Adaptive aggregation for longitudinal quantile regression based on censored history process

Area of Science:

• Statistics
• Biostatistics
• Longitudinal Data Analysis

Background:

• Longitudinal quantile regression models often assume correct specification, which is difficult to achieve in practice.
• Misspecification in mixed-effects models can lead to inaccurate random effect predictions and inefficient estimators.
• There is a need for methods that incorporate multiple candidate procedures for robust longitudinal data analysis.

Purpose of the Study:

• To propose an exponential aggregation weighting algorithm for longitudinal quantile regression.
• To address challenges in model specification and improve the accuracy of cumulative quantile function estimation.
• To develop an aggregation-based best linear prediction for random effects in mixed-effects models.

Main Methods:

• Developed an exponential aggregation weighting algorithm for longitudinal quantile regression.
• Utilized a secondary smoothing loss function to establish oracle inequalities for the aggregated estimator.
• Applied the method to additive mixed-effects models with right-censored history processes.

Main Results:

• The proposed algorithm provides an aggregated estimator with established oracle inequalities.
• The method effectively evaluates cumulative quantile functions for mixed-effects models with censored data.
• An aggregation-based best linear prediction for random effects was constructed, demonstrating improved properties.

Conclusions:

• The smoothing scheme facilitates the imposition of asymptotic properties for the aggregated estimator.
• Simulation studies confirm the rationality and effectiveness of the proposed aggregation method.
• The method was successfully applied to real-world data from a multicenter automatic defibrillator implantation trial.