J. Anim. Breed. Genet. ISSN 0931-2668
ORIGINAL ARTICLE
Application of multiple-trait finite mixture model to test-day records of milk yield and somatic cell score of Canadian Holsteins J. Jamrozik & L.R. Schaeffer Centre for Genetic Improvement of Livestock, Department of Animal and Poultry Science, University of Guelph, Guelph, ON, Canada
Keywords Bayesian methods; mastitis; mixture model; somatic cell score; test-day data. Correspondence J. Jamrozik, Centre for Genetic Improvement of Livestock, Department of Animal and Poultry Science, University of Guelph, Guelph, ON N1G 2W1, Canada. Tel: +1 519 824 4120; Fax: +1 519 836 9873; E-mail:
[email protected] Received: 21 December 2009; accepted: 24 March 2010.
Summary Multiple-trait (MT) finite mixture random regression (MIX) model was applied using Bayesian methods to first lactation test-day (TD) milk yield and somatic cell score (SCS) of Canadian Holsteins, allowing for heterogeneity of distributions with respect to days in milk (DIM) in lactation. The assumption was that the associations between patterns of variation in these traits and mastitis would allow revealing the hidden structure in the data distribution because of unknown health status of cows. The MIX model assumed separate means and residual co-variance structures for two components in four intervals of lactation, in addition to fitting the fixed effect of herd-test-day, and fixed and random regressions with Legendre polynomials. Results indicated that the mixture model was superior to standard MT model, as supported by the Bayes factor. Approximately 20% of TD records were classified as originated from cows with a putative, sub-clinical form of mastitis. The proportion of records from mastitic cows was the largest at the beginning of lactation. The MIX model exhibited different distributions of data from healthy and infected cows in different parts of lactation. Records from sick cows were characterized by larger (smaller) means for SCS (milk) and larger variances. Residual, and daily genetic and environmental correlations between milk and SCS were smaller from the MIX model when compared with MT estimates. Heritabilities of both traits differed significantly among records from healthy, sick and MT model estimates. Both models fitted milk records from healthy cows relatively well. The ability of the MT model in handling SCS records, measured by model residuals, was low, but improved substantially, however, where the data were allowed to be separated into two components in the MIX parameterization. Correlations between estimated breeding values (EBV) for sires from both models were very high for cumulative milk yield (>0.99) and slightly lower (0.95 in the interval from 5 to 45 DIM) for daily SCS. EBV for SCS from MT and MIX models were weakly correlated with posterior probability of sub-clinical mastitis on the phenotypic scale.
Introduction Mastitis is the most frequent and costly disease in dairy cattle. Data on health status of cows are usually not routinely collected in the majority of dairy ª 2010 Blackwell Verlag GmbH • J. Anim. Breed. Genet. (2010) 1–8
populations and indirect selection against mastitis utilizes somatic cell scores (SCS), as a correlated trait (Mark et al. 2002). The level of SCS on a test-day (TD) can serve as a measure of response to the infection and as an indicator of mastitis. Bacterial doi:10.1111/j.1439-0388.2010.00875.x
Mixture model for milk and somatic cell score
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The objectives of this research were to analyse 1st lactation TD milk yield and SCS of Canadian Holsteins cows with a two-trait normal mixture random regression model allowing for heterogeneity of distributions in different parts of lactation. Estimates of co-variance components, genetic parameters and estimated breeding values (EBV) of sires from the mixture model were contrasted with corresponding estimates from the standard MT model. Material and methods Data
