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Statistical inference methods for recurrent event processes with shape and size parameters.

Mei-Cheng Wang1, Chiung-Yu Huang2

  • 1Department of Biostatistics, Bloomberg School of Public Health, Johns Hopkins University, 615 N. Wolfe Street, Baltimore, Maryland 21205, U.S.A.

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Summary
This summary is machine-generated.

This study introduces shape and size parameters to analyze recurrent event processes, offering a new framework for understanding population-averaged event rates. These parameters help distinguish sources of variation in event occurrence, improving statistical analysis.

Keywords:
Intensity functionPoint processPoisson processRate functionRate-independenceShape-independenceSize-independence

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Area of Science:

  • Statistics
  • Survival Analysis
  • Biostatistics

Background:

  • Recurrent event processes are common in various fields, but characterizing their underlying rates remains challenging.
  • Existing methods often focus on conditional rates (intensity function), neglecting unconditional population-averaged rates (rate function).

Purpose of the Study:

  • To propose a unified framework for characterizing the rate function of recurrent event processes using shape and size parameters.
  • To develop statistical tests for assessing the association and independence between a random variable and the rate function.

Main Methods:

  • Introduction of shape and size parameters to define the rate function.
  • Development of shape- and size-based coefficients to measure association.
  • Formulation of tests for shape- and size-independence, applicable with covariates or censoring times.

Main Results:

  • The proposed framework provides a novel way to analyze the unconditional rate function.
  • Shape and size parameters allow for a nuanced understanding of the association between covariates/censoring and recurrent events.
  • Tests can distinguish the source of violation when the null hypothesis is rejected.

Conclusions:

  • The introduced shape and size parameters offer a powerful tool for characterizing recurrent event processes.
  • The developed tests enhance the ability to analyze the relationship between external factors and event occurrence rates.
  • This framework improves the interpretability and diagnostic power in survival and recurrent event data analysis.