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Genetic Analysis of Somatic Cell Score in Danish Holsteins Using a Liability-Normal Mixture Model

P. Madsen^*,1, M. M. Shariati^*, and J. Ødegård^,

^* Department of Genetics and Biotechnology, Faculty of Agricultural Sciences, University of Aarhus, PO Box 50, DK-8830 Tjele, Denmark
Department of Animal Science, Faculty of Agriculture, University of Yasuj, 75914-353 Yasuj, Iran
NOFIMA Marin, PO Box 5010, N-1432 Ås, Norway
Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, PO Box 5003, N-1432 Ås, Norway

¹ Corresponding author: Per.Madsen{at}agrsci.dk

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
Mixture models are appealing for identifying hidden structures affecting somatic cell score (SCS) data, such as unrecorded cases of subclinical mastitis. Thus, liability-normal mixture (LNM) models were used for genetic analysis of SCS data, with the aim of predicting breeding values for such cases of mastitis. Here, putative mastitis statuses and breeding values for liability to putative mastitis were inferred solely from SCS observations. In total, there were 395,906 test-day records for SCS from 50,607 Danish Holstein cows. Four different statistical models were fitted: A) a classical (nonmixture) random regression model for test-day SCS; B1) an LNM test-day model assuming homogeneous (co)variance components for SCS from healthy (IMI-) and infected (IMI+) udders; B2) an LNM model identical to B1, but assuming heterogeneous residual variances for SCS from IMI- and IMI+ udders; and C) an LNM model assuming fully heterogeneous (co)variance components of SCS from IMI- and IMI+ udders. For the LNM models, parameters were estimated with Gibbs sampling. For model C, variance components for SCS were lower, and the corresponding heritabilities and repeatabilities were substantially greater for SCS from IMI- udders relative to SCS from IMI+ udders. Further, the genetic correlation between SCS of IMI- and SCS of IMI+ was 0.61, and heritability for liability to putative mastitis was 0.07. Models B2 and C allocated approximately 30% of SCS records to IMI+, but for model B1 this fraction was only 10%. The correlation between estimated breeding values for liability to putative mastitis based on the model (SCS for model A) and estimated breeding values for liability to clinical mastitis from the national evaluation was greatest for model B1, followed by models A, C, and B2. This may be explained by model B1 categorizing only the most extreme SCS observations as mastitic, and such cases of subclinical infections may be the most closely related to clinical (treated) mastitis.

Key Words: Bayesian method • mastitis • mixture model • somatic cell score

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
Breeding programs using SCC records in genetic selection for improved udder health to date have been based on either cross-sectional models (e.g., lactation mean SCS) or test-day models (e.g., repeatability models, random regression models) for genetic evaluations. These models are typically focused on selecting animals with the lowest average SCS. Several studies have found a positive genetic correlation between SCS level and risk of clinical mastitis (Mrode and Swanson, 1996). However, simply selecting for lower average SCS might not be the most optimal way of utilizing SCC data in selection for improved udder health. To illustrate this, Green et al. (2004) found that the within-lactation variation of test-day SCS and the maximum test-day SCS were the best indicators of clinical mastitis, rather than mean SCS. Lactation average and standard test-day models for SCS do not discriminate between SCS from healthy and diseased animals (because health status is usually unknown), and will thus assume identical location and dispersion parameters for SCS irrespective of infection status. Further, selection for lower SCS might favor not only cows having lower incidence of IMI, but also cows having lower levels of SCC when healthy ("baseline" SCC). Detilleux and Leroy (2000) have argued that high "baseline" SCC may increase resistance to IMI, and they have therefore suggested the use of mixture models for analysis of SCC test-day data.

