The Frailty Model pp 43-75 | Cite as

# Parametric proportional hazards models with gamma frailty

This chapter discusses the parametric shared frailty model, with a oneparameter gamma frailty factor. The simplicity of this model is twofold: (i) the choice of a gamma frailty makes it possible to formally integrate out the frailties in the conditional survival likelihood resulting in an explicit and simple expression for the marginal likelihood. Although the integration is also feasible for some other frailty distributions, it leads to much more complex expressions (see Chapter 4); (ii) the choice of a parametric baseline hazard means that the marginal likelihood is fully parametric so that we can rely on classical maximum likelihood techniques to estimate the parameters. For most of the examples in this chapter we assume a baseline hazard corresponding to Weibull distributed event times; in a number of practical situations this is an appropriate assumption. The methodology presented in this chapter can easily be extended to other parametric models.

## Keywords

Posterior Density Baseline Hazard Marginal Likelihood Somatic Cell Count Frailty Model## Preview

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