Concept Architecture
Concept
Theoretically, Censoring is the incomplete observation of the time to an event because the event has not occurred, the individual is lost to follow-up or observation ends before the event is observed. It is a fundamental concept in survival analysis and time-to-event statistics, ensuring that partially observed survival times contribute valid information to statistical estimation. In health economics, censoring is routinely encountered in clinical trials, registries and observational studies used to estimate survival, costs and health outcomes.
Mathematically, censoring is incorporated into survival models through likelihood functions that distinguish observed events from censored observations. Right censoring is the most common form, although left censoring and interval censoring are also recognised. Survival estimation methods, including the Kaplan?Meier estimator, Cox proportional hazards model and parametric survival models, explicitly account for censored observations without treating them as events.
In practice, censoring is identified during data collection whenever participants remain event-free at the end of follow-up, withdraw from a study or are lost to follow-up. Appropriate statistical methods are then applied to obtain unbiased estimates of survival probabilities, hazard functions and treatment effects, providing essential inputs for health economic evaluations and decision models.
Purpose
Used to incorporate incomplete time-to-event observations into survival analysis, produce unbiased estimates of survival and hazard functions, evaluate treatment effects and generate reliable inputs for health economic models.
Mathematical Formulae
Primary Formula
L = ?S(t?)???? ? f(t?)??
where:
- L = likelihood
- S(t?) = survival function
- f(t?) = probability density function
- �? = 1 if the event is observed, 0 if censored
Supporting Formulae
Survival function:
S(t) = P(T > t)
Relationship between hazard and survival:
S(t) = exp(???? h(u) du)
Related Mathematical Methods
- Kaplan?Meier estimation
- Cox proportional hazards model
- Parametric survival modelling
- Maximum likelihood estimation
- Competing risks analysis
Example
A clinical trial follows 250 patients for five years. During follow-up, 70 patients die, 20 withdraw from the study and 30 remain alive when the study ends. The 50 patients who withdraw or remain alive contribute censored observations, allowing their observed follow-up time to inform survival estimation without being treated as deaths.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| IF | =IF(C2="Event",1,0) | Create an event indicator where 1 = observed event and 0 = censored observation. |
| COUNTIF | =COUNTIF(C2:C251,"Censored") | Count censored observations within a study population. |
| MAX | =MAX(B2:B251) | Determine the maximum observed follow-up time for survival analysis. |
VBA (Optional)
Automate identification of censored observations, preparation of survival datasets and generation of summary statistics for survival modelling.
Sources
- Collett D. Modelling Survival Data in Medical Research. CRC Press.
- Klein JP, Moeschberger ML. Survival Analysis: Techniques for Censored and Truncated Data. Springer.
- Kalbfleisch JD, Prentice RL. The Statistical Analysis of Failure Time Data. Wiley.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
- NICE. Health Technology Evaluation Manual.
Related Concepts (2)
Library
Publications
6
Economic Evaluation in Clinical Trials — Glick, Doshi, Sonnad & Polsky, 2nd Edition ed., 2015 (Oxford University Press)
Practical guidance on conducting cost-effectiveness analyses alongside controlled trials, covering trial design, measurement of costs and quality-adjusted life years, handling censored and missing data, and reporting stochastic uncertainty. Volume 4 in the Handbooks in Health Economic Evaluation series.
BookView source →NICE DSU Technical Support Document 14: Survival analysis for economic evaluations alongside clinical trials – extrapolation with patient-level data — Nicholas R. Latimer, TSD 14 ed., 2013 (NICE Decision Support Unit (University of Sheffield))
The reference guidance on survival analysis for economic evaluation: fitting standard parametric models (exponential, Weibull, Gompertz, log-logistic, log-normal) to censored trial data and extrapolating to estimate lifetime survival benefit, with a process guide for model selection and justification.
NICE DSU Technical Support Document 6: Embedding Evidence Synthesis in Probabilistic Cost-Effectiveness Analysis — Software Choices — Dias, Welton, Sutton & Ades, TSD 6 ed., 2011 (NICE Decision Support Unit (University of Sheffield))
Guidance on the software options and practical steps for embedding a Bayesian evidence synthesis directly within a probabilistic cost-effectiveness model so that parameter uncertainty is propagated consistently.
Survival Analysis: A Self-Learning Text — David G. Kleinbaum & Mitchel Klein, 3rd Edition ed., 2012 (Springer)
A practical introduction to survival data, censoring, Kaplan-Meier methods, Cox regression, proportional hazards and model interpretation.
BookView source →Statistical Models and Methods for Lifetime Data — Jerald F. Lawless, 2nd Edition ed., 2003 (John Wiley & Sons)
An advanced reference on lifetime and event-time data, including censoring, parametric distributions, hazard functions, regression and model assessment.
BookView source →Modelling Survival Data in Medical Research — David Collett, 3rd Edition ed., 2015 (Chapman & Hall / CRC Press)
A medical-research guide to survival modeling, including censored outcomes, parametric models, Cox regression, diagnostics and practical interpretation.
BookView source →
Frequently Asked Questions (6)
What is censoring?
A situation in survival analysis where the exact time of an event is not observed, either because the study ended or follow-up was lost.
Source: Kalbfleisch & Prentice 2002
What information does a censored observation still provide?
A censored observation is one where the event was not seen, because the study ended or the patient was lost, so the exact event time is unknown. It is not useless, however, since it shows the patient survived at least up to the point they were last observed. Survival methods use exactly this partial information, counting the patient as at risk until censoring and then removing them, rather than discarding the case or guessing an event time. Ignoring it would waste evidence and bias the result. Collett (2015) explains this handling.
Source: Collett 2015
What are the types of censoring?
The main types of censoring are right censoring, the most common, where the event has not occurred by the end of observation, so the true event time lies beyond the last follow-up; left censoring, where the event occurred before observation began, so the time is known only to be earlier; and interval censoring, where the event is known to have occurred within a time interval but not exactly when. Right censoring arises when a study ends or follow-up is lost before the event.
Source: Kalbfleisch & Prentice 2002
Why does censoring require special methods?
Censoring requires special methods because censored individuals have not experienced the event by the end of observation, so their exact event times are unknown, and standard analyses that ignore this would discard information or bias results. Survival methods use both observed event times and censored times, the latter contributing the information that the event had not occurred by a certain point. This allows unbiased estimation of survival and event risk despite incomplete follow-up, which ordinary methods that require complete outcomes cannot achieve.
Source: Collett 2015
How is censoring handled in survival analysis?
Censoring is handled in survival analysis by methods that incorporate both observed and censored times: the Kaplan-Meier estimator uses the number at risk, which decreases as individuals are censored or have events, to estimate the survival curve; the actuarial method adjusts the number at risk within intervals; and regression models such as the Cox model include censored observations through their contribution to the risk set. These methods use censored individuals' partial follow-up rather than discarding it, giving unbiased estimates under appropriate assumptions.
Source: Kalbfleisch & Prentice 2002
What assumption underlies the handling of censoring?
The handling of censoring generally assumes that censoring is non-informative, meaning that individuals who are censored are, at the time of censoring, representative of those still at risk, so that censoring is unrelated to the risk of the event. If censoring is informative, for instance if sicker patients are lost to follow-up, this assumption fails and estimates can be biased. Non-informative censoring is therefore an important assumption in survival analysis, and its plausibility is considered when interpreting results.
Source: Kalbfleisch & Prentice 2002
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 20 Oct 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/censoring
- Term code
- HE-EM-SM-006
Stable URI · Machine-readable · Resolvable · CC BY 4.0