A Nonparametric Frailty Model for Clustered Survival Data

Clayton-type counting process formulations for survival data and parametric gamma models for cluster-specific frailty quantities are now routinely applied in analyses of clustered survival data. On the other hand, although nonparametric frailty models have been studied, they are not used much in pra...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2011-02, Vol.40 (5), p.863-875
Main Author: Manda, Samuel O. M.
Format: Article
Language:English
Subjects:
Algorithms
Applications
Bayesian nonparametric statistics
Clinical trials
Clustering
Clusters
Dirichlet problem
Distribution theory
Exact sciences and technology
Frailty
Frailty modeling
General topics
Mathematical models
Mathematics
Medical sciences
Multivariate analysis
Poly urn sampling
Probability and statistics
Probability theory and stochastic processes
Proportional hazards model
Regression
Risk
Sciences and techniques of general use
Statistics
Studies
Survival
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Summary:Clayton-type counting process formulations for survival data and parametric gamma models for cluster-specific frailty quantities are now routinely applied in analyses of clustered survival data. On the other hand, although nonparametric frailty models have been studied, they are not used much in practice. In this article, the distribution of the frailty terms is assumed to be an unknown random variable. The unknown frailty distribution is then modelled completely with a Dirichlet process prior. This prior assigns cluster units into sub-classes whose members have the same random frailty effect. The Gibbs sampler algorithm is used for computing posterior parameter estimates of the fixed effect hazards regression and the frailty distribution. The methodology is used to analyze community-clustered child survival in sub-Saharan Africa. The results show that the communities could be separated into fewer distinct classes of risk of childhood mortality; the fewer classes could be studied easily in order to provide useful guidance on the more effective use of resources for child health intervention programmes.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610920903480882