Regression on quantile residual life.

Area of Science:

• Biostatistics
• Survival Analysis
• Medical Statistics

Background:

• Accurate prediction of long-term survival is crucial in clinical research.
• Existing methods may not fully capture covariate effects on residual lifetime beyond a specific time point.
• Right-censored data is common in survival studies, posing analytical challenges.

Purpose of the Study:

• To propose a time-specific log-linear regression method for quantile residual lifetime.
• To establish the statistical properties (consistency, asymptotic normality) of the proposed regression estimator.
• To develop and evaluate an asymptotic test statistic for covariate effects on quantile residual lifetimes.

Main Methods:

• Development of a time-specific log-linear regression model for quantile residual lifetime.
• Theoretical establishment of consistency and asymptotic normality for the regression estimator.
• Proposal of an asymptotic test statistic that bypasses the need for variance-covariance matrix estimation.

Main Results:

• The proposed regression model establishes associations between covariates and quantiles of residual lifetime.
• Consistency and asymptotic normality of the regression estimator are theoretically proven.
• Simulation studies confirm the finite sample performance of the estimator and test statistic.

Conclusions:

• The novel regression method effectively analyzes covariate effects on residual survival.
• The proposed test statistic provides a robust tool for evaluating prognostic factors.
• Application to breast cancer data demonstrates utility in estimating median residual lifetimes for long-term survivors.