Partially linear single-index generalized mean residual life models.

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• The mean residual life (MRL) function is crucial for understanding remaining life expectancy, often used alongside the hazard function.
• Current MRL models often assume linear relationships, which may not capture complex interactions or nonlinear effects of risk factors.
• Advanced statistical frameworks are needed to model intricate associations between risk factors and time-to-event outcomes.

Purpose of the Study:

• To propose novel partially linear single-index generalized mean residual life (MRL) models.
• To address limitations of existing MRL models by incorporating nonlinear effects and complex correlations of risk factors.
• To develop robust statistical methods for analyzing time-to-event data with potentially complex predictor relationships.

Main Methods:

• Developed partially linear single-index generalized MRL models using regression splines for nonparametric functions.
• Employed an iterative algorithm for parameter estimation and proposed double-robust estimators.
• Introduced a nonparametric test to assess the linearity of the single-index function.

Main Results:

• Established asymptotic properties for the proposed estimators.
• Demonstrated the finite-sample performance through extensive numerical simulations.
• Validated the models using a New York University Langone Health (NYULH) COVID-19 dataset.

Conclusions:

• The proposed partially linear single-index generalized MRL models effectively capture complex relationships between risk factors and survival outcomes.
• Double-robust estimators provide protection against model misspecification.
• The developed methods offer a flexible and robust approach for survival data analysis, as shown in the COVID-19 dataset analysis.