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

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 […]

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

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

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

Multivariate joint longitudinal-survival models

Joint longitudinal-survival models have been widely developed, but there are many avenues of research where they are lacking in terms of methodological development, and importantly, accessible implementations. We think merlin fills a few gaps. In this post, we’ll take a look at the extension to modelling multiple continuous longitudinal outcomes, jointly with survival. For simplicity, I’ll concentrate […]

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 […]

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 […]

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 […]

Videos

State-of-the-art statistical models for modern HTA

At @RedDoorAnalytics, we develop methodology and software for efficient modelling of biomarkers, measured repeatedly over time, jointly with survival outcomes, which are being increasingly used in cancer settings. We have also developed methods and software for general non-Markov multi-state survival analysis, allowing for the development of more plausible natural history models, where patient history can […]

Videos

Introduction to Epidemiological Study Designs

This video offers a comprehensive introduction to epidemiological study designs, emphasising their classification, key definitions, strengths, limitations, and practical applications. We will dive into the most commonly used study designs, exploring their structure, purpose, and the contexts in which they are most effective. Throughout the video, real-world case studies of landmark research will be used […]

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 […]

Specialist subjects

Haematology

Haematological malignancies At Red Door Analytics, we have extensive experience in working with haematological malignancies, demonstrated through 18 publications in peer-reviewed journals. Our expertise spans epidemiological studies on prognosis and late effects, as well as randomised clinical trials. Based in Stockholm, we have unique experience in accessing and working with registry data from the Nordic […]

All Resources