What is censoring?

Statistical Primers

Censoring refers to a situation in survival analysis where the event of interest is not observed for some of the individuals under study.

In this Statistical Primer, we’ll define three types of censoring often seen in survival analysis studies.

Censoring occurs when the information on the survival time is incomplete or only partially observed.

Censoring can have a significant impact on the analysis and interpretation of survival data. It is essential to appropriately handle censoring in survival analysis to obtain accurate estimates of survival times, covariate effects, and other related parameters.

There are different types of censoring in survival analysis:

Right-censoring: This occurs when a participant is still alive or event-free at the end of the study period. In other words, the follow-up time for the participant ends before the event occurs. This is the most common type of censoring in survival analysis.
Left-censoring: This occurs when the true event time is known to be less than a certain time, but the exact time is unknown. For example, if an individual is diagnosed with a disease before the study begins but the date of onset of the disease is not known, we have left-censoring.
Interval-censoring: This occurs when the event time is known to fall within a certain interval, but the exact time of the event is unknown. For example, if a person develops glaucoma in between visits to the optician but the exact onset is unknown, we have interval censoring.

Want to learn more?

Latest Resources

Tutorials

Simulation and estimation of three-level survival models: IPD meta-analysis of recurrent event data

In this example I’ll look at the analysis of clustered survival data with three levels. This kind of data arises in the meta-analysis of recurrent event times, where we have observations (events or censored), k (level 1), nested within patients, j (level 2), nested within trials, i (level 3). Random intercepts The first example will […]

Statistical Primers

Censoring refers to a situation in survival analysis where the event of interest is not observed for some of the individuals under study. In this Statistical Primer, we’ll define three types of censoring often seen in survival analysis studies. Censoring occurs when the information on the survival time is incomplete or only partially observed. Censoring […]

Statistical Primers

What is the Cox model?

The Cox model The Cox model, also known as the proportional hazards model, is a popular statistical tool used to analyse survival data. It was developed by British statistician Sir David Cox, and published in 1972. It has gained popularity largely by avoiding making parametric assumptions about the shape of the baseline rate in a […]

Tutorials

A user-defined/custom hazard model

This tutorial will illustrate some of the more advanced capabilities of merlin when modelling survival data, but with the aim of using an accessible example. During my PhD, Paul Lambert and I developed stgenreg in Stata for modelling survival data with a general user-specified hazard function, with the generality achieved by using numerical integration to calculate the cumulative hazard […]

Statistical Primers

What is the proportional hazards assumption?

Proportional hazards Proportional hazards in survival analysis means that the rate at which an event of interest occurs over time for two or more groups or individuals is proportional over time. Specifically, it assumes that the hazard ratio, which represents the relative rate of an event occurring between two groups or individuals, is constant over […]

Tutorials

Probabilistic sensitivity analysis and survival models

Today we’re going to take a little look into probabilistic sensitivity analysis (PSA), and how it can be implemented within the context of survival analysis. Now PSA is used extensively in health economic modelling, where a particular parameter (or parameters) of interest, are altered or varied, to represent different scenarios and levels of variation. We […]

Statistical Primers

What is immortal time bias?

Immortal time bias Immortal time bias is a type of bias that can occur in observational research when the study design allows for a period of time during which the outcome of interest cannot occur, often referred to as “immortal time”. Simply put, immortal time bias occurs when information from a future event is incorporated into the […]

Tutorials

Relative survival analysis

Relative survival models are predominantly used in population based cancer epidemiology (Dickman et al. 2004), where interest lies in modelling and quantifying the excess mortality in a population with a particular disease, compared to a reference population, appropriately matched on things like age, gender and calendar time. One of the benefits of the approach is […]

Specialist subjects

Methods Development

Methods Development We provide expert guidance in finding the appropriate statistical approach to answer your question… and if there isn’t yet a method, well, we can develop one. While applying biostatistics to address your research question is essential, there may be times when existing methods fall short for your specific problem. In such cases, we’re […]

Statistical Primers

What is survival analysis?

Survival analysis is a statistical method used to analyse the time until an event of interest occurs. The key feature of survival analysis is that the outcome has two dimensions: – an event indicator (yes/no), and – the time spent at risk for the event All survival analyses require precise definitions of start and end of […]

Tutorials

Simulation, modelling and prediction with a non-linear covariate effect in survival analysis

Let’s begin. There will be a single continuous covariate, representing age, with a non-linear effect influencing survival. We’ll simulate survival times under a data-generating model that incorporates a non-linear effect of age. We’ll then fit some models accounting for the non-linear effect of age, and finally make predictions for specified values of age. Sounds simple, […]

Tutorials

Flexible parametric survival analysis with frailty

This example takes a look at incorporating a frailty, or random intercept, into a flexible parametric survival model, and how to fit them in Stata. First we’ll use merlin to estimate our model, and then the more user-friendly wrapper function stmixed. More details on these models can be found in the following papers: Crowther MJ, Look MP, Riley […]

All Resources