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Estimation and Efficiency with Recurrent Event Data under Informative Monitoring.

Akim Adekpedjou¹, Edsel A Peña, Jonathan Quiton

¹A. Adekpedjou ( akima@umr.edu ) is Assistant Professor, Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409. He acknowledges research support by NSF Grant DMS 0243594 (PI: J. Lynch) and NIH Grant GM 056182 (PI: E. Peña).

Journal of Statistical Planning and Inference

|February 18, 2010

Summary

This study introduces a statistical model for recurrent events, accounting for informative monitoring times. Exploiting this informative structure significantly enhances the efficiency of estimating event distributions.

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Area of Science:

Statistics
Survival Analysis
Reliability Engineering

Background:

Recurrent event data analysis is crucial in various fields.
Standard methods often overlook the impact of monitoring periods on event data.
Informative monitoring can bias or reduce the efficiency of parameter estimation.

Purpose of the Study:

To develop and analyze statistical methods for recurrent event data where monitoring times are informative.
To estimate parameters of the underlying inter-event time distribution (F) and a related parameter (beta).
To assess the efficiency gains achieved by incorporating informative monitoring into statistical models.

Main Methods:

Utilizing a generalized Koziol-Green model where survival functions are related (1 - G = (1 - F)(beta)).
Developing estimators for the inter-event time distribution parameters (theta), the monitoring time parameter (beta), and the distribution function (F).
Deriving asymptotic properties of these estimators and comparing their efficiencies.

Main Results:

Asymptotic properties of estimators for theta, beta, and F are established.
Significant efficiency gains are demonstrated when the informative monitoring aspect is exploited.
The proposed methods show superior performance compared to ignoring the monitoring structure.

Conclusions:

The informative monitoring structure in recurrent event studies provides valuable information for statistical inference.
Exploiting this structure leads to more efficient estimation of event and monitoring parameters.
The developed methodology is demonstrated for exponential and Weibull inter-event time distributions.