Estimating the Survival and Hazard Functions
This chapter gives an introduction to the simplest concept: estimating the survival curve when there are no covariates. Although simple, it forms a platform for understanding the more complex material that follows. We do it twice, once informally (although making use of counting process ideas) in Section 1, and then a second time with the connections to counting processes and martingales much more complete. Sections 2 and 3 first give an overview of the necessary theory and then apply it to the informal results of Section 1, both validating and extending them. Section 4 discusses the extension to tied data. The reader might want to focus on Section 1 on the first reading, perhaps supplemented with the results (but not derivations) of Sections 3 and 4.
KeywordsHazard Function Failure Time Counting Process Cumulative Hazard Asymptotic Relative Efficiency
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