Monotone spline-based least squares estimation for panel count data with informative observation times.

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• Panel count data analysis is crucial for understanding recurrent events over time.
• Correlations between event and observation processes can bias traditional statistical models.
• Existing methods often require specific models for the observation process, limiting flexibility.

Purpose of the Study:

• To develop a novel semiparametric mean model for panel count data accommodating correlated processes.
• To introduce a robust inference procedure for model parameters that does not depend on the observation process model.
• To provide a flexible statistical framework for analyzing complex recurrent event data.

Main Methods:

• Proposed a new class of semiparametric mean models for recurrent event processes.
• Incorporated interaction terms between observation history and covariates.
• Developed a monotone spline-based least squares estimation approach for parameter inference.
• Ensured estimators are consistent and asymptotically normal.

Main Results:

• The new semiparametric models effectively handle correlated recurrent event and observation processes.
• The spline-based estimation provides consistent and asymptotically normal parameter estimates.
• Simulation studies demonstrate the proposed inference procedure's strong performance.
• The method was successfully applied to real-world bladder tumor data.

Conclusions:

• The developed statistical approach offers a flexible and robust method for analyzing panel count data with correlated processes.
• The new models and inference procedure advance the statistical toolkit for recurrent event analysis.
• The approach provides reliable insights without needing to pre-specify the observation process model.