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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.
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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.
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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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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
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Semiparametric estimation of structural failure time models in continuous-time processes.

S Yang1, K Pieper2, F Cools3

  • 1Department of Statistics, North Carolina State University, 2311 Stinson Drive, Raleigh, North Carolina 27695, U.S.A.

Biometrika
|November 9, 2020
PubMed
Summary

This study introduces continuous-time structural failure time models for causal inference with time-varying treatments. The new models offer doubly robust estimators and handle dependent censoring without computational nonsmoothness.

Keywords:
CausalityCox proportional hazards modelDiscretizationObservational studySemiparametric analysisSurvival data

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Area of Science:

  • Biostatistics
  • Causal Inference
  • Survival Analysis

Background:

  • Structural failure time models estimate time-varying treatment effects on survival outcomes.
  • Existing methods often require data discretization and face computational challenges with artificial censoring.

Purpose of the Study:

  • To propose continuous-time structural failure time models that preserve data's natural time scale.
  • To develop semiparametric doubly robust estimators for improved causal analysis.
  • To address dependent censoring using a novel weighting strategy.

Main Methods:

  • Developed continuous-time structural failure time models.
  • Utilized martingale theory for parameter identifiability under no unmeasured confounding.
  • Applied semiparametric efficiency theory to derive doubly robust estimators.
  • Implemented inverse probability of censoring weighting for dependent censoring.

Main Results:

  • Model parameters are identifiable from a potentially infinite number of estimating equations.
  • Derived the first semiparametric doubly robust estimators, consistent under partial model misspecification.
  • Inverse probability of censoring weighting avoids nonsmoothness, enabling resampling-based inference.

Conclusions:

  • Continuous-time models offer a more natural framework for causal inference in survival analysis.
  • Doubly robust estimators enhance reliability by relaxing strong distributional assumptions.
  • The proposed weighting method simplifies inference for dependent censoring scenarios.