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Marginal analysis of panel counts through estimating functions.

X Joan Hu1, Stephen W Lagakos, Richard A Lockhart

  • 1Department of Statistics and Actuarial Science, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia V5A 1S6, Canada, joanh@stat.sfu.ca.

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Summary
This summary is machine-generated.

We present new statistical methods for estimating counting process means from periodic data. These methods provide consistent estimates, even without assuming a Poisson process, and are validated through simulations and a bladder cancer study.

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Area of Science:

  • Biostatistics
  • Statistical Inference
  • Survival Analysis

Background:

  • Counting processes are fundamental in modeling event occurrences over time.
  • Periodic observations present unique challenges for statistical estimation.
  • Nonparametric methods offer flexibility when distributional assumptions are uncertain.

Purpose of the Study:

  • To develop robust nonparametric estimation procedures for the marginal mean function of counting processes.
  • To introduce two novel self-consistent estimating equations for periodic count data.
  • To assess the performance and applicability of these methods in real-world scenarios.

Main Methods:

  • Development of two types of self-consistent estimating equations.
  • Derivation of a nondecreasing estimator from a Poisson likelihood, consistent beyond the Poisson assumption.
  • Construction of data-adaptive quasi-score functions inspired by generalized estimating equations.

Main Results:

  • The first method yields a consistent, nondecreasing estimator, equivalent to the nonparametric maximum likelihood estimator.
  • The second method provides likelihood estimating functions under a mixed-Poisson assumption.
  • Simulations demonstrate the procedures' effectiveness, and application to bladder cancer data illustrates practical utility.

Conclusions:

  • The proposed nonparametric estimation procedures are effective for analyzing counting processes with periodic observations.
  • These methods offer consistent and flexible estimation, particularly valuable when standard assumptions may not hold.
  • The study highlights the utility of these techniques in biomedical research, exemplified by the bladder cancer study.