Abstract
Shared frailty explains correlations between subjects within clusters. However, it does have some limitations. First, it forces the unobserved factors to be the same within the cluster, which may not always reflect reality. For example, at times, it may be inappropriate to assume that all partners in a cluster share all their unobserved risk factors. Second, the dependence between survival times within the cluster is based on marginal distributions of survival times. However, when covariates are present in a proportional hazards model with gamma-distributed frailty, the dependence parameter and the population heterogeneity are confounded (Clayton and Cuzick 1984)
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Clayton, D.G., Cuzick, J.: Multivariate generalizations of the proportional hazard model (with discussion). J. Roy. Stat. Soc. A, 148, 82–117 (1985)
Hanagal, D.D.: Correlated compound Poisoon frailty model for the bivariate survival data. Int. J. Stat. Manag. Syst. 5, 127–140 (2010)
Hanagal, D.D., Pandey, A.: Correlated inverse Gaussian frailty model for bivariate survival data. Commun. Stat. Theory Methods 48, (to appear) (2019)
Hanagal, D.D., Pandey, A., Ganguly, A.: Correlated gamma frailty models for bivariate survival data. Commun. Stat.: Simul. Comput. 46(5), 3627–3644 (2017)
Hens, N., Wienke, A., Aerts, M., Molenberghs, G.: The correlated and shared frailty model for bivariate current status data: an illustration for cross-sectional serological data. Stat. Med. 28(22), 2785–2800 (2009)
Hougaard, P.: Survival models for hetrogeneous populations derived from stable distributions. Biometrika 73, 387–396 (1986)
Iachine, I.A.: Correlated frailty concept in the analysis of bivariate survival data. Bachelor project, Department of Mathematics and Computer Science, Odense University, Denmark (1995a)
Iachine, I.A.: Parameter estimation in the bivariate correlated frailty model with observed covariates via the EM-algorithm. Working Paper Series: Population Studies of Aging 16, CHS, Odense University, Denmark (1995b)
Kheiri, S., Kimber, A., Meshkani, M.R.: Bayesian analysis of an inverse Gaussian correlated frailty model. Comput. Stat. Data Anal. 51, 5317–5326 (2007)
McGilchrist, C.A., Aisbett, C.W.: Regression with frailty in survival analysis. Biometrics 47, 461–466 (1991)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Hanagal, D.D. (2019). Correlated Gamma and Inverse Gaussian Frailty Models. In: Modeling Survival Data Using Frailty Models. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-15-1181-3_13
Download citation
DOI: https://doi.org/10.1007/978-981-15-1181-3_13
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-1180-6
Online ISBN: 978-981-15-1181-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)