Holstein first lactation TD data with calving years from 1988 to 2007 were obtained from the Canadian Dairy Network, Guelph, ON, Canada. A computationally manageable data set was selected by random sampling of herds with minimum of 50 cows each and with minimum of seven TD records per cow. This resulted in 214 813 TD milk (kg) and SCS records on 25 950 cows. Each cow had both milk yield and SCS recorded on a given TD. SCS were calculated from somatic cell counts (SCC) as SCS = log2(SCC ⁄ 100 000) + 3. Days in milk (DIM) were from 5 to 305. Plots of average lactation curves are in Figures 1 and 2 for milk and SCS, respectively. The number of herd-test-day (HTD) classes was 23 984, and there were 80 levels of region-age-season of calving (RAS). Pedigree data included 66 244 animals. As records from clinically infected cows are normally excluded from the recording on a given TD, the data contained
35 All
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30
25
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15
85 10 5 12 5 14 5 16 5 18 5 20 5 22 5 24 5 26 5 28 5 30 5
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infection of the mammary gland results in an increase in the concentration of somatic cells in cow’s milk. de Haas et al. (2004) showed that cases of clinical mastitis were significantly associated with an increase in SCS. Selection against cows with higher SCS is expected to reduce prevalence of mastitis, as indicated by moderate genetic correlation between these traits (Shook & Schutz 1994). High producing cows are genetically prone to udder infections (Carle´n et al. 2004) because of positive correlations between milk yield and susceptibility to mastitis. Windig et al. (2005) showed that cows with higher milk yield exhibited more peaks in distributions of SCS around the same TD, and they concluded that a high milk yield increases the risk of mastitis. Mammary infection is also associated with reduced milk yield on a TD basis. Lukas et al. (2009) documented an average decrease of 2 kg of daily milk yield observed as early as 4 days before diagnosis for cows with a mild form of mastitis. Du¨rr et al. (2008) reported milk losses per unit increase in SCS from 0.33 to 0.55 kg ⁄ day in the first lactation of Canadian Holsteins. Negative phenotypic effects of SCS on milk yield and a smaller positive reciprocal effect were estimated in Canadian Holsteins using models with simultaneous causal links between these traits (Jamrozik et al. 2010). The same authors indicated heterogeneity of phenotypic relationships between milk and SCS in different parts of lactation. Patterns of changes in milk yield and SCS during lactation can be utilized in detecting cases of mastitis. Milk yield and SCS from cows with mastitis (IM+) and from healthy cows (IM)) may exhibit different distributions. Detilleux & Leroy (2000) proposed a finite mixture model approach for analysis of SCS in the absence of information regarding infection status. In the mixture model, observations are assigned to two or more groups (originated from healthy versus infected cows) based on probabilities estimated from the data. Mixture models have been applied to analysis of SCS of US Holsteins (Boettcher et al. 2007) and Danish Holsteins (Madsen et al. 2008). Mixture models could be more powerful when more than one trait (i.e. milk yield in addition to SCS) is used for assigning group membership. Thus, the multiple-trait (MT) mixture model for joint analysis of SCS and milk yield on a TD basis seems to be justified. Frequency of mastitis changes during lactation, with the largest proportion of mammary infection cases occurring early after calving (Heringstad et al. 2003). Joint distributions of milk yield and SCS might, therefore, also be different in different parts of lactation.
J. Jamrozik & L. R. Schaeffer
DIM
Figure 1 Average milk yield for all test-day records, and for records from the HEALTHY1 and SICK2 categories, by DIM. 1Posterior mean of classification variable (zij) smaller than 0.5. 2Posterior mean of classification variable (zij) larger than 0.5.
ª 2010 Blackwell Verlag GmbH • J. Anim. Breed. Genet. (2010) 1–8
Mixture model for milk and somatic cell score
J. Jamrozik & L. R. Schaeffer
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Figure 2 Average somatic cell score for all test-day records, and for records from the HEALTHY1 and SICK2 categories, by DIM. 1Posterior mean of classification variable (zij) smaller than 0.5. 2Posterior mean of classification variable (zij) larger than 0.5.
