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Bayesian estimation of generalized gamma shared frailty model

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Abstract

Multivariate survival analysis comprises of event times that are generally grouped together in clusters. Observations in each of these clusters relate to data belonging to the same individual or individuals with a common factor. Frailty models can be used when there is unaccounted association between survival times of a cluster. The frailty variable describes the heterogeneity in the data caused by unknown covariates or randomness in the data. In this article, we use the generalized gamma distribution to describe the frailty variable and discuss the Bayesian method of estimation for the parameters of the model. The baseline hazard function is assumed to follow the two parameter Weibull distribution. Data is simulated from the given model and the Metropolis–Hastings MCMC algorithm is used to obtain parameter estimates. It is shown that increasing the size of the dataset improves estimates. It is also shown that high heterogeneity within clusters does not affect the estimates of treatment effects significantly. The model is also applied to a real life dataset.

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Acknowledgements

The first author is grateful to University Grants Commission, Govt. of India for providing financial support for carrying out this work. The authors are also thankful to Department of Science and Technology (DST), Govt. of India for providing support under PURSE grant and are grateful to the referees for their constructive suggestions which have helped immensely in improving the quality of the paper.

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Authors and Affiliations

  1. Department of Statistics, Panjab University, Chandigarh, 160014, India

    Sukhmani Sidhu, Kanchan Jain & Suresh Kumar Sharma

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  1. Sukhmani Sidhu
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  2. Kanchan Jain
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  3. Suresh Kumar Sharma
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Correspondence to Kanchan Jain.

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Sidhu, S., Jain, K. & Sharma, S.K. Bayesian estimation of generalized gamma shared frailty model. Comput Stat 33, 277–297 (2018). https://doi.org/10.1007/s00180-017-0728-0

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  • DOI: https://doi.org/10.1007/s00180-017-0728-0

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