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A covariance-based test for shared frailty in multivariate lifetime data

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  • Alan Kimber
  • Shah-Jalal Sarker

Abstract

We decompose the score statistic for testing for shared finite variance frailty in multivariate lifetime data into marginal and covariance-based terms. The null properties of the covariance-based statistic are derived in the context of parametric lifetime models. Its non-null properties are estimated using simulation and compared with those of the score test and two likelihood ratio tests when the underlying lifetime distribution is Weibull. Some examples are used to illustrate the covariance-based test. A case is made for using the covariance-based statistic as a simple diagnostic procedure for shared frailty in a parametric exploratory analysis of multivariate lifetime data and a link to the bivariate Clayton--Oakes copula model is shown.

Suggested Citation

  • Alan Kimber & Shah-Jalal Sarker, 2012. "A covariance-based test for shared frailty in multivariate lifetime data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2509-2522, August.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:11:p:2509-2522
    DOI: 10.1080/02664763.2012.720966
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    1. Manatunga, Amita K. & Oakes, David, 1996. "A Measure of Association for Bivariate Frailty Distributions," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 60-74, January.
    2. Klara Goethals & Paul Janssen & Luc Duchateau, 2008. "Frailty models and copulas: similarities and differences," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(9), pages 1071-1079.
    3. Hsieh, Jin-Jian, 2010. "Estimation of Kendall's tau from censored data," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1613-1621, June.
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