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Methods and Applications of Statistics in Clinical Trials, Volume 2: Planning, Analysis, and Inferential Methods by N. Balakrishnan

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Chapter 50

Survival Analysis, Overview

Per Kragh Andersen and Niels Keiding

50.1 Introduction

Survival analysis is the study of the distribution of lifetimes, that is, the times from an initiating event (birth, start of treatment, employment in a given job) to some terminal event (death, relapse, disability pension). A distinguishing feature of survival data is the inevitable presence of incomplete observations, particularly when the terminal event for some individuals is not observed; instead, it is only known that this event is at least later than a given point in time: right censoring.

The aims of this entry are to provide a brief historical sketch of the long development of survival analysis and to survey what we have found to be central issues in the current methodology of survival analysis. Necessarily, this entry is rich in cross-references to other entries that treat specific subjects in more detail. However, we have not attempted to include cross-references to all specific entries within survival analysis.

50.2 History

50.2.1 The Prehistory of Survival Analysis in Demography and Actuarial Science

Survival analysis is one of the oldest statistical disciplines, with roots in demography and actuarial science in the seventeenth century; see References 49 (Chapter 2) and 51 for general accounts of the history of vital statistics and Reference 22 for specific accounts of the work before 1750.

The basic life table methodology in modern terminology amounts to the estimation of ...

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