standardized therapeutic treatment. Demographic and clinical data were recorded, disease activity score 28 (DAS 28), as well as serology tests (ELISA) for RF (IgM, IgG, and IgA), anti-CCP (CCP2, CCP3, and CCP3.1) and anti-Sa in the initial evaluation and at 3, 6, 12, 18, 24, and 36 months of follow-up. The outcome evaluated was the percentage of patients with clinical remission, which was defined by DAS 28 lower than 2.6. Comparisons were made through the Student t test, mixed-effects regression analysis, and analysis of variance (significance level of 5%). The mean age was 45 years, and a female predominance was observed (90%). At the time of diagnosis, RF was observed in 50% of cases (RF IgA-42%, RF IgG-30%, and RF IgM-50%), anti-CCP in 50% (no difference between CCP2, CCP3, and CCP3.1) and anti-Sa in 10%. After 3 years, no change in the RF prevalence and anti-CCP was observed, but the anti-Sa increased to 17.5% (P = 0.001). The percentage of patients in remission, low, moderate, and intense disease activity, according to the DAS 28, was of 0, 0, 7.5, and 92.5% (initial evaluation) and 22.5, 7.5, 32.5, and 37.5% (after 3 years). There were no associations of the presence of autoantibodies in baseline evaluation and in serial analysis with the percentage of clinical remission during follow-up of 3 years The presence of autoantibodies in early RA has no predictive value for clinical remission in early RA.

Variance Effective Population Size for Dioecious Species

The concept of effective population size (N(e)) is an important measure of representativeness in many areas. In this research, we consider the statistical properties of the number of contributed gametes under practical situations by adapting Crow and Denninston's (1988) N(e) formulas for dioecious species. Three sampling procedures were considered. In all circumstances, results show that as the offspring sex ratio (r) deviates from 0.5, N(e) values become smaller, and the efficiency of gametic control for increasing N(e) is reduced. For finite populations, where all individuals are potentially functional parents, the reduction in N(e) due to an unequal sex ratio can be compensated for through female gametic control when 0.28 <= r <= 0.72. This outcome is important when r is unknown. When only a fraction of the individuals in a population is taken for reproduction, N(e) is meaningful only if the size of the reference population is clearly defined. Gametic control is a compensating factor in accession regeneration when the viability of the accession is around 70 or 75%. For germ-plasm collection, when parents are a very small fraction of the population, maximum N(e) will be approximately 47 and 57% of the total number of offspring sampled, with female gametic control, r varying between 0.3 and 0.5, and being constant over generations.

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.