Parametric counting process models
In biostatistics it has become a tradition to use non- and semiparametric methods, like those considered in the previous two chapters, to analyze censored survival data, while parametric methods are more common in reliability studies of failure times of technical equipment. In our opinion biostatistics would gain from the use of a wider range of statistical methods, including parametric methods, than is the current practice. In this chapter, we discuss the basic modeling and inferential issues for parametric counting process models. More advanced models and methods are discussed in Chapters 6, 7, 10, and 11.
We focus on likelihood inference in this chapter. In Section 5.1 we derive the likelihood for parametric counting process models, review the basic properties of the maximum likelihood estimator, and give some simple examples of parametric inference. Parametric regression models are considered in Section 5.2, with a focus on the so-called Poisson regression model. In Section 5.3, we give an outline of the derivations of the large sample properties of the maximum likelihood estimator.
KeywordsMaximum Likelihood Estimator Baseline Hazard Intensity Process Partial Likelihood Marriage Cohort
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