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Related Concept Videos

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...
Piecewise-Defined Functions01:28

Piecewise-Defined Functions

Piecewise defined functions are mathematical models where different expressions define a function over distinct intervals of the domain. These functions are useful for representing systems with varying behaviors depending on input values.For example, the function:  uses a linear rule for inputs less than or equal to –1 and a quadratic rule for values greater than –1. Although it has two formulas, it still defines a single function.Another common type is the absolute value function, given...
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...
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...
Types of Functions III01:28

Types of Functions III

Logarithmic and piecewise functions play central roles in mathematical modeling, particularly when capturing nonlinear or segmented behaviors in real-world phenomena. Although these functions differ fundamentally in structure and application, both serve to represent complex relationships in simplified mathematical terms.A logarithmic function is defined as the inverse of an exponential function, expressed as These functions grow quickly for small values of x but slow down as x increases,...
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...

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A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types
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A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types

Published on: December 10, 2012

Detecting multiple change points in piecewise constant hazard functions.

Melody S Goodman1, Yi Li, Ram C Tiwari

  • 1Graduate Program in Public Health, Department of Preventive Medicine, Stony Brook University School of Medicine, Stony Brook, NY, USA.

Journal of Applied Statistics
|June 19, 2012
PubMed
Summary
This summary is machine-generated.

Prostate cancer mortality rates have decreased due to effective treatments and early screening. This study introduces a new method to pinpoint changes in survival trends, aiding in understanding medical intervention impacts.

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Area of Science:

  • Biostatistics
  • Cancer Epidemiology
  • Survival Analysis

Background:

  • Prostate cancer mortality rates have shown a notable decline, attributed to advancements in screening and treatment.
  • Understanding the impact of medical interventions on population survival trends is crucial.

Purpose of the Study:

  • To develop and apply a data-driven method for estimating changes in the hazard function over time.
  • To identify multiple change points in survival trends and understand their correlation with medical practice evolution.

Main Methods:

  • Proposed a piecewise constant hazard model with a sequential testing algorithm for model selection.
  • Developed methods to estimate the number and location of change points in the hazard function.
  • Utilized the National Cancer Institute (NCI) Surveillance, Epidemiology, and End Results (SEER) dataset for prostate cancer mortality analysis.

Main Results:

  • The study provides a robust framework for analyzing time-varying hazard functions.
  • The methodology allows for the identification of significant shifts in survival trends.
  • Applied to prostate cancer data, the method can reveal impacts of medical practice changes on mortality.

Conclusions:

  • The proposed model selection algorithm effectively identifies multiple change points in hazard rates.
  • This approach enhances the understanding of how medical breakthroughs influence patient survival experiences.
  • The methods are applicable to various populations and interventions impacting survival trends.