a mix of records from non-mastitic cows and cows with a sub-clinical form of mastitis. Restriction on minimal number of records per cow was applied to ensure good quality data for the estimation of cow-specific regression coefficients. These excluded cows culled early in lactation because of udder health-related problems and could possibly lead to selection bias. Canadian Holstein cows, however, are culled because of mastitis or high level of SCS relatively late, on average after at least 3 years of productive life (Van Doormaal 2009). This restrictive editing, therefore, should not be a source of any significant biases in our inferences. Models
The finite mixture model assigns records on milk and SCS on a given TD into one of the two components, depending on the unknown health status of the cows. DIM were split into four disjoint intervals: 5–45, 46–115, 116–265 and 266–305 DIM, as in Schaeffer et al. (2000), and group membership (healthy or infected) of the j-th record in the i-th interval was defined by a binary vector zi where zij = 0 (1) indicated record from the IM) (IM+) cow. The equation for the mixture model (MIX) can be written following Ødega˚rd et al. (2003) as y i ¼ X0i b0 þ Mzi X1i b1i þ Zi a þ Wi p þ ei ; where yi = vector of observations (milk and SCS) in the i-th DIM interval, b0 = vector of fixed effects common to all records, b1i = vector of fixed effect corresponding to data from infected cows, a = vector ª 2010 Blackwell Verlag GmbH • J. Anim. Breed. Genet. (2010) 1–8
of random animal additive genetic effects, p = vector of random permanent environmental (PE) effects, ei = vector of random residuals, Mzi = matrix with diagonal elements of zij, and X0i, X1i, Zi, Wi = known incidence matrices. The fixed effects in b0 were HTD effects and regression on DIM within RAS levels, and elements of b1i included mean differences between ‘sick’ and ‘healthy’ components for milk and SCS. Additive genetic and PE effects were regressions on DIM; all regressions (fixed and random) were modelled with orthogonal Legendre polynomials of order 4. Residuals of records on different TD were uncorrelated. The conditional distribution of yi was assumed to be: y i jb0 ; b1i ; a; p; Ri ; zi N½X0i b0 þ Mz X1i b1i þ Zi a þ Wi p; Ri ; where Ri = (Ii ) Mzi) Ri0 + Mzi Ri1; Ri0 and Ri1 are residual co-variance matrices for IM) and IM+ records, respectively. The MIX model allowed for different means and residual dispersion parameters for milk and SCS depending on the group membership, but the co-variance components for genetic and PE effects were independent of group membership. MT model for milk and SCS was the same as MIX assuming all elements of zi equal to 0. Bayesian assumptions
Proper normal distributions (mean = 0 and variance = 10 000) were assumed for fixed effects. Random effects were also a priori normally distributed, conditionally on genetic and PE co-variance components. Elements of zi were assumed to be independent and following the same Bernoulli distribution, Br(Pi), where Pi was the proportion of IM+ records (stage-specific mixing proportion). Priors for co-variance components were independent inverted Wishart distributions with minimal numbers of degrees of belief, and prior distributions for Pi were beta distribution with both hyper-parameters equal to 2. Prior values for all co-variance components were taken from Bohmanova et al. (2008). Methods
Gibbs sampling scheme for the scalar 2-component mixture model (Ødega˚rd et al. 2003) was generalized for the MT scenario and a heterogeneous data structure. Conditional distributions for the MIX model were: multivariate normal for location parameters, 3
Mixture model for milk and somatic cell score
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inverted Wishart for co-variance components, Bernoulli for the group memberships, and beta distributions for the mixing proportions. The sampling for the MT model followed standard algorithms. Single chains of 120 000 samples were generated for both models. Convergence of Gibbs chains was determined by visual inspection of trace plots for selected parameters. All posterior inferences were based on 100 000 samples after burn-in. Models were compared via Bayes factors (Kass & Raftery 1995). The marginal likelihood was estimated by the harmonic mean of the likelihood values from the Gibbs chain as p(y | M = Mk) = {1 ⁄ m R [p(y | hik , Mk)] )1})1, where hik (i = 1, 2, …, m) were draws obtained from the posterior distribution under model k with parameters hk. TD records were further assigned a posteriori to healthy (HEALTHY) and sick (SICK) categories based on the 50% threshold and the posterior mean of the group membership binary parameter (zij) for each observation. Records for which posterior average of zij was smaller (larger) than 0.5 were assigned to the HEALTHY (SICK) groups. This was performed to examine records and model residuals from healthy and mastitic cows. Posterior probability of mastitis (PPM) for each TD record from the MIX model was estimated following Ødega˚rd et al. (2003). Finally, posterior means and standard deviations of co-variance components and genetic parameters on a daily basis, and EBV for cumulative milk yield and average daily SCS within four DIM intervals (for sires with at least 200 TD records) from the MIX and MT models were compared.
