where jointijkl is the joint test result (of BC and SCC) of the ith udder half of the jth goat of the kth herd at the lth sampling,SCC is the somatic cell count as a binary variable with a cut-off of 2000×103 cells/mL, BC is the bacteriological culture as a binary variable (culture of a major pathogen or not), IMIijkl is the true (but latent) infection status, Se is the
sensitivity, Sp is the specificity, represents the intercept,Xijkl represents the effects of the independent variables, jkl
represents the random effect of the jth goat in the kth herd at the lth sampling and ık represents the random effect of the kth herd. Hierarchical centering was used in an attempt to improve the correlation properties of the chains and to reduce the time per update (the OpenBUGS code for the model is given in Appendix A, together with a brief discussion
on an alternative specification of the same model).
The estimated fixed effects in the above model correspond
to cluster specific (CS) estimates, which essentially
model the effect of the RF within a goat within a herd,
something which is meaningless for say, parity. Thus,more informative inference can be made from populationaverage
(PA) estimates, i.e. the effect of an RF across goats
within the same herd. Population-averaged odds ratios
of the fixed effects were calculated in OpenBUGS by first
transforming the obtained regression coefficients (betas) to
population-averaged parameters, using the formula from
Dohoo et al. (2009):
where jointijkl is the joint test result (of BC and SCC) of the ith udder half of the jth goat of the kth herd at the lth sampling,SCC is the somatic cell count as a binary variable with a cut-off of 2000×103 cells/mL, BC is the bacteriological culture as a binary variable (culture of a major pathogen or not), IMIijkl is the true (but latent) infection status, Se is the
sensitivity, Sp is the specificity, represents the intercept,Xijkl represents the effects of the independent variables, jkl
represents the random effect of the jth goat in the kth herd at the lth sampling and ık represents the random effect of the kth herd. Hierarchical centering was used in an attempt to improve the correlation properties of the chains and to reduce the time per update (the OpenBUGS code for the model is given in Appendix A, together with a brief discussion
on an alternative specification of the same model).
The estimated fixed effects in the above model correspond
to cluster specific (CS) estimates, which essentially
model the effect of the RF within a goat within a herd,
something which is meaningless for say, parity. Thus,more informative inference can be made from populationaverage
(PA) estimates, i.e. the effect of an RF across goats
within the same herd. Population-averaged odds ratios
of the fixed effects were calculated in OpenBUGS by first
transforming the obtained regression coefficients (betas) to
population-averaged parameters, using the formula from
Dohoo et al. (2009):
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