SEMIPARAMETRIC LINEAR REGRESSION WITH AN INTERVAL-CENSORED COVARIATE IN THE ATHEROSCLEROSIS RISK IN COMMUNITIES STUDY

Area of Science:

• Biostatistics
• Epidemiology
• Longitudinal Data Analysis

Background:

• Longitudinal studies frequently assess the impact of intermediate events on future outcomes.
• Intermediate events are often asymptomatic, with their occurrence only identified within intervals from periodic examinations.
• Accurate modeling is needed for time-since-event, especially with interval-censored data.

Purpose of the Study:

• To propose a novel linear regression model for analyzing time-since-event data in longitudinal studies.
• To incorporate a rectified linear unit activation function to model the relationship between time since an intermediate event and a future outcome.
• To formulate the distribution of time to the intermediate event using the Cox proportional hazards model.

Main Methods:

• Developed a statistical model combining a rectified linear unit (ReLU) activation function with the Cox proportional hazards model.
• Employed nonparametric maximum likelihood estimation (NPMLE) for arbitrary sequences of examination times.
• Utilized an Expectation-Maximization (EM) algorithm for stable convergence with arbitrary datasets.

Main Results:

• The proposed method provides consistent, asymptotically normal, and asymptotically efficient estimators for regression parameters.
• The EM algorithm demonstrates stable convergence for diverse datasets.
• Simulation studies confirm the performance of the developed statistical methods.

Conclusions:

• The proposed statistical framework effectively analyzes longitudinal data with interval-censored time-to-event intermediate events.
• The method offers robust estimation of regression parameters, crucial for understanding event-outcome relationships.
• The approach is applicable to real-world epidemiological studies, such as the Atherosclerosis Risk in Communities Study.