Survival analysis: Methods for analyzing data with censored observations

Abstract

Censoring occurs when we do not observe exactly the value that we are interested in, but we only learn about some bounds for it. For instance, an observation is right-censored (left-censored) when it is smaller (larger) than the true value.

Censoring is most often encountered when observing a time to event, i.e., the time that elapses between a well-defined starting moment until a particular event of interest (for example, the age until the first dental caries). However, it may apply to any measurement or observation. For instance, left- and right-censoring applies to diagnostic assays with, respectively, a lower and an upper limit of detection.

The presence of censored observations has important consequences for the statistical analysis. This is because, in such a case, the use of classical statistics (such as, e.g., the sample mean) or statistical models (such as, e.g., linear regression) will result in biased results. Analysis of data that include censored observations requires the use of methods that take explicitly into account censoring. Collectively, in medicine, these methods are referred to as survival analysis. In this article, we provide a review of the basic (parametric and non-parametric) statistical methods of survival analysis.