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.

Latest Resources

Statistical Primers

What is censoring?

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 […]
Read more

Specialist subjects

Applied Biostatistics

Applied Biostatistics Biostatistics plays a crucial role in advancing medical research. Whether it’s clinical trials, epidemiological studies, or pre-clinical research, biostatistics is essential for drawing meaningful, impactful conclusions from complex data. Our team consists of internationally recognized experts in applied biostatistics, with deep experience in a wide range of areas such as survival analysis, multi-state […]
Read more

Tutorials

Joint longitudinal and competing risks models: Simulation, estimation and prediction

This post takes a look at an extension of the standard joint longitudinal-survival model, which is to incorporate competing risks. Let’s start by formally defining the model. We will assume a continuous longitudinal outcome, $$y_{i}(t) = m_{i}(t) \epsilon_{i}(t)$$ where $$m_{i}(t) = X_{1i}(t)\beta_{1} + Z_{i}(t)b_{i}$$ and \(\epsilon_{i}(t)\) is our normally distributed residual variability. We call \(m_{i}(t)\) our […]
Read more

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 […]
Read more

Tutorials

multistate v4.4.0: semi-parametric multi-state modelling

The headlines: predictms now supports the Cox model as a transition model, estimated using merlin or stmerlin Predictions from a multi-state Cox model are implemented using a simulation approach Supported predictions from a multi-state Cox model include transition probabilities, probability, and length of stay, los Let’s take a look at what we can now do with multistate and in particular, the predictms command. We’ll […]
Read more

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 […]
Read more

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 […]
Read more

Videos

Multilevel (hierarchical) survival models: Estimation, prediction, interpretation

Hierarchical time-to-event data is common across various research domains. In the medical field, for instance, patients are often nested within hospitals and regions, while in education, students are nested within schools. In these settings, the outcome is typically measured at the individual level, with covariates recorded at any level of the hierarchy. This hierarchical structure […]
Read more

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 […]
Read more

Tutorials

Survival analysis with interval censoring

Interval censoring occurs when we don’t know the exact time an event occurred, only that it occurred within a particular time interval. Such data is common in ophthalmology and dentistry, where events are only picked up at scheduled appointments, but they actually occurred at some point since the previous visit. Arguably, we could say all survival data […]
Read more

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 […]
Read more

Tutorials

Joint longitudinal-survival models with time-dependent effects (non-proportional hazards)

In this post we’ll focus on how to model time-dependent effects (non-proportional hazards), specifically within a joint longitudinal-survival model. Now joint models are becoming commonplace in medical research, but as always, the fundamentals still matter, and indeed are often ignored. We’re going to look at how to account for time-dependency in both baseline covariates in […]
Read more
All Resources