Previous studies (Detilleux et al., 1997; de Haas et al., 2004) have found that SCC and the proportion of different somatic cell types differ dramatically with respect to IMI status. Generally, the proportion of poly-morphonuclear neutrophils in SCC changes dramatically, from mainly 5 to 20% in healthy glands to more than 95% in infected glands. Consequently, SCS from udders with or without IMI might be partially different traits and might be under different genetic control. Further, the cows’ response to infection, with respect to both increase in SCC and change in composition, might be associated with the subsequent recovery rate.

Two-component normal mixture models have been developed, taking the mixture distribution of SCS into account, by using either Bayesian (Ødegård et al., 2003) or maximum likelihood techniques (Gianola et al., (2004). In these models, SCS was assumed to be normally distributed, with either homogeneous (Gianola et al., 2004) or heterogeneous residual variances (Ødegård et al., 2003), and with location parameters including both systematic and random effects. The expected increase in test-day SCS as a result of IMI was accounted for by including the effect of putative IMI status among the location parameters for SCS (in addition to effects such as herd-year-season, age at calving, and stage of lactation). However, these models assumed identical a priori probabilities of IMI for all animals and all observations within animal. Previous analyses of clinical mastitis field data have identified numerous systematic (e.g., herd-year-season, age at calving, stage of lactation) and random effects (e.g., genetic, permanent environment) that affect the probability of mastitis infection (Chang et al., 2004). Hence, assigning the same prior probability of IMI to all animals at all test-days is not realistic in real data. Further, these mixture models did not provide a sufficient tool for genetic selection for a lower probability of mastitis, given the observed SCS, because all genetic effects were calculated for the SCS level, adjusted for mastitis effects. A more realistic hierarchical statistical model was developed by Ødegård et al. (2005), based on the method and model described in Ødegård et al. (2003). The new model was described as a liability-normal mixture (LNM) model.

In the LNM, udder health status (which is an unobserved binary variable) is assumed to be fully determined by an unobserved underlying liability (threshold model). Further, location parameters for the liability may include both systematic and random effects, allowing for the probability that IMI may differ among animals (e.g., because of herd-year-season, genetic, and permanent environmental effects) as well as between observations within animal (e.g., because of effects of lactation stage, herd-test-day). Based on observed test-day SCS, the LNM model predicts genetic effects for both SCS and the unobserved liability to IMI (mastitis), where the latter can be used in genetic selection for improved udder health. As previously stated, genetic level of "baseline" SCS may have some relevance for risk of subsequent infection, and may therefore contain valuable information for genetic improvement of udder health. Such potentially valuable information was used by including a covariance structure between the random effects for SCS and liability to IMI in the model.

The original LNM model (Ødegård et al., 2003) assumed that random animal effects (genetic and nongenetic) were independent of IMI categories. This assumption could be relaxed by introducing separate, but possibly correlated, random animal effects (genetic and nongenetic) for SCS in healthy (IMI-) and diseased (IMI+) cows. Because both IMI categories can be represented within the test-day observations of a single cow (although not at the same time), it should be possible to obtain estimates describing this covariance structure. This results in 2 breeding values for SCS (under IMI- and IMI+) for all animals in the relationship matrix, and in 2 nongenetic animal effects for all animals with data.

Our first aim was to implement this idea in a modified LNM model and apply it on real test-day SCS data. The second aim was to compare its suitability with simpler models for use in practical selection for improved resistance to mastitis.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
Data
A data set consisting of monthly SCS records collected from 10 to 315 d postpartum from 50,607 first-lactation Danish Holstein cows was extracted from the Danish national cattle database. To be included, the following criteria were required: calving from 1990 through 2003, age at calving from 18 through 38 mo, and belonging to a herd with at least 5 primiparous cows per year in the period 1999 through 2003. Summary statistics for the sampled data are provided in Table 1.

