Statistical analysis of somatic cell scores via mixed model methodology for longitudinal data

Abstract

-The aim of this study was to analyze somatic cell counts which is an indirect criterion. to assess susceptibility to mastitis. Data analyzed were weekly records (6448 somatic cell scores) out of 159 primiparous Holsteins and Holsteins x Normande cows raised at the INRA" Le Pin au Haras" experimental farm, France. Given the longitudinal structure of this data set, the analysis consists of modeling both the mean and the individual profiles. This was achieved via the use of mixed models including fixed effects for the average profiles and random effects for the adjusted individual profiles. As far as fixed effects are concerned, the main issue is to fit a time trend to the average profiles. For this, we employed the technique of fractional polynomials described in Royston and Altman (Appl. Stat. 43 (1994) 429-467) under several variance-covariance structures. The best second degree polynomial involved an intercept plus the time at the power (-1/3) (i.e., ) plus the latter times the logarithm of the time (i.e., × log (t)). Regarding random effects, model comparisons involved random coefficient models, exponential stationary stochastic processes and heterogeneous variances. The models that simultaneously included all these three structures turned out to be the best. For instance, random coefficient models did not fit the variance function well, even when the degree of the polynomial was high. This phenomenon partly justified the introduction of heteroskedastic models.longitudinal data / mixed models / fractional polynomials / robust estimators / somatic cell scores Résumé -Analyse statistique des scores de cellules somatiques par la méthodologie des modèles mixtes appliquée à des données longitudinales. L'objectif de cette étude est d'analyser les comptages de cellules somatiques, qui constituent un critère indirect d'appréciation de la sensibilité aux mammites. Les données analysées étaient relatives à 6448 contrôles hebdomadaires de cellules somatiques du lait effectués sur 159 génisses de race Holstein et croisées Holstein x Normande, entretenues au domaine expérimental INRA-Le pin au Haras. Eu égard à la structure longitudinale * Corresponding author: robert@germinal.toulouse.inra.fr des données, l'analyse a consisté à modéliser les profils moyens et individuels de réponse. À ce propos, ont été mis en oeuvre des modèles mixtes dont les effets fixes décrivent les profils moyens et les effets aléatoires les profils individuels. Concernant les effets fixes, on a utilisé la technique des polynômes fractionnaires, décrite par Royston et Altman [29] assortie de différentes structures de variance-covariance. Le meilleur ajustement est fourni par un polynôme de second degré comportant un terme constant, le temps à la puissance moins un tiers (i.e., ) et ce même terme multiplié par le logarithme du temps (i.e., × log(t)). Concernant la partie aléatoire du modèle, les modèles mis en comparaison faisaient appel à une régression sur le temps à coefficients aléatoires, à des processus stochastiques stationnaires e...

Response to somatic cell count-based selection for mastitis resistance in a divergent selection experiment in sheep

“…In a first step, for each trait, a variance-covariance matrix was assumed and a model for the mean was chosen by selecting fixed effects via the robust estimators proposed by Liang and Zeger (1986). After selection of the fixed effects, the second step consisted of selecting and testing several covariance structures for animal and residual effects, following the strategy and methodology used by Robert-Granie et al (2004). To account for the correlation of measures within subjects (longitudinal recording), 5 R matrix covariance structures were tested (Table 1).…”

“…For traits measured for each udder half (SCS and bacteriological results), modeling the covariance structure of the random animal part (G matrix) aimed at testing different variances for each udder half and the correlation between udder halves (Table 1). Selection of the best models was based on the Akaike criteria for nonnested models and on the likelihood ratio test when models were nested, as proposed by Robert-Granie et al (2004).…”

An enzymatic cow immunity-targeted approach to reducing milk somatic cell count: 3. A comparative field trial

“…Thus, the somatic cell count (SCC) as an indicator of the inflammatory response to an intramammary infection or another trigger of the immune system is a convenient (and commonly used) measure of udder health as well as milk quality (Rivas et al 2001, Schukken et al 2003, Green et al 2004, Robert-Granie et al 2004, de Haas et al 2005, Hillerton & Berry 2005. Moreover, various mastitis control programmes developed throughout the world, those aimed at genetic selection for mastitis resistance included, are almost all based on the use of this criterion (Shook 1993, Hillerton 1996, Kadarmideen & Pryce 2001, Beaudeau et al 2002, Samoré et al 2003, Barnouin et al 2004, Juozaitiene et al 2004, Kadarmideen 2004.…”

Specific Emitter Identification Based on Transient Energy Trajectory

“…7, when the order is 10 ∼ 40, the MSE is smaller, and that means the performance is better. When the order is higher than 40, the MSE increases because of the waviness and endeffects [21]. The lower the order is, the less the computation is, so the order n = 10 in this paper.…”