Statistical Inference for Counting Processes Under Shape Heterogeneity.

Area of Science:

• Biostatistics
• Survival Analysis
• Epidemiology

Background:

• Proportional rate models are widely used for recurrent event data analysis.
• The proportional rate assumption restricts covariate effects to magnitude changes, not shape modifications.
• Violation of this assumption necessitates alternative modeling strategies.

Purpose of the Study:

• To propose a novel statistical framework for analyzing recurrent event data when the proportional rate assumption fails.
• To characterize covariate effects on both the shape and magnitude of the rate function.
• To develop robust estimation methods for these complex covariate effects.

Main Methods:

• Introduced shape and size parameters to model flexible covariate effects on the rate function.
• Proposed a conditional pseudolikelihood approach to estimate shape parameters by eliminating size parameters.
• Utilized an event count projection approach for estimating size parameters.

Main Results:

• The proposed estimators for shape and size parameters are asymptotically normal with a root-n convergence rate.
• Simulation studies demonstrated the effectiveness of the new methods.
• Application to SEER-Medicare data on recurrent hospitalizations showcased practical utility.

Conclusions:

• The developed methods provide a flexible and interpretable way to analyze recurrent event data beyond the proportional rates assumption.
• This framework enhances the understanding of covariate impacts on event rates over time.
• The approach is validated through simulations and real-world healthcare data analysis.