Setting and notation are as in Ødegård et al. (2005). In short, the data consist of n measurements of SCS. A 2-component normal mixture model poses that the ith measurement of SCS, given some location and dispersion parameters (a) and probabilities (P) has the mixture density

[1]

with P = [P₁, P₂, ... , P_n]’ where P_i is the a priori probability that SCS_i is drawn from distribution N(•) [i.e., the a priori probability of being infected (IMI+)], whereas (1 - P_i) is the a priori probability that SCS_i is drawn from N^*(•) [i.e., the a priori probability of not being infected (IMI-)]. Further, f_i (), g_i (), f_i^*(), and g_i^*() are functions of the parameter vector . Typically, f_i () and f_i^*() are linear combinations of fixed and random effects, g_i^*() = ²_e0SCS and g_i() = ²_e1SCS, for all i = 1, 2, ..., n, where ²_e0SCS and ²_e1SCS are variance parameters. Given and P, observations were assumed to be conditionally independent, so that the joint density of the data vector SCS is

[2]

Estimation is facilitated by augmenting the density above with auxiliary binary indicator (IMI – 0, IMI+ 1) variables Z_i (i = 1, 2, ..., n). Assuming that the indicator variables are Bernoulli distributed and are conditionally independent a priori, one can write

[3]

Given P, Z does not depend on , and Pr(Z_i = 1 P_i) = P_i is the prior probability that the status of i is IMI+, allowing for individual prior probabilities of mastitis.

An underlying continuous random variable, called liability ( ), is assumed, which determines the mastitis status associated with each observation (Z_i). It is assumed that Z_i switches from 0 to 1 if liability exceeds a given threshold T (assumed T = 0). Further, according to Z_i, the "true" distribution of SCS switches from N*(•) to N(•), and putative mastitis status may therefore be inferred from the observed SCS. Thus, the a priori probability of IMI+ for a specific SCS observation i can be written as

[4]

so that

As in Ødegård et al. (2005), it is assumed that

[5]

implying that the residual correlation between SCS and liability is set to zero.

Modeling SCS and Liabilities
Let

where

and

are vectors of "fixed" (β), random herd-test-day (h), random additive genetic (a), and random permanent environmental (pe) effects on SCS and liability to mastitis, where the subvector β_0SCS, a_0SCS, or pe_0SCS includes effects affecting SCS in all cows irrespective of IMI status, whereas β_1SCS, a_1SCS, or pe_1SCS includes effects peculiar to SCS in cows with IMI. Further, H₀ is the 2 x 2 (co)variance matrix of herd-test-day effects, G₀ is the 3 x 3 (co)variance matrix of additive genetic effects, and Pe₀ is the 3 x 3 (co)variance matrix of permanent environmental effects; _e0SCS² and _e1SCS² are the residual variances of SCS in IMI- and IMI+ classes, respectively. Given IMI status (Z) and a, SCS can be modeled as a Gaussian trait, allowing for heterogeneous (co)variance components for the 2 disease categories. The density of the conditional distribution of all SCS, given Z = z and a is

[6]

where I(.) is an indicator function taking the value of 1 if the condition (.) is true and zero otherwise.

It is assumed that

where x' and w' with appropriate subscripts are incidence row vectors. Further, it is assumed that the _i, given a are mutually independent, so that the density of the vector, given is

[7]

where the distribution of , given , is

With this structure, [4] is equivalent to

[8]

where (•) is the standard normal cumulative distribution function and _i is the expectation of the liability of observation i, conditionally on β, h, a, and pe .

Bayesian Structure
Conditional Density of SCS.
The conditional distribution of the data given the parameters (P, ) is p (SCS P, ) as in [2]. Further, the conditional distribution of SCS, given and Z, is given in [6]. Also from [5],

Prior Density of All Unknown Parameters.
The joint prior density of all unknown parameters, including the liabilities (), is

[9]

Given , Z is completely specified, and Pr(Z = z|) is therefore a degenerate distribution. The density p (|) is defined in [7], and the density p () is

[10]

where

and

were assigned bounded uniform priors. To achieve vague priors, the absolute values of the bounds were large. Further, to avoid "label-switching" problems (Mclachlan and Peel, 2000), constraints must be imposed on parameters of the SCS distributions of putative IMI- and IMI+ animals; for example, the mean SCS in the IMI- group was set to be lower than that in the IMI+ group.

