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Related Concept Videos

Hazard Rate01:11

Hazard Rate

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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...
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Hazard Ratio01:12

Hazard Ratio

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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.
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Parametric Survival Analysis: Weibull and Exponential Methods01:14

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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
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Relative Risk01:12

Relative Risk

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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...
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Design Example: Analyzing Capacity Contours for Flood Risk Assessment01:17

Design Example: Analyzing Capacity Contours for Flood Risk Assessment

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Flood risk assessment involves careful planning and analysis to ensure the safety of communities near water retention structures. Capacity contours are a vital tool in this process, as they illustrate the potential spread of water at specific levels in a given area. In the context of building a bund across a small valley, these contours play a critical role in evaluating the safety of nearby residential areas.In this example, the bund is intended to store stormwater in the valley. The engineers...
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Probability Histograms01:17

Probability Histograms

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A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
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Updated: Nov 11, 2025

An R-Based Landscape Validation of a Competing Risk Model
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Regularized bidimensional estimation of the hazard rate.

Vivien Goepp1,2,3,4, Jean-Christophe Thalabard1, Grégory Nuel5

  • 1MAP5, CNRS UMR 8145, 45, rue des Saints-Pères, 75006, Paris, France.

The International Journal of Biostatistics
|March 26, 2021
PubMed
Summary

This study introduces a new method for estimating disease incidence in large populations, improving upon traditional age-period-cohort analysis by incorporating complex interactions. The novel approach enhances the accuracy of cancer incidence and survival rate estimations.

Keywords:
adaptive ridge procedureage-period-cohort analysispenalized likelihoodpiecewise constant hazardsurvival analysis

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Area of Science:

  • Epidemiology
  • Biostatistics
  • Demographic Studies

Background:

  • Estimating disease incidence, such as cancer incidence, is crucial in epidemiological and demographic studies.
  • Individuals in these studies exhibit heterogeneity in birth dates (cohort) and are observed over calendar time (period).
  • Classical age-period-cohort analysis requires appropriate estimation methods to handle this heterogeneity.

Purpose of the Study:

  • To present a novel estimation method extending classical age-period-cohort analysis.
  • To allow for interactions between age, period, and cohort effects in disease incidence estimation.
  • To develop a parsimonious representation of the hazard rate using penalized likelihood.

Main Methods:

  • Introduced a bidimensional regularized estimate of the hazard rate.
  • Incorporated a penalty on the model's likelihood to smooth the hazard rate or enforce equality of consecutive values.
  • Utilized an iterative penalized likelihood scheme approximating the L0 norm for computational tractability.

Main Results:

  • The proposed method was evaluated using simulated data.
  • The method was applied to real-world breast cancer survival data from the SEER program.
  • Demonstrated the ability to handle complex interactions between age, period, and cohort effects.

Conclusions:

  • The new estimation method provides a more flexible and parsimonious approach to hazard rate modeling.
  • This method enhances the accuracy of incidence and survival rate estimations in heterogeneous populations.
  • The approach is valuable for epidemiological studies, particularly in cancer research.