Accelerated failure time model for case-cohort design with longitudinal covariates subject to measurement error and detection limits.

Biomarkers are often measured over time in epidemiological studies and clinical trials for better understanding of the mechanism of diseases. In large cohort studies, case-cohort sampling provides a cost effective method to collect expensive biomarker data for revealing the relationship between biomarker trajectories and time to event. However, biomarker measurements are often limited by the sensitivity and precision of a given assay, resulting in data that are censored at detection limits and prone to measurement errors. Additionally, the occurrence of an event of interest may preclude biomarkers from being further evaluated. Inappropriate handling of these types of data can lead to biased conclusions. Under a classical case cohort design, we propose a modified likelihood-based approach to accommodate these special features of longitudinal biomarker measurements in the accelerated failure time models. The maximum likelihood estimators based on the full likelihood function are obtained by Gaussian quadrature method. We evaluate the performance of our case-cohort estimator and compare its relative efficiency to the full cohort estimator through simulation studies. The proposed method is further illustrated using the data from a biomarker study of sepsis among patients with community acquired pneumonia.