Modelling udder infection data using copula models for quadruples. (English) Zbl 1169.62348
Summary: We study copula models for correlated infection times in the four udder quarters of dairy cows. Both a semi-parametric and a nonparametric approach are considered to estimate the marginal survival functions, taking into account the effect of a binary udder quarter level covariate. We use a two-stage estimation approach and we briefly discuss the asymptotic behaviour of the estimators obtained in the first and the second stage of estimation. A pseudo-likelihood ratio test is used to select an appropriate copula from the power variance copula family that describes the association between the outcomes in a cluster.
We propose a new bootstrap algorithm to obtain the \(p\)-value for this test. This bootstrap algorithm also provides estimates for the standard errors of the estimated parameters in the copula. The proposed methods are applied to udder infection data. A small simulation study for a setting similar to the setting of the udder infection data gives evidence that the proposed method provides a valid approach to select an appropriate copula within the power variance copula family.
We propose a new bootstrap algorithm to obtain the \(p\)-value for this test. This bootstrap algorithm also provides estimates for the standard errors of the estimated parameters in the copula. The proposed methods are applied to udder infection data. A small simulation study for a setting similar to the setting of the udder infection data gives evidence that the proposed method provides a valid approach to select an appropriate copula within the power variance copula family.
MSC:
| 62N02 | Estimation in survival analysis and censored data |
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
| 62G10 | Nonparametric hypothesis testing |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 62N01 | Censored data models |
| 62F40 | Bootstrap, jackknife and other resampling methods |
| 62G09 | Nonparametric statistical resampling methods |
| 62G20 | Asymptotic properties of nonparametric inference |
Software:
timeregReferences:
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