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A semiparametric additive rate model for a modulated renewal process.

Xin Chen1, Jieli Ding2, Liuquan Sun3

  • 1Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People's Republic of China.

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|November 30, 2017
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Summary

This study introduces a new statistical model for analyzing recurrent event data, improving the understanding of long-term event patterns in areas like cardiovascular health.

Keywords:
Additive rate modelBlock bootstrapEstimating equationMixing conditionModulated renewal processRecurrent event data

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Area of Science:

  • Statistics
  • Biostatistics
  • Survival Analysis

Background:

  • Recurrent event data from long single realizations are common in point process applications.
  • Analyzing dependent data structures in long sequences requires specialized statistical methods.
  • Existing methods may not adequately capture the complexities of long-term recurrent event data.

Purpose of the Study:

  • To propose a semiparametric additive rate model for modulated renewal processes.
  • To develop an estimating equation approach for model parameter estimation.
  • To provide a robust statistical framework for analyzing long single realizations of recurrent events.

Main Methods:

  • Developed a semiparametric additive rate model for modulated renewal processes.
  • Utilized an estimating equation approach for parameter estimation.
  • Applied limit theory for stationary mixing sequences to establish asymptotic properties.
  • Implemented a block-based bootstrap procedure for variance estimation.

Main Results:

  • The proposed semiparametric model effectively handles dependent recurrent event data.
  • Asymptotic properties of the estimators were rigorously established.
  • Simulation studies demonstrated good finite-sample performance of the proposed estimators.
  • The method was successfully applied to a cardiovascular mortality dataset.

Conclusions:

  • The proposed semiparametric additive rate model offers a valuable tool for analyzing recurrent event data from long single realizations.
  • The developed methods provide reliable parameter estimation and variance estimation.
  • This approach enhances the analysis of complex event data in various scientific fields, including public health.