Herd-test-day effects (h), additive breeding values (a), and permanent environmental effects (pe) were assumed to be normally distributed, with the densities

[11]

[12]

[13]

where A is the additive relationship matrix with dimension q_a; I_h and I_pe are identity matrices, with dimensions q_h (number of herd-test-days) and q_pe (number of individuals with at least one SCS record); and H₀, G₀, and Pe₀ are as previously defined.

Joint Posterior Density.
The augmented joint posterior density of all unknowns is

[14]

with p (, ,Z = z) as defined in [9].

Fully Conditional Posterior Distributions.
As in Ødegård et al. (2005), all fully conditional posterior distributions have a standard form, given Z and . The required posterior distributions are as in a linear Gaussian model: 1) the conditional posterior distribution of each element of β is normal, truncated in some interval [d₁, d₂]; 2) the conditional distributions of h, a, and pe are multivariate normal; 3) the densities of H₀, G₀, and Pe₀ are inverse Wishart; and 4) the conditional distributions of ²_e0SCS and ²_e1SCS are inverse gamma

Further,

[15]

with p(|,Z =z, SCS) = p(|,Z= z), because the liabilities are independent of SCS, given ± and Z = z. The parameter _i (Pr(Z_i =1 SCS_i , )) of the fully conditional posterior distribution of Z_i is

[16]

where _i is the expected liability. Hence, Z_i can be sampled from a Bernoulli distribution with probability of success (putative mastitis) _i. Subsequently, given Z_i, _i can be sampled from a distribution with density

[17]

In other words, the fully conditional distribution of _i, given Z_i, is a truncated standard normal distributionTN(_i|) , with right truncation for Z_i = 0, and left truncation for Z_i = 1.

The Gibbs sampling procedure, as described in Ødegård et al. (2005) and implemented in the DMU package (Madsen and Jensen, 2007), was used for the analysis. In total, 120,000 cycles were generated; the first 20,000 were discarded as burn-in, and posterior means and standard deviations were calculated based on retaining samples from every 10th cycle of the remaining cycles.

Model Comparison
For comparison purposes, 4 statistical models were used to analyze these data, a nonmixture repeatability model for test-day SCS (A); 2 LNM models assuming identical random effects irrespective of IMI status, one assuming identical ²_e0SCS and ²_e1SCS (B1), and one accommodating specific residual variances for SCS in the 2 mixture components (B2, as in Ødegård et al., 2005); and an LNM model assuming the random effects to be mixtures depending on IMI status (C). More specifically,

A:

B1 and B2:

C:

where β_0SCS and β vectors include effects of age and regression coefficients for days carrying calf, proportion of Holstein genes, total breed heterozygosity, Legendre polynomials of DIM up to the second order, and a Wilmink polynomial (e^–0.09DIM) (adapted from Finnish work on an SCS test-day model; Negussie et al., 2006), with X as the appropriate incidence matrix. The vector β_1SCSC includes only the systematic effect of mastitis on the SCS level, and is associated with the observations through a diagonal matrix M_z. The latter is a diagonalization of Z (the vector containing the assumed health status for all observations).

It should be noted that models A, B1, and B2 are submodels of model C, because model B2 can be obtained from model C by restricting the elements of a_1SCS and pe_1SCS to be null, model B1 can be obtained from model B2 by restricting the residual variances to be identical, and model A can be obtained from B1, B2, and C by restricting M_z to be a null matrix and assume no liability variation.