Results Estimates of marginal log-likelihood were )746 450 and )645 855 for MT and MIX models, respectively, indicating very strong arguments in favour of the mixture model specification. Proportions of TD records with putative mastitis (Table 1) decreased from 0.24 (5–45 DIM) to 0.16 (116–305 DIM). The overall mixing proportion (average across four DIM intervals) was equal to 0.19. Mixing probabilities were larger than reported by Boettcher et al. (2007) for the US Holstein (5%) but lower than estimates of Madsen et al. (2008) for Danish Holsteins (30%). No restriction on the number of TD records per cow was applied for the Danish Holsteins that could explain higher mixing probability obtained in that study. TD records were grouped into HEALTHY and SICK categories based on posterior means of the group membership variable. Proportions of records assigned to the SICK group were lower (from 0.18 to 0.11) than respective mixing proportions, most likely because of conservative threshold of 50% (Table 1). Based on this classification, almost 40% of cows had TD records free of mastitis; 32% had only one record, and less than 1% had more than four records in the SICK category. Plots of average milk yield and SCS from HEALTHY and SICK groups are in Figures 1 and 2. Milk yield in the HEALTHY category was in general slightly lower than in the SICK group. Very large differences (around two points) were observed between infected and healthy records for SCS. Averages of SCS in the HEALTHY category
Table 1 Estimates (posterior SD in brackets) of residual variance (r2) and residual correlations (r) for milk yield (M) and somatic cell score (SCS) from multiple-trait (MT) and mixture (MIX) models, and mixing proportion (P), frequency of 50% mastitic records (M-50) and difference (b1) between SICK (IM+) and HEALTHY (IM)) groups from the mixture model, by days in milk (DIM) interval Model
Mixture component
Parameter
DIM interval
r2M r2SCS r r2M r2SCS r r2M r2SCS r P M-50 b1M b1SCS
5–45 7.7 (0.15) 1.1 (0.02) )0.2 (0.01) 4.1 (0.14) 0.3 (0.01) )0.1 (0.02) 21.7 (0.61) 3.4 (0.08) )0.1 (0.02) 0.24 (0.01) 0.18 )1.7 (0.11) 1.5 (0.04)
MT
MIX
IM)
IM+
4
46–115 4.8 (0.05) 0.9 (0.01) )0.1 (0.01) 2.8 (0.04) 0.2 (0.01) )0.0 (0.01) 15.5 (0.34) 3.2 (0.06) )0.1 (0.01) 0.19 (0.01) 0.14 )0.9 (0.06) 1.2 (0.03)
116–265 3.9 (0.02) 0.7 (0.01) )0.1 (0.01) 1.9 (0.02) 0.2 (0.01) )0.0 (0.01) 15.0 (0.24) 2.8 (0.04) )0.1 (0.01) 0.16 (0.01) 0.11 )0.8 (0.04) 1.2 (0.02)
266–305 3.4 (0.9) 0.6 (0.01) )0.2 (0.02) 1.3 (0.07) 0.2 (0.01) )0.1 (0.02) 15.1 (0.57) 2.6 (0.08) )0.1 (0.02) 0.16 (0.01) 0.11 )1.2 (0.10) 1.1 (0.04)
ª 2010 Blackwell Verlag GmbH • J. Anim. Breed. Genet. (2010) 1–8
Mixture model for milk and somatic cell score
J. Jamrozik & L. R. Schaeffer
were marginally smaller than the overall means for the whole population. Average residuals of records in HEALTHY and SICK groups from both models are in Figures 3 and 4 for milk and SCS, respectively. For both traits, residuals from the MT model were larger in absolute values than corresponding residuals from the MIX model. Differences between models and HEALTHY and SICK components were more profound for SCS. The MT model fitted SCS records from infected cows more accurately than the data from the healthy cows. The reverse was observed for the MIX model. The mixture model gave very good fit for SCS records from the HEALTHY group (average residuals were close to 0); some biases, although smaller than those from the MT model, were still observed for the SICK records. Residual distributions differed substantially between MT and MIX, and between mixture compo5
