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Hazard Rate

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...

Hazard Ratio

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...

Actuarial Approach

Actuarial Approach

The actuarial approach, a statistical method originally developed for life insurance risk assessment, is widely used to calculate survival rates in clinical and population studies. This method accounts for participants lost to follow-up or those who die from causes unrelated to the study, ensuring a more accurate representation of survival probabilities.
Consider the example of a high-risk surgical procedure with significant early-stage mortality. A two-year clinical study is conducted,...

Survival Curves

Survival Curves

Survival curves are graphical representations that depict the survival experience of a population over time, offering an intuitive way to track the proportion of individuals who remain event-free at each time point. These curves are widely used in fields such as medicine, public health, and reliability engineering to visualize and compare survival probabilities across different groups or conditions.
The Kaplan-Meier estimator is the most common method for constructing survival curves. This...

Relative Risk

Relative Risk

Relative risk (RR) is a statistical measure commonly used in epidemiology to compare the likelihood of a particular event occurring between two groups. This metric is important for evaluating the relationship between exposure to a specific risk factor and the probability of a particular outcome. It plays a crucial role in medical research, public health studies, and risk assessment. Relative risk quantifies how much more (or less) likely an event is to occur in an exposed group compared to an...

Kaplan-Meier Approach

Kaplan-Meier Approach

The Kaplan-Meier estimator is a non-parametric method used to estimate the survival function from time-to-event data. In medical research, it is frequently employed to measure the proportion of patients surviving for a certain period after treatment. This estimator is fundamental in analyzing time-to-event data, making it indispensable in clinical trials, epidemiological studies, and reliability engineering. By estimating survival probabilities, researchers can evaluate treatment effectiveness,...

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Related Experiment Video

Updated: Jun 23, 2026

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Published on: October 23, 2020

Estimating the case fatality rate using a constant cure-death hazard ratio.

Zheng Chen¹, Kohei Akazawa, Tsuyoshi Nakamura

¹Department of Biostatistics, School of Public Health and Tropical Medicine, Southern Medical University, Guangzhou, China. zheng-chen@hotmail.com

Lifetime Data Analysis

|May 22, 2009

Summary

Accurate estimation of disease severity, like the case fatality rate for severe acute respiratory syndrome (SARS), is crucial. New methods using a constant cure-death hazard ratio provide reliable estimates, performing well across various sample sizes.

Related Experiment Videos

Last Updated: Jun 23, 2026

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Published on: October 23, 2020

Area of Science:

Epidemiology
Biostatistics
Public Health

Background:

The case fatality rate (CFR) is a key metric for assessing disease severity during outbreaks.
Accurate CFR estimation is vital for understanding epidemic dynamics, as demonstrated by severe acute respiratory syndrome (SARS).

Purpose of the Study:

To develop and evaluate novel statistical methods for estimating the case fatality rate.
To introduce a semiparametric model incorporating a constant cure-death hazard ratio for CFR estimation.

Main Methods:

A semiparametric model was developed with the cure-death hazard ratio as a key parameter.
A profile likelihood-based technique was proposed for estimating the case fatality rate.
Extensive simulations were conducted using both summary and individual data for small and medium sample sizes.

Main Results:

The proposed estimation technique's performance is contingent on model validity rather than sample size.
Simulations indicated robust performance across different data scenarios.

Conclusions:

The developed method offers a reliable approach for estimating case fatality rates, particularly in the context of infectious disease outbreaks.
The technique was successfully applied to real-world SARS data from Hong Kong and Singapore.