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Related Concept Videos

Censoring Survival Data01:09

Censoring Survival Data

Survival analysis is a statistical method used to analyze time-to-event data, often employed in fields such as medicine, engineering, and social sciences. One of the key challenges in survival analysis is dealing with incomplete data, a phenomenon known as "censoring." Censoring occurs when the event of interest (such as death, relapse, or system failure) has not occurred for some individuals by the end of the study period or is otherwise unobservable, and it might have many different reasons...
Assumptions of Survival Analysis01:15

Assumptions of Survival Analysis

Survival models analyze the time until one or more events occur, such as death in biological organisms or failure in mechanical systems. These models are widely used across fields like medicine, biology, engineering, and public health to study time-to-event phenomena. To ensure accurate results, survival analysis relies on key assumptions and careful study design.
Comparing the Survival Analysis of Two or More Groups01:20

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Survival analysis is a cornerstone of medical research, used to evaluate the time until an event of interest occurs, such as death, disease recurrence, or recovery. Unlike standard statistical methods, survival analysis is particularly adept at handling censored data—instances where the event has not occurred for some participants by the end of the study or remains unobserved. To address these unique challenges, specialized techniques like the Kaplan-Meier estimator, log-rank test, and Cox...
Hazard Rate01:11

Hazard Rate

The hazard rate, also known as the hazard function or failure rate, is a statistical measure used to describe the instantaneous rate at which an event occurs, given that the event has not yet happened. From a probabilistic perspective, it represents the likelihood that a subject will experience the event in a very small time interval, conditional on surviving up to the beginning of that interval. In terms of frequency, the hazard rate can be viewed as the ratio of the number of events to the...
Introduction To Survival Analysis01:18

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Survival analysis is a statistical method used to study time-to-event data, where the "event" might represent outcomes like death, disease relapse, system failure, or recovery. A unique feature of survival data is censoring, which occurs when the event of interest has not been observed for some individuals during the study period. This requires specialized techniques to handle incomplete data effectively.
The primary goal of survival analysis is to estimate survival time—the time until a...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...

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Censoring, Competing Events, and Multistate Models: Comment on Beyersmann et al. "Hazards Constitute Key Quantities

Malka Gorfine1, Daniel Nevo1

  • 1Department of Statistics and Operations Research, Tel Aviv University, Tel Aviv, Israel.

Biometrical Journal. Biometrische Zeitschrift
|July 14, 2026
PubMed
Summary

This commentary explores functional hazards for causal inference in survival analysis. It highlights how censoring, competing events, and multistate models impact hazard-based estimands and generalizability in clinical trials.

Keywords:
causal inferencecensoringclinical trialsmultistate modelstransportability

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Area of Science:

  • Biostatistics
  • Clinical Trials
  • Epidemiology

Background:

  • Traditional hazard interpretation focuses on pointwise contrasts.
  • A functional view interprets hazards as evolving quantities over the event process.

Purpose of the Study:

  • Elaborate on the implications of functional hazards for causal inference in survival outcomes.
  • Discuss challenges in clinical trials with censoring, competing events, and multistate structures.

Main Methods:

  • Commentary and theoretical discussion on functional hazard interpretation.
  • Analysis of identifiability, definition, and transportability of hazard-based estimands.
  • Examination of censoring mechanisms and their impact on statistical estimands.

Main Results:

  • Censoring mechanisms can implicitly define statistical estimands via time-dependent weighting.
  • Functional hazard interpretation necessitates careful consideration of intercurrent events.
  • Multistate structures and competing risks amplify challenges in causal interpretation.

Conclusions:

  • The functional interpretation of hazards offers a nuanced view for causal inference in survival analysis.
  • Understanding the interplay of censoring, competing events, and multistate models is crucial for valid causal conclusions.
  • Generalizability of findings is directly impacted by censoring mechanisms and study design in survival data.