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

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 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 […]
Read more

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 […]
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

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

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 […]
Read more

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 […]
Read more

Tutorials

Joint frailty models for recurrent and terminal events

In this post we’re going to take a look at joint frailty models, and how to fit them with our merlin command. Importantly, we’ll also discuss how to interpret the results. Joint frailty models An area of intense research in recent years is in the field of joint frailty models, which has become the commonly used name for […]
Read more

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, […]
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

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 […]
Read more

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 […]
Read more
All Resources