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Related Concept Videos

Hazard Ratio01:12

Hazard Ratio

The hazard ratio (HR) is a widely used measure in clinical trials to compare the risk of events, such as death or disease recurrence, between two groups over time. It reflects the ratio of hazard rates—the instantaneous risk of the event occurring—between a treatment group and a control group. This measure provides valuable insights into the relative effectiveness of a treatment by assessing how the risk of an event differs between the two groups.
For example, in a clinical trial evaluating a...
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...
Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
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.
Hypothesis Test for Test of Independence01:16

Hypothesis Test for Test of Independence

The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis test is used to examine the independence of the variables. One can construct two qualitative survey questions or experiments based on the variables in a contingency table. The goal is to see if the two variables are unrelated (independent) or related (dependent). The null and alternative hypotheses for this test are:
H0: The two variables (factors)...
Comparing the Survival Analysis of Two or More Groups01:20

Comparing the Survival Analysis of Two or More Groups

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...

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Establishing a Competing Risk Regression Nomogram Model for Survival Data
04:57

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Published on: October 23, 2020

Bayesian analysis for monotone hazard ratio.

Yongdai Kim1, Jin Kyung Park, Gwangsu Kim

  • 1Seoul National University, Seoul, Korea. ydkim0903@gmail.com

Lifetime Data Analysis
|July 17, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces a Bayesian method for estimating hazard functions with a monotone hazard ratio. The approach uses Cox

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An R-Based Landscape Validation of a Competing Risk Model
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Last Updated: Jun 10, 2026

Establishing a Competing Risk Regression Nomogram Model for Survival Data
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Establishing a Competing Risk Regression Nomogram Model for Survival Data

Published on: October 23, 2020

An R-Based Landscape Validation of a Competing Risk Model
05:37

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Area of Science:

  • Biostatistics
  • Survival Analysis
  • Statistical Modeling

Background:

  • Estimating hazard functions is crucial in survival analysis.
  • Monotone hazard ratios are common in medical and reliability studies.
  • Existing methods may lack computational efficiency or flexibility.

Purpose of the Study:

  • To develop a Bayesian approach for hazard function estimation under a monotone hazard ratio constraint.
  • To model monotone hazard ratios using Cox's proportional hazards model with time-dependent coefficients.
  • To enhance computational efficiency through specific prior choices and MCMC algorithms.

Main Methods:

  • Bayesian inference for hazard function estimation.
  • Modeling monotone hazard ratios via Cox's model with monotone time-dependent coefficients.
  • Utilizing signed gamma process prior for time-dependent coefficients.
  • Employing Bayesian bootstrap prior for the baseline hazard function.
  • Developing an efficient Markov Chain Monte Carlo (MCMC) algorithm.

Main Results:

  • The proposed Bayesian method effectively estimates hazard functions with monotone hazard ratios.
  • The use of signed gamma and Bayesian bootstrap priors reduces computational complexity.
  • The efficient MCMC algorithm facilitates practical application.
  • The method demonstrates utility on both simulated and real-world data.

Conclusions:

  • The proposed Bayesian approach provides a computationally efficient and flexible tool for survival data analysis.
  • It successfully incorporates the monotone hazard ratio constraint.
  • The method is validated through simulations and real data applications, suggesting its potential for broader use.