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nents (Table 1). Heterogeneity of parameters with respect to DIM interval was also evident. Records of cows with mastitis were characterized by larger variances, and smaller (larger) means for milk (SCS). MT model gave estimates of residual variance that were in-between parameters for the two mixture components. Residual correlations between milk and SCS from the MIX model were marginally smaller than estimates from the MT model. Daily genetic (Figures 5 and 6) variances from the MIX model were smaller than the MT estimates, especially for SCS and early in the lactation. Similar pattern was observed for the daily PE variances, with slightly larger differences between models for these components. Estimates of correlations between milk yield and SCS on a daily basis followed general trends from other studies (e.g. Samore et al. 2008). The MIX model reduced daily genetic (Figure 7) and PE (results not shown) correlations between milk and SCS when compared with the MT estimates. Daily heritabilities of milk and SCS (Figures 8 and 9, respectively) were the largest for IM) records from
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Figure 3 Average residuals of milk yield for records from the HEALTHY1 and SICK2 groups, from the multiple-trait (MT) and the mixture (MIX) models, by days in milk (DIM). 1Posterior mean of classification variable (zij) smaller than 0.5. 2Posterior mean of classification variable (zij) larger than 0.5.
DIM
Figure 5 Genetic and permanent environmental (PE) variance of milk yield from the multiple-trait (MT) and the mixture (MIX) models, by days in milk (DIM).
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Figure 4 Average residuals of somatic cell score for records from the HEALTHY1 and SICK2 groups, from the multiple-trait (MT) and the mixture (MIX) models, by days in milk (DIM). 1Posterior mean of classification variable (zij) smaller than 0.5. 2Posterior mean of classification variable (zij) larger than 0.5.
ª 2010 Blackwell Verlag GmbH • J. Anim. Breed. Genet. (2010) 1–8
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Figure 6 Genetic and permanent environmental (PE) variance of somatic cell score from the multiple-trait (MT) and the mixture (MIX) models, by days in milk (DIM).
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Mixture model for milk and somatic cell score
J. Jamrozik & L. R. Schaeffer
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Figure 7 Genetic correlation between milk yield and somatic cell score from the multiple-trait (MT) and the mixture (MIX) models, by days in milk (DIM).
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Figure 9 Heritability of somatic cell score from the multiple-trait (MT) model, and IM) and IM+ components from the mixture (MIX) models, by days in milk (DIM).
