Methods and Applications of Statistics in Clinical Trials, Volume 1: Concepts, Principles, Trials, and Designs

Chapter 12

Censored Data

Per Kragh Andersen

12.1 Introduction

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

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

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)

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