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
The posterior means of putative mastitis frequencies (mixing proportions) and estimated means for test-day SCS and SCC of cows in the IMI- and IMI+ classes for the 3 LNM models are shown in Table 2. The models B2 and C resulted in almost similar mixing proportions of approximately 30% and estimated SCC in the IMI- and IMI+ groups. The typical SCC level for putatively mastitic cows predicted by using these models (157,500 and 146,000 cells/mL for models B2 and C, respectively) are lower than the expected level of SCC in cows with clinical mastitis (Lam et al., 1997). On the contrary, model B1 allocates only 10% of records to the IMI+ class with a rather high SCC level (787,500 cells/mL). In model B1, the heterogeneity in residual variances in mixture components is not taken into account. This could possibly explain why only records with very high SCS are allocated to the IMI+ component. It should be noted, however, that putative mastitis based on SCC records is probably more closely connected with subclinical cases of mastitis than with clinical cases, because farmers usually do not take samples from cows with clinical mastitis. In general, this will lead to missing observations for SCC from cows with clinical mastitis on a given test day. Implementing a mixture model with 3 components representing healthy, mild subclinical mastitis, and severe subclinical mastitis classes might be appealing in future research

Table 4 has estimates of residual variances, heritabilities, and repeatabilities for the models A, B1, B2, and C. The residual variance for the repeatability model A is twice the one from LNM model B1 (0.604 vs. 0.295), which is because classical SCS models do not take mean differences of mixture components into account (Ødegård et al., 2005; Boettcher et al., 2007). This also holds for genetic and permanent environmental variance components (not shown). Mean SCS equal to 4.30 and 6.67 for IMI– and IMI+ groups (Table 2) and a common residual variance equal to 0.295 (Table 4) represent a mixture distribution with well-separated components for model B1. By contrast, LNM models B2 and C produced highly overlapping mixture components. For these models, estimated means of mixture components were not far apart (Table 2), and residual variance for putatively infected cows (_e1SCS²) was very large (Table 4). Further, LNM models B2 and C yielded almost identical posterior means of residual variance for healthy cows (_e0SCS²), whereas the posterior mean of residual variance for mastitic cows (_e1SCS²) from model B2 was larger than the one from model C. The reduction in residual variance for model C indicates that this model fits the data better than model B2, probably because model C allows for different genetic and permanent environmental variances in the 2 classes. The variability in heritabilities and repeatabilities for different models is mostly determined by the magnitude of their residual variances.

To compare the performance of the LNM submodels, correlations among predicted breeding values for liability to putative mastitis and correlation between phenotypic probabilities for mastitis when using the different LNM models were calculated (Table 6). Predictions from model B2 and model C showed correlations near unity, indicating that one can implement the simpler model (B2) if predicting breeding values for liability to mastitis is the target. The full LNM model (C) is greatly demanding computationally. Therefore, reducing the number of parameters and high dimensional genetic effects can lower the computing costs accordingly.

	CONCLUSIONS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

	ACKNOWLEDGEMENTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
This research was financially supported by a grant form the Danish Cattle Federation (Aarhus, Denmark). The Danish Agricultural Advisory Service, Aarhus, Denmark, is acknowledged for providing data.

Received for publication February 27, 2008. Accepted for publication June 26, 2008.

	REFERENCES

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 


Boettcher, P. J., D. Caraviello, and D. Gianola. 2007. Genetic analysis of somatic cell scores in US Holsteins with a Bayesian mixture model. J. Dairy Sci. 90:435–443.[Abstract/Free Full Text]

Calo, L. L., R. E. McDowell, L. D. VanVleck, and P. D. Miller. 1973. Genetic aspects of beef production among Holstein-Friesians pedigree selected for milk production. J. Anim. Sci. 37:676–682.[Abstract/Free Full Text]

Chang, Y. M., D. Gianola, B. Heringstad, and G. Klemetsdal. 2004. Longitudinal analysis of clinical mastitis at different stages of lactation in Norwegian cattle. Livest. Prod. Sci. 88:251–261.[CrossRef]

Danish Cattle Federation. 2006. Principles of Danish cattle breeding. http://www.lr.dk/kvaeg/diverse/principles.pdf Accessed Jan. 20, 2008.

