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Recurrent events and the exploding Cox model.

Håkon K Gjessing1, Kjetil Røysland, Edsel A Pena

  • 1Division of Epidemiology, Department of Genes and Environment, Norwegian Institute of Public Health, Oslo, Norway. hakon.gjessing@fhi.no

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|July 14, 2010
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Summary
This summary is machine-generated.

Complex counting process models with dynamic covariates are essential for analyzing recurrent events. We provide conditions for defining valid stochastic processes, ensuring models avoid explosions, especially with linear feedback structures.

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Area of Science:

  • Statistics
  • Survival Analysis
  • Event History Analysis

Background:

  • Counting process models are foundational in survival and event history analysis.
  • Existing models often possess overly simplistic structures.
  • Recurrent event analysis necessitates more sophisticated models incorporating dynamic covariates.

Purpose of the Study:

  • To discuss the definition of valid counting process models for recurrent events.
  • To establish conditions for ensuring these models are well-defined stochastic processes.
  • To address potential issues like model explosions, particularly in Cox-type models with feedback.

Main Methods:

  • Formulating counting process models with dynamic covariates.
  • Developing conditions for stochastic process validity.
  • Analyzing Cox-type models with exponential structures and feedback.
  • Investigating linear feedback structures for model stability.

Main Results:

  • Identified conditions for well-defined counting process models.
  • Demonstrated that Cox-type models with feedback can lead to exploding models.
  • Showed that general counting process models with dynamic covariates can be formulated to avoid explosions.
  • Confirmed that linear feedback structures prevent model explosions.

Conclusions:

  • Careful validation is crucial when defining counting process models with dynamic covariates.
  • Linear feedback structures offer a robust approach for modeling recurrent events without explosions.
  • These findings enhance the utility of counting process models in complex event history analysis.