From Basic Survival Analytic Theory to a Non-Standard Application

verfasst von: Georg Zimmermann

Verlag: Springer Fachmedien Wiesbaden

Buchreihe : BestMasters

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Georg Zimmermann provides a mathematically rigorous treatment of basic survival analytic methods. His emphasis is also placed on various questions and problems, especially with regard to life expectancy calculations arising from a particular real-life dataset on patients with epilepsy. The author shows both the step-by-step analyses of that dataset and the theory the analyses are based on. He demonstrates that one may face serious and sometimes unexpected problems, even when conducting very basic analyses. Moreover, the reader learns that a practically relevant research question may look rather simple at first sight. Nevertheless, compared to standard textbooks, a more detailed account of the theory underlying life expectancy calculations is needed in order to provide a mathematically rigorous framework.

Inhaltsverzeichnis

Frontmatter

Introduction

Abstract

Survival analysis, or, more generally speaking, the analysis of timeto-event data, is an important issue in mathematical theory as well as in many fields of applied statistics. To begin with, at least some basic examples concerning waiting times are done at school. When studying Mathematics at university, the discussion of “waiting time distributions” like the geometric or exponential distribution is part of every introductory course to Stochastics.

Georg Zimmermann

Basic terminology and quantities

Abstract

We first describe how survival time can be appropriately modeled and define some basic quantities which characterize the survival time distribution. Then, we introduce some terminology and notation of survival time samples. In this context, we will also precisely state what censoring means.

Georg Zimmermann

Regression models for survival data

Abstract

In this chapter, we, at first, give a short explanation why regression models are needed for many different types of survival data. Then, we introduce two very popular classes of survival analytic regression models and discuss the relationship between them. When examining the epilepsy dataset, we repeatedly use a particular parametric model called the Weibull model, which is therefore defined in this chapter.

Georg Zimmermann

Model checking procedures

Abstract

In this chapter, we will basically address two important issues: Firstly, we will present some methods for checking, let’s say, the basic assumptions underlying a particular model. For example, when considering a Weibull model, we have to answer the following questions.

Georg Zimmermann

Life expectancy

Abstract

The main goal of this chapter is to discuss a method for comparing life expectancies, as proposed in Zimmermann [31]. To begin with, let us recall some facts about the interpretation of several survival analytic key quantities. Especially, I’d like to emphasize once again that the survival function S basically provides information on surviving beyond a specified time point t, whereas the hazard rate can be interpreted as a measure of the instantaneous risk of experiencing the event at time t.

Georg Zimmermann

Epilogue

Abstract

Instead of merely summarizing the main results of the previous chapters, I want to give a short outline of the “pathway” which led to my master’s thesis. In this short final part, the focus won’t be on scientific writing any more. Now, the main goal is to give the reader the possibility to see how I actually worked on this topic.

Georg Zimmermann

Backmatter

Titel: From Basic Survival Analytic Theory to a Non-Standard Application
verfasst von: Georg Zimmermann
Verlag: Springer Fachmedien Wiesbaden
Electronic ISBN: 978-3-658-17719-5
Print ISBN: 978-3-658-17718-8
DOI: https://doi.org/10.1007/978-3-658-17719-5