Abstract
A mixed hidden Markov model (HMM) was developed for predicting breeding values of a biomarker (here, somatic cell score) and the individual probabilities of health and disease (here, mastitis) based upon the measurements of the biomarker. At a first level, the unobserved disease process (Markov model) was introduced and at a second level, the measurement process was modeled, making the link between the unobserved disease states and the observed biomarker values. This hierarchical formulation allows joint estimation of the parameters of both processes. The flexibility of this approach is illustrated on the simulated data. Firstly, lactation curves for the biomarker were generated based upon published parameters (mean, variance, and probabilities of infection) for cows with known clinical conditions (health or mastitis due to Escherichia coli or Staphylococcus aureus). Next, estimation of the parameters was performed via Gibbs sampling, assuming the health status was unknown. Results from the simulations and mathematics show that the mixed HMM is appropriate to estimate the quantities of interest although the accuracy of the estimates is moderate when the prevalence of the disease is low. The paper ends with some indications for further developments of the methodology.
Highlights
Studies have shown variability among cows for natural resistance to intramammary infection (IMI)
Let ztk 1⁄4 0 if ytk is from an unknown IMIÀ sample and ztk 1⁄4 1 if ytk is from an unknown IMI+ sample
Convergence rates were checked with an EM algorithm and the Gibbs sampler on models similar to those used in the simulation of this study but without genetic covariance structure (SCSi = Mili + ei)
Summary
Studies have shown variability among cows for natural resistance to intramammary infection (IMI). Since these are usually unidentified, breeding values tend to be biased. To reduce this bias and to infer more precisely the cows’ individual probabilities to be IMIÀ or IMI+, several authors have used the mixture model methodology on SCS [2,9,12,17]. A generalization of the mixture model is the hidden Markov model (HMM) that presents the advantages of estimating individual probabilities of being infected and of predicting individual probabilities of new infection and of recovery Both are useful to compute epidemiological measures of IMI spread within a population and to assist mastitis control programs
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