de Haas, Y., R. F. Veerkamp, H. W. Barkema, Y. T. Grohn, and Y. H. Schukken. 2004. Associations between pathogen-specific cases of clinical mastitis and somatic cell count patterns. J. Dairy Sci. 87:95–105.[Abstract/Free Full Text]

Detilleux, J., P. Leroy, and D. Volckaert. 1997. Alternative use of somatic cell counts in genetic selection for mastitis resistance. Pages 34–44 in Proc. Int. Workshop on Genetic Improvement of Functional Traits in Cattle: Health. Interbull Bull. No. 15. Int. Bull Eval. Serv., Uppsala, Sweden.

Detilleux, J., and P. L. Leroy. 2000. Application of a mixed normal mixture model for the estimation of mastitis-related parameters. J. Dairy Sci. 83:2341–2349.[Abstract]

Gianola, D., J. Ødegård, B. Heringstad, G. Klemetsdal, D. Sorensen, P. Madsen, J. Jensen, and J. Detilleux. 2004. Mixture model for inferring susceptibility to mastitis in dairy cattle: A procedure for likelihood-based inference. Genet. Sel. Evol. 36:3–27.[Medline]

Green, M. J., L. E. Green, Y. H. Schukken, A. J. Bradley, E. J. Peeler, H. W. Barkema, Y. de Haas, V. J. Collis, and G. F. Medley. 2004. Somatic cell count distributions during lactation predict clinical mastitis. J. Dairy Sci. 87:1256–1264.[Abstract/Free Full Text]

Heringstad, B., R. Rekaya, D. Gianola, G. Klemetsdal, and K. A. Weigel. 2001. Bayesian analysis of liability of clinical mastitis in Norwegian cattle with a threshold model: Effects of data sampling method and model specification. J. Dairy Sci. 84:2337–2346.[Abstract]

Lam, T. J.,, J. H. vanVliet, Y. H. Schukken, F. J. Grommers, A. vanVelden-Russcher, H. W. Barkema, and A. Brand. 1997. The effect of discontinuation of postmilking teat disinfection in low somatic cell count herds. 2. Dynamics of intramammary infections. Vet. Q. 19:47–53.[Medline]

Madsen, P., and J. Jensen. 2007. DMU: A User’s Guide. A Package for Analysing Multivariate Mixed Models. Version 6, Release 4.7. http://dmu.agrsci.dk/dmuv6_guide-R4-6-7.pdf Accessed Nov. 15, 2007.

Mclachlan, G., and D. Peel. 2000. Finite Mixture Models. Wiley, New York, NY.

Mrode, R. A., and G. J. T. Swanson. 1996. Genetic and statistical properties of somatic cell count as an indirect measure of reducing the incidence of mastitis in dairy cattle. Anim. Breeding Abstr. 64:847–857.

Negussie, E., M. Koivula, E. A. Mantysaari, and M. Lidauer. 2006. Genetic evaluation of somatic cell score in dairy cattle considering first and later lactations as two different but correlated traits. J. Anim. Breed. Genet. 123:224–238.[CrossRef][Medline]

Ødegård, J., J. Jensen, P. Madsen, D. Gianola, G. Klemetsdal, and B. Heringstad. 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.[Abstract/Free Full Text]

Ødegård, J., P. Madsen, D. Gianola, G. Klemetsdal, J. Jensen, B. Heringstad, and I. R. Korsgaard. 2005. A Bayesian threshold-normal mixture model for analysis of a continuous mastitis-related trait. J. Dairy Sci. 88:2652–2659.[Abstract/Free Full Text]

Robertson, A. 1959. The sampling variance of the genetic correlation coefficient. Biometrics 15:469–485.[CrossRef]

This Article Abstract Full Text (PDF) Interpretive Summary Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Madsen, P. Articles by Ødegård, J. Search for Related Content PubMed Articles by Madsen, P. Articles by Ødegård, J.