Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-26T20:09:22.941Z Has data issue: false hasContentIssue false
  • English
  • Français

A hidden Markov model to predict early mastitis from test-day somatic cell scores

Published online by Cambridge University Press:  17 September 2010

J. C. Detilleux
J. C. Detilleux*
Affiliation:
Veterinary Faculty, Department of Quantitative Genetics, University of Liège, 4000 Liège, Belgium
*
†E-mail: [email protected]
Get access

Abstract

In many countries, high somatic cell scores (SCS) in milk are used as an indicator for mastitis because they are collected on a routine basis. However, individual test-day SCS are not very accurate in identifying infected cows. Mathematical models may improve the accuracy of the biological marker by making better use of the information contained in the available data. Here, a simple hidden Markov model (HMM) is described mathematically and applied to SCS recorded monthly on cows with or without clinical mastitis to evaluate its accuracy in estimating parameters (mean, variance and transition probabilities) under healthy or diseased states. The SCS means were estimated at 1.96 (s.d. = 0.16) and 4.73 (s.d. = 0.71) for the hidden healthy and infected states, and the common variance at 0.83 (s.d. = 0.11). The probability of remaining uninfected, recovering from infection, getting newly infected and remaining infected between consecutive test days was estimated at 78.84%, 60.49%, 11.70% and 15%, respectively. Three different health-related states were compared: clinical stages observed by farmers, subclinical cases defined for somatic cell counts below or above 250 000 cells/ml and infected stages obtained from the HMM. The results showed that HMM identifies infected cows before the appearance of clinical and subclinical signs, which may critically improve the power of the studies on the genetic determinants of SCS and reduce biases in predicting breeding values for SCS.

