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

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 […]
Read more

Tutorials

Simulation and estimation of three-level survival models: IPD meta-analysis of recurrent event data

In this example I’ll look at the analysis of clustered survival data with three levels. This kind of data arises in the meta-analysis of recurrent event times, where we have observations (events or censored), k (level 1), nested within patients, j (level 2), nested within trials, i (level 3). Random intercepts The first example will […]
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

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

Real-world evidence (RWE)

Real-world evidence (RWE) Data and information that, unlike data generated in clinical trials conducted in controlled environments, has been obtained from everyday clinical practice, patient registers, or other sources outside the clinical trial setting.   RWE plays a crucial role in complementing traditional clinical trial data, providing insights into the safety, effectiveness, and overall performance […]
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

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

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

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

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

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

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 […]
Read more
All Resources