Abstract
The identification of biomarkers for disease onset in longitudinal studies necessitates precise estimation of the association between longitudinal markers and survival outcomes. Currently, methods for estimating these associations in the context of left-truncated and clustered survival outcomes are lacking. In this study, we propose a novel model tailored to this scenario and develop several estimation methods: last observation carried forward, regression calibration, and a two-stage likelihood approach for joint modeling of longitudinal and survival processes. Simulation results indicate that the last observation carried forward method performs well only with a dense grid and no marker measurement error. For less dense grids and low measurement error, regression calibration approaches are preferred. Joint modeling approaches outperform calibration methods in the presence of measurement error, although they may suffer from numerical instability. In cases of numerical instability, calibration methods might be a good alternative. We applied these methodologies to the TwinsUK data to estimate the effect of bone mineral density (BMD) as a longitudinal marker on fracture incidence in 766 elderly females, 138 of whom experienced a fracture. The survival model included a shared gamma-distributed frailty to account for correlation between the times to fracture of twin pairs. Estimates obtained using calibration and joint modeling approaches indicated a larger BMD effect compared to the last observation carried forward method, likely due to the irregular BMD measurement process and minimal measurement error. Overall, our methods offer valuable tools for modeling the effect of a longitudinal marker on survival outcomes in complex designs.