Improved kth power expectile regression with nonignorable dropouts.

Area of Science:

• Statistics
• Biostatistics
• Longitudinal Data Analysis

Background:

• Longitudinal studies often face challenges with non-random dropouts and within-subject correlations.
• Existing methods like ordinary quantile regression and standard expectile regression have limitations in balancing robustness and effectiveness.
• The ACTG 193A dataset serves as a motivating example for developing advanced statistical techniques.

Purpose of the Study:

• To develop a robust statistical framework for analyzing longitudinal data with nonignorable dropouts.
• To propose a novel two-stage estimation procedure and inference methods based on kth power expectile regression (ER) and empirical likelihood.
• To effectively accommodate both within-subject correlations and nonignorable dropouts in statistical modeling.

Main Methods:

• A two-stage estimation procedure combining kth power ER and inverse probability weighting for bias correction.
• Generalized estimating equations (GEE) and generalized method of moments (GMM) for parameter estimation.
• Empirical likelihood procedures incorporating an informative working correlation structure via quadratic inference functions.

Main Results:

• The proposed methods provide bias-corrected estimators for longitudinal data with nonignorable dropouts.
• Asymptotic properties of the estimators and their confidence regions are theoretically derived.
• The finite-sample performance is validated through simulations and application to real-world data.

Conclusions:

• The kth power expectile regression offers a balanced approach to robustness and effectiveness in statistical analysis.
• The developed methods successfully address challenges posed by nonignorable dropouts and within-subject correlations.
• The study provides a valuable tool for analyzing complex longitudinal data, demonstrated by its application to the ACTG 193A data.