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Related Concept Videos

Assumptions of Survival Analysis01:15

Assumptions of Survival Analysis

173
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.
173
Hazard Rate01:11

Hazard Rate

159
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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Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

525
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...
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Introduction To Survival Analysis01:18

Introduction To Survival Analysis

334
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...
334
Comparing the Survival Analysis of Two or More Groups01:20

Comparing the Survival Analysis of Two or More Groups

247
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...
247
Censoring Survival Data01:09

Censoring Survival Data

185
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...
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Consistent and robust inference in hazard probability and odds models with discrete-time survival data.

Zhiqiang Tan1

  • 1Department of Statistics, Rutgers University, Piscataway, NJ, 08854, USA. ztan@stat.rutgers.edu.

Lifetime Data Analysis
|December 23, 2022
PubMed
Summary

New methods for discrete-time survival data analysis address challenges with tied events and large time intervals. These approaches offer robust estimation for hazard probability and odds models, improving survival data analysis.

Keywords:
Breslow–Peto estimatorMantel–Haenszel estimatorModel-robust variance estimationProportional hazards model

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Area of Science:

  • Biostatistics
  • Survival Analysis

Background:

  • Conditional likelihood inference in Cox's hazard odds model is computationally challenging for discrete-time survival data with many tied events.
  • Unconditional maximum likelihood estimation faces issues with numerous time intervals.

Purpose of the Study:

  • To develop novel, computationally tractable methods for survival data analysis using discrete-time hazard probability and odds models.
  • To provide robust variance estimation techniques for these models.

Main Methods:

  • Development of numerically simple estimating functions for hazard probability and odds models.
  • Derivation of the Breslow-Peto estimator as a consistent estimator for the probability hazard model.
  • Proposal of a weighted Mantel-Haenszel estimator for the hazard odds model, ensuring conditional unbiasedness.

Main Results:

  • The proposed methods are consistent and perform well across various settings, including those with numerous tied events or time intervals.
  • The Breslow-Peto estimator is shown to be a consistent estimator.
  • The weighted Mantel-Haenszel estimator achieves conditional unbiasedness.

Conclusions:

  • The new methods offer practical and reliable solutions for analyzing discrete-time survival data, overcoming limitations of existing techniques.
  • These advancements are implemented in the R package dSurvival for broader accessibility.