What is censoring? - Red Door Analytics

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 […]

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

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 […]

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 […]

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 […]

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

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 […]

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 […]

Tutorials

Defining a transition matrix for multi-state modelling

In this post we’ll take a look at how to define a custom transition matrix for use with our multistate package in Stata. The transition matrix A transition matrix governs the movement of a process between possible states. Within multi-state survival analysis, and particularly, the implementation of multi-state models in Stata, the transition matrix contains the most […]

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 […]

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 […]

All Resources