Nonparametric inference for reversed mean models with panel count data

Area of Science:

• Biostatistics
• Survival Analysis
• Longitudinal Data Analysis

Background:

• Panel count data involves recurrent events observed at discrete time points.
• Recurrent event processes can be truncated by informative terminal events.
• Understanding event behavior near the terminal event is crucial.

Purpose of the Study:

• To propose a novel statistical framework for analyzing recurrent event data truncated by informative terminal events.
• To develop a robust method for estimating the mean function of recurrent events, particularly near the terminal event.
• To establish the theoretical properties and practical utility of the proposed methods.

Main Methods:

• A reversed mean model is proposed for estimating the mean function of the recurrent event process.
• A two-stage sieve likelihood-based method is developed to overcome computational challenges with nuisance parameters.
• General weak convergence theory for M-estimators with nuisance functional parameters is established and applied.

Main Results:

• The consistency and convergence rate of the two-stage estimator are theoretically established.
• Asymptotic normality of the proposed estimator is derived using the developed weak convergence theory.
• A class of two-sample tests is developed for comparing recurrent event processes.

Conclusions:

• The proposed two-stage sieve likelihood method provides a computationally feasible and statistically sound approach for analyzing truncated recurrent event data.
• The developed methods demonstrate good performance in simulation studies and are applicable to real-world panel count data.
• This research contributes to the statistical methodology for handling complex event data in longitudinal studies.