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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.
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.
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