In biomedical applications, non-parametric (e.g. the product-limit survival curve estimator) and semi-parametric (e.g. the Cox proportional hazards model) methods play the most important role, since they have the flexibility to accommodate a wide range of hazard function forms. Still, parametric methods have a place in biomedical research, and may be appropriate when survival data can be shown to approximately follow a particular parametric form. Parametric models are often much easier to work with than the partial-likelihood-based models we have discussed in earlier chapters, since the former are defined by a small and fixed number of unknown parameters. This allows us to use standard likelihood theory for parameter estimation and inference. Furthermore, accommodating complex censoring and truncation patterns is much more direct with parametric models than with partial likelihood models. Of course, the validity of these techniques depends heavily on the appropriateness of the particular parametric model being used. In Chap. 2 we introduced the exponential, Weibull, and gamma distributions, and mentioned several others that could potentially serve as survival distribution models. In this chapter we will emphasize the exponential and Weibull distributions, since these are the most commonly used parametric distributions. We will also briefly discuss the use of some other parametric models in analyzing survival data.
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