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Figure 8 Heritability of milk yield from the multiple-trait (MT) model, and IM) and IM+ components from the mixture (MIX) model, by days in milk (DIM).
the MIX model, followed by MT model and IM+ estimates (MIX). The general trend of differences in heritability of SCS between healthy and infected records was in agreement with Heringstad et al. (2006) and Madsen et al. (2008). Heringstad et al. (2006) esti-
mates, although smaller than reported here, were 0.03 and 0.08 for mastitic (clinical form) and healthy cows, respectively. Correlations between EBV of 156 sires for milk yield from both models were larger than 0.99 within all four DIM intervals. Corresponding correlations for SCS were smaller, from 0.95 in 5–45 DIM to 0.99 in 116–265 DIM, indicating possible re-rankings of sires between models. Correlations between PPM in different DIM intervals were moderate (Table 2) and larger between adjacent intervals. As expected, EBV for SCS from the MIX model were not good indicators of PPM on the phenotypic scale. The only significantly different from 0 correlation (0.29) between EBV for SCS from the MIX model and PPM was associated with the beginning of lactation (5–45 DIM). Estimates of breeding values for both traits from the MT model seemed to be more related to the PPM on the phenotypic scale than corresponding EBV from the MIX model.
Table 2 Correlations among estimated breeding values for milk yield and somatic cell score (SCS) from the mixture (upper line) and the multipletrait (bottom line) models, and posterior probability of mastitis (PPM) for bulls with at least 20 daughters, by DIM interval (1–4)1 PPM
Milk
SCS
Trait ⁄ interval
2
3
4
1
2
3
4
1
PPM 1
0.41
0.51
0.11
0.44
0.21
0.22 0.19 0.16 0.15 0.17 0.16 0.09 0.11
0.35 0.36 0.35 0.34 0.42 0.41 0.23 0.23
0.44 0.45 0.39 0.39 0.51 0.50 0.25 0.24
0.49 0.49 0.39 0.39 0.53 0.52 0.20 0.19
0.29 0.46 0.11 0.22 0.12 0.23 0.05 0.05
2 3 4
0.45
2
0.13 0.22 0.05 0.17 0.00 0.09 )0.02 0.03
3
0.00 0.05 0.02 0.06 )0.07 0.01 )0.05 )0.01
4
)0.05 )0.04 0.01 0.02 )0.10 )0.07 )0.04 0.05
1
1 = 5–45 DIM, 2 = 46–115 DIM, 3 = 116–265 DIM, 4 = 266–305 DIM.
6
ª 2010 Blackwell Verlag GmbH • J. Anim. Breed. Genet. (2010) 1–8
J. Jamrozik & L. R. Schaeffer
Discussion MT mixture model for TD milk and SCS allowed splitting the data into two classes: originated from cows with putative, sub-clinical form of mastitis and those from cows free of mastitis. Distributions of data differed largely between mixture components, as well as within intervals of DIM in lactation. Records from healthy cows exhibited more relative genetic variation (measured by heritability) when compared with infected data and estimates obtained from joint analysis with the MT model. Partitioning data into different distributions with the mixture model limited the magnitude of genetic and environmental associations between milk and SCS, as expressed in reduced genetic and PE correlations. Classification of TD records into IM) and IM+ groups based on TD milk and SCS should ideally be verified, either by bacteriological tests or by health data. Neither was possible with the current (genetic evaluation) data. Results of the simulation study by Ødega˚rd et al. (2003) indicated that finite mixture models for SCS were characterized by higher specificity (correct identification of records from healthy animals) than sensitivity (correct identification of records from sick animals). Models used for genetic analysis of SCS in dairy cattle are usually the same as for production traits. This is also the case for Canadian genetic evaluation system (Schaeffer et al. 2000). Analysis of residuals indicated relatively low accuracy of modelling SCS with the standard MT model. Records from cows with mastitis are likely those that generate outliers in the framework of robust methods. Jamrozik et al. (2007) showed that SCS exhibited the largest number of outliers (from 10 to 23%) in the Canadian Test-Day Model. Elevated levels of SCS caused by infection of the mammary system are likely not handled in an optimal way by the standard models. Accuracy of fitting records from healthy cows improved