Keywords

mastitishidden Markov modelsomatic cell counts
Type
Full Paper
Information
animal , Volume 5 , Issue 2 , February 2011 , pp. 175 - 181
Copyright
Copyright © The Animal Consortium 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, RM, May, RM 1992. Infectious diseases of humans. Oxford Science Publications, Oxford.Google Scholar
Altman, RM 2007. Mixed hidden Markov model: an extension of the hidden Markov model to the longitudinal data setting. Journal of the American Statistical Association 102, 201–210.CrossRefGoogle Scholar
Barkema, HW, Schukken, YH, Lam, TJGM, Beiboer, ML, Wilmink, H, Benedictus, G, Brand, A 1998. Incidence of clinical mastitis in dairy herds grouped in three categories by bulk milk somatic cell counts. Journal of Dairy Science 81, 411–419.CrossRefGoogle ScholarPubMed
Bilmes, JA 1998. A gentle tutorial of the EM algorithm and its application to parameter estimation for Gaussian mixture and Hidden Markov models. Technical report, University of Berkeley.Google Scholar
Bishop, SC, Woolliams, JA 2010. On the genetic interpretation of disease data. PLoS ONE 5 (1), e8940, doi:10.1371/journal.pone.0008940.CrossRefGoogle ScholarPubMed
Boettcher, PJ, Moroni, P, Pisoni, G, Gianola, D 2005. Application of finite mixture model to somatic cell scores of Italian goats. Journal of Dairy Science 88, 2209–2216.CrossRefGoogle ScholarPubMed
Brookhart, MA, Hubbard, AE, van der Laan, MJ, Colford, JM Jr, Eisenberg, JN 2002. Statistical estimation of parameters in a disease transmission model: analysis of a Cryptosporidium outbreak. Statistics in Medicine 21, 3627–3638.CrossRefGoogle Scholar
Buyske, S, Yang, G, Matise, TC, Gordon, D 2009. When a case is not a case: effects of phenotype misclassification on power and sample size requirements for the transmission disequilibrium test with affected child trios. Human Heredity 67, 287–292.CrossRefGoogle Scholar
Cooper, B, Lipstich, M 2004. The analysis of hospital infection data using hidden Markov models. Biostatistics 5, 223–237.CrossRefGoogle ScholarPubMed
de Haas, Y, Barkema, HW, Veerkamp, RF 2002. The effect of pathogen-specific clinical mastitis on the lactation curve for somatic cell count. Journal of Dairy Science 85, 1314–1323.CrossRefGoogle ScholarPubMed
de Haas, Y, Veerkamp, RF, Barkema, HW, Gröhn, YT, Schukken, YH 2004. Associations between pathogen-specific cases of clinical mastitis and somatic cell count patterns. Journal of Dairy Science 87, 95–105.CrossRefGoogle ScholarPubMed
Detilleux, JC, Leroy, P 2000. Application of a mixed normal mixture model for the estimation of mastitis-related parameters. Journal of Dairy Science 83, 2341–2349.CrossRefGoogle ScholarPubMed
Detilleux, JC, Vangroenweghe, F, Burvenich, C 2006. Mathematical model of the acute inflammatory response to Escherichia coli intramammary challenge. Journal of Dairy Science 89, 3455–3465.CrossRefGoogle ScholarPubMed
Detilleux, JC 2008. The analysis of disease biomarker data using a mixed hidden Markov model. Genetics Selection Evolution 40, 491–509.Google ScholarPubMed
Djabri, B, Bareille, N, Beaudeau, F, Seegers, H 2002. Quarter milk somatic cell count in infected dairy cows: a meta-analysis. Veterinary Research 33, 335–357.CrossRefGoogle ScholarPubMed
Ephraim, Y, Roberts, W 2005. Revisiting autoregressive hidden Markov modeling of speech signals. IEEE Signal Processing Letters 12, 166–169.CrossRefGoogle Scholar
Eisner, J 2002. An interactive spreadsheet for teaching the forward-backward algorithm. Conference at the ACL-02 Workshop on Effective Tools and Methodologies for Teaching Natural Language Processing and Computational Linguistics, Philadelphia, Pennsylvania, pp. 10–18.CrossRefGoogle Scholar
Gianola, D 2005. Prediction of random effects in finite mixture models with Gaussian components. Journal of Animal Breeding and Genetics 122, 145–159.CrossRefGoogle ScholarPubMed
Godden, SM, Jansen, JT, Leslie, KE, Smart, NL, Kelton, DF 2002. The effect of sampling time and sample handling on the detection of Staphylococcus aureus in milk from quarters with subclinical mastitis. Canadian Veterinary Journal 43, 38–42.Google ScholarPubMed
Horton, NJ, Kleinman, KP 2007. Much ado about nothing: a comparison of missing data methods and software to fit incomplete data regression models. The American Statistician 61, 79–90.CrossRefGoogle ScholarPubMed
Jaakkola, T, Jordan, MI 2000. Bayesian parameter estimation via variational methods. Statistics and Computing 10, 25–37.CrossRefGoogle Scholar
Lam, T, van Wuijckhuise, LA, Franken, P, Morselt, ML, Hartman, EG, Schukken, YH 1996. Use of composite milk samples for diagnosis of Staphylococcus aureus mastitis in dairy cattle. Journal America Veterinary Medical Association 208, 1705–1708.CrossRefGoogle ScholarPubMed
Laverty, WH, Miket, MJ, Kelly, IW 2002. Simulation of hidden Markov models with EXCEL. The Statistician 51, 31–40.CrossRefGoogle Scholar
Le Strat, Y, Carrat, F 1999. Monitoring epidemiologic surveillance data using hidden Markov models. Statistics in Medicine 18, 3463–3478.3.0.CO;2-I>CrossRefGoogle ScholarPubMed
Moroni, P, Pisoni, G, Vimercati, C, Rinaldi, M, Castiglioni, B, Cremonesi, P, Boettcher, P 2005. Characterization of Staphylococcus aureus isolated from chronically infected dairy goats. Journal of Dairy Science 88, 3500–3509.CrossRefGoogle ScholarPubMed
Paape, M, Mehrzad, J, Zhao, X, Detilleux, J, Burvenich, C 2002. Defense of the bovine mammary gland by polymorphonuclear neutrophil leukocytes. Journal of Mammary Gland Biology Neoplasia 7, 109–121.CrossRefGoogle ScholarPubMed
Rabiner, LR 1989. A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE 77, 257–268.CrossRefGoogle Scholar
Sargeant, JM, Leslie, KE, Shirley, JE, Pulkrabek, BJ, Lim, GH 2001. Sensitivity and specificity of somatic cell count and California mastitis test for identifying intramammary infection in early lactation. Journal of Dairy Science 84, 2018–2024.CrossRefGoogle ScholarPubMed
SAS OnlineDoc™ (1999). Version 8. Statistical Analysis System.Google Scholar
Sears, PM, Smith, BS, English, PB, Herer, PS, Gonzales, RN 1990. Shedding pattern of Staphylococcus aureus from bovine intramammary infections. Journal of Dairy Science 73, 2785–2789.CrossRefGoogle ScholarPubMed
Shook, GE, Schutz, MM 1994. Selection on somatic cell score to improve resistance to mastitis in the United States. Journal of Dairy Science 77, 648–658.CrossRefGoogle ScholarPubMed
Suriyasathaporn, W, Schukken, YT, Nielen, M, Brand, A 2000. Low somatic cell count: a risk factor for subsequent clinical mastitis in a dairy herd. Journal of Dairy Science 83, 1248–1255.CrossRefGoogle Scholar