Abstract
Starting from the distribution of frailty amongst individuals with lifetimes between t 1 and t 2, we construct a graphical diagnostic for the correct choice of frailty distribution in a proportional hazards model. This is based on a closure property of certain frailty distributions in the case t 2 → ∞ (i.e., among survivors at time t 1), namely that the conditional frailty distribution has the same form as the unconditional, with some parameters remaining the same. We illustrate the plot on the Stanford heart transplant data. We investigate the application of the same principle to the case of shared frailty, where the members of a cluster share a common value of frailty. A similar plot can be used when the cluster lifetime is defined as the shortest lifetime of the cluster’s members. Other definitions of cluster lifetime are less useful for this purpose because the closure property does not apply.
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Economou, P., Caroni, C. (2008). Closure Properties and Diagnostic Plots for the Frailty Distribution in Proportional Hazards Models. In: Vonta, F., Nikulin, M., Limnios, N., Huber-Carol, C. (eds) Statistical Models and Methods for Biomedical and Technical Systems. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4619-6_4
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DOI: https://doi.org/10.1007/978-0-8176-4619-6_4
Publisher Name: Birkhäuser Boston
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Online ISBN: 978-0-8176-4619-6
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