significantly with the use of the mixture model. Precision of the mixture model for data from infected cows was also poor as documented by very large residual variances. Current models used for genetic evaluation of SCS seem therefore to lack both accuracy and precision. This does not mean, however, that using EBV for SCS from the mixture model would give a larger response in selection against mastitis. The mastitis effect in the TD data was accounted for in the MIX model and EBV for SCS were less correlated with phenotypic posterior probabilities of mastitis than EBV for SCS from the regular MT model. EBV for SCS from the MT model seem therefore to be a more useful selection criteª 2010 Blackwell Verlag GmbH • J. Anim. Breed. Genet. (2010) 1–8
Mixture model for milk and somatic cell score
rion against mastitis. Improvement in this respect could be achieved by fitting different but correlated genetic effects for separate mixture components or by using liability mixture models (Ødega˚rd et al. 2005). Computing requirements, however, still seem to be a limiting factor for routine applications of these models. Within-lactation heterogeneity of joint distributions of milk yield and SCS on the TD was documented in this research. The partitioning of lactations into four intervals was arbitrary, following pattern of changes in residual variation of milk production traits in Canadian Holstein (Schaeffer et al. 2000). Different definitions of DIM intervals could be considered for the purpose of mixture model applications. Modelling heterogeneity of distributions in a continuous manner, with a family of distributions assigned to particular days in lactation through parametric functions of parameters of distribution, could also be contemplated. Random genetic and PE effects are likely to be different in both mixture components (Boettcher et al. 2007; Madsen et al. 2008). Attempts to fit separate (but correlated) effects in the MIX model did not succeed, most likely because of limited TD data for IM+ group. Other traits associated with events of mastitis, like electrical conductivity of milk (Lukas et al. 2009) or milking speed, would possibly contribute to better performance of the mixture model for detection of events of putative mastitis. More mixture components (different pathogens) with possible different functional forms of distributions could also be considered. Liability-normal mixture model that would allow for different prior probabilities of putative mastitis for different TD records (Ødega˚rd et al. 2005) would make a further improvement in modelling. Such a model would allow ranking animals on the basis of the genetic component of PPM. Only TD records from healthy cows and cows with sub-clinical mastitis were used in this study. Milk yield from cows with severe (clinical) forms of this disease are most likely discarded and they do not enter genetic evaluation data sets. Approximately only 0.03% of TD records that are currently in the Canadian evaluation database are flagged as records from cows infected with mastitis (Peter Brand, CDN, personal communication). Data collection of dairy health events (including mastitis) started in Canada in 2007 and the genetic evaluation system for resistance to disease is being developed. Ranking of dairy animals on SCS level will likely be continued even when the genetic evaluation for mastitis is in place, and the mammary health index should optimally 7
Mixture model for milk and somatic cell score
utilize information from both sources. Data on cow’s health status on a given TD can be introduced into the current genetic evaluation model for SCS. More work is needed in this area. Conclusions Heterogeneous finite mixture model with two components for TD milk and SCS exhibited a hidden structure in these traits because of occurrence of putative mastitis in different parts of lactation. The mixture model was statistically superior over a standard MT specification in describing these two traits over the course of lactations. Distributions differed significantly between records of healthy and infected cows. Standard MT model for milk and SCS seems not to perform optimally in handling data of