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

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 […]

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 […]

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 […]

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 […]

Tutorials

An introduction to joint modelling of longitudinal and survival data

This post gives a gentle introduction to the joint longitudinal-survival model framework, and covers how to estimate them using our merlin command in Stata. A joint model consists of a continuous, repeatedly measured (longitudinal) outcome, and a time-to-event, with the two models linked by random effects, or functions of them. Let’s formally define everything we need. For […]

Statistical Primers

What are competing risks?

Competing risks In survival analysis, competing risks refer to the situation when an individual is at risk of experiencing an event that precludes the event under study to occur. Competing risks commonly occur in studies of cause-specific mortality, as all other causes of death than the one under study might happen before the individuals “have […]

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

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

Clinical Trial Services

Clinical Trial Services Biostatistics services of RDA are the cornerstone of clinical trial design, execution, and interpretation. Biostatistical support by RDA will ensure that your clinical development programme and inherent studies are scientifically rigorous, appropriately powered, and capable of generating reliable evidence for regulatory approval and clinical use. RDA’s expertise for clinical development is focused […]

Tutorials

Simulating survival data with a continuous time-varying covariate…the right way

In this post we’ll take a look at how to simulate survival data with a continuous, time-varying covariate. The aim is to simulate from a data-generating mechanism appropriate for evaluating a joint longitudinal-survival model. We’ll use the survsim command to simulate the survival times, and the merlin command to fit the corresponding true model. Let’s assume a proportional hazards […]

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 […]

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 […]

All Resources