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Modeling interval-censored, clustered cow udder quarter infection times through the shared gamma frailty model

Klara Goethals (UGent) , Bart Ampe (UGent) , Dirk Berkvens (UGent) , Hans Laevens, Paul Janssens and Luc Duchateau (UGent)
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Abstract
Time to infection data are often simultaneously clustered and interval-censored. The time to infection is not known exactly; it is only known to have occurred within a certain interval. Moreover, observations often occur in clusters. Consequently, the independence assumption does not hold. Here we propose an extension of the shared gamma frailty model to handle the interval censoring and clustering simultaneously. We show that the frailties can be integrated out analytically, allowing maximization of the marginal likelihood to obtain parameter estimates. We apply our method to a longitudinal study with periodic follow-up on dairy cows to investigate the effect of parameters at the cow level (e.g., parity) and also parameters that can change within the cow (e.g., front or rear udder quarter) on time to infection. Dairy cows were assessed approximately monthly for the presence of a bacterial infection at the udder-quarter level, thus generating interval-censored data. Obviously, the four udder quarters are clustered within the cow. Based on simulations, we find that ignoring the interval-censored nature of the data can lead to biased parameter estimates.
Keywords
Interval censoring, CLINICAL MASTITIS, Mastitis, Multivariate survival data, PROPORTIONAL HAZARDS MODEL, Dairy cow, SOMATIC-CELL COUNT, BOVINE UDDER

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Chicago
Goethals, Klara, Bart Ampe, Dirk Berkvens, Hans Laevens, Paul Janssens, and Luc Duchateau. 2009. “Modeling Interval-censored, Clustered Cow Udder Quarter Infection Times Through the Shared Gamma Frailty Model.” Journal of Agricultural Biological and Environmental Statistics 14 (1): 1–14.
APA
Goethals, Klara, Ampe, B., Berkvens, D., Laevens, H., Janssens, P., & Duchateau, L. (2009). Modeling interval-censored, clustered cow udder quarter infection times through the shared gamma frailty model. JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS, 14(1), 1–14.
Vancouver
1.
Goethals K, Ampe B, Berkvens D, Laevens H, Janssens P, Duchateau L. Modeling interval-censored, clustered cow udder quarter infection times through the shared gamma frailty model. JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS. 2009;14(1):1–14.
MLA
Goethals, Klara et al. “Modeling Interval-censored, Clustered Cow Udder Quarter Infection Times Through the Shared Gamma Frailty Model.” JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS 14.1 (2009): 1–14. Print.
@article{701769,
  abstract     = {Time to infection data are often simultaneously clustered and interval-censored. The time to infection is not known exactly; it is only known to have occurred within a certain interval. Moreover, observations often occur in clusters. Consequently, the independence assumption does not hold. Here we propose an extension of the shared gamma frailty model to handle the interval censoring and clustering simultaneously. We show that the frailties can be integrated out analytically, allowing maximization of the marginal likelihood to obtain parameter estimates. We apply our method to a longitudinal study with periodic follow-up on dairy cows to investigate the effect of parameters at the cow level (e.g., parity) and also parameters that can change within the cow (e.g., front or rear udder quarter) on time to infection. Dairy cows were assessed approximately monthly for the presence of a bacterial infection at the udder-quarter level, thus generating interval-censored data. Obviously, the four udder quarters are clustered within the cow. Based on simulations, we find that ignoring the interval-censored nature of the data can lead to biased parameter estimates.},
  author       = {Goethals, Klara and Ampe, Bart and Berkvens, Dirk and Laevens, Hans and Janssens, Paul and Duchateau, Luc},
  issn         = {1085-7117},
  journal      = {JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS},
  keywords     = {Interval censoring,CLINICAL MASTITIS,Mastitis,Multivariate survival data,PROPORTIONAL HAZARDS MODEL,Dairy cow,SOMATIC-CELL COUNT,BOVINE UDDER},
  language     = {eng},
  number       = {1},
  pages        = {1--14},
  title        = {Modeling interval-censored, clustered cow udder quarter infection times through the shared gamma frailty model},
  url          = {http://dx.doi.org/10.1198/jabes.2009.0001},
  volume       = {14},
  year         = {2009},
}

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