cows with sub-clinical mastitis. Acknowledgements Data were provided by Canadian Dairy Network (CDN), Guelph, ON, Canada. DairyGen and NSERC are acknowledged for financial support. Thanks go to Jarmila Bohmanova for her assistance with data preparation. References Boettcher P.J., Caraviello D., Gianola D. (2007) Genetic analysis of somatic cell scores in US Holsteins with Bayesian mixture model. J. Dairy Sci., 90, 435–443. Bohmanova J., Miglior F., Jamrozik J., Misztal I., Sullivan P.G. (2008) Comparison of random regression models with Legendre polynomials and linear splines for production traits and somatic cell score of Canadian Holstein cows. J. Dairy Sci., 91, 3627–3638. Carle´n E., Strandberg E., Roth A. (2004) Genetic parameters for clinical mastitis, somatic cell score, and production in the first three lactations of Swedish Holstein cows. J. Dairy Sci., 87, 3062–3070. Detilleux J., Leroy P.L. (2000) Application of a mixed normal mixture model for the estimation of mastitisrelated parameters. J. Dairy Sci., 83, 2341–2349. Du¨rr J.W., Cue R.I., Monardes H.G., Moreo-Mendez J., Wade K. (2008) Milk losses associated with somatic cell count per breed, parity and stage of lactation in Canadian dairy cattle. Livest. Sci., 117, 225–232. de Haas Y., Veerkamp R.F., Barkema H.W., Gro¨hn Y.T., Schunken Y.H (2004) Associations between pathogenspecific cases of clinical mastitis and somatic cell count patterns. J. Dairy Sci., 87, 95–105. Heringstad B., Chang Y.M., Gianola D., Klemetsdal G. (2003) Genetic analysis of longitudinal trajectory of
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clinical mastitis in first-lactation Norwegian cattle. J. Dairy Sci., 86, 2676–2683. Heringstad B., Gianola D., Chang Y.M., Ødega˚rd J., Klemetsdal G. (2006) Genetic associations between clinical mastitis and somatic cell score in early firstlactation cows. J. Dairy Sci., 89, 2236–2244. Jamrozik J., Fatehi J., Schaeffer L.R. (2007) Application of robust procedures for estimation of breeding value in multiple-trait random regression test-day model. J. Anim. Breed. Genet., 124, 3–11. Jamrozik J., Bohmanova J., Schaeffer L.R. (2010) Relationships between milk yield and somatic cell score in Canadian Holsteins from simultaneous and recursive random regression models. J. Dairy Sci., 93, 1216–1233. Kass R.E., Raftery A.E. (1995) Bayes factors. J. Am. Stat. Assoc., 90, 773–795. Lukas J.M., Reneau J.K., Wallace R., Hawkins D., Munoz-Zanzi C. (2009) A novel method of analyzing daily milk production and electrical conductivity to predict disease onset. J. Dairy Sci., 92, 5964–5976. Madsen P., Shariati M.M., Ødega˚rd J. (2008) Genetic analysis of somatic cell score in Danish Holsteins using a liability-normal mixture model. J. Dairy Sci., 91, 4355–4364. Mark T., Fikse W.F., Emanuelson U., Philipson J. (2002) International genetic evaluation for Holstein sires for somatic cell and clinical mastitis. J. Dairy Sci., 85, 2384–2392. Ødega˚rd J., Jensen J., Madsen P., Gianola D., Heringstad B. (2003) Detection of mastitis in dairy cattle by use of mixture models for repeated somatic cell scores: a Bayesian approach via Gibbs sampling. J. Dairy Sci., 86, 3694–3703. Ødega˚rd J., Madsen P., Gianola D., Klemendstal G., Jensen J., Heringstad B., Korsgaard I.R. (2005) A Bayesian threshold-normal mixture model for analysis of a continuous mastitis-related trait. J. Dairy Sci., 88, 2652– 2659. Samore A.B., Groen A.F., Boettcher P.J., Jamrozik J., Canavesi F., Bagnato A. (2008) Genetic correlation patterns among SCS and protein yield in Italian Holstein Friesian population. J. Dairy Sci., 91, 4013–4021. Schaeffer L.R., Jamrozik J., Kistemaker G.J., Van Doormaal B.J. (2000) Experience with a test day model. J. Dairy Sci., 83, 1135–1144. Shook G.E., Schutz M.M. (1994) Selection on SCC to improve resistance to mastitis in the United States. J. Dairy Sci., 77, 648–658. Van Doormaal B. (2009) Trends in disposal reasons. Holstein J, 72, 40. Windig J.I., Calus M.P.L., de Jong G., Veerkamp R.F. (2005) The association between somatic cell patterns and milk production prior to mastitis. Livest. Prod. Sci., 96, 291–299.
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