O'Reilly logo

Methods and Applications of Statistics in Clinical Trials, Volume 1: Concepts, Principles, Trials, and Designs by N. Balakrishnan

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Chapter 12

Censored Data

Per Kragh Andersen

12.1 Introduction

In classical statistics, the observations are frequently assumed to include independent random variables X1, …, Xn, with Xi having the density function

equation

where αiθ(x) is the hazard function, Siθ(x) is the survival function, and θ is a vector of unknown parameters. Then inference on θ may be based on the likelihood function,

equation

in the usual way. In survival analysis, however, one can rarely avoid various kinds of incomplete observation. The most common form of this is right-censoring where the observations are

(1) equation

where Di is the indicator I{i = Xi}, and i = Xi, the true survival time, if the observation of the lifetime of i is uncensored and i = Ui, the time of right-censoring, otherwise. Thus, Di = 1 indicates an uncensored observation, Di = 0 corresponds to a right-censored observation. Other kinds of incomplete observation will ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required