Semiparametric joint modeling for biomarker trajectory before disease onset.

Understanding how biomarkers change in relation to disease pathogenesis is a key area in biomedical research. We propose a semiparametric joint model to analyze the temporal evolution of biomarkers prior to the onset of disease. The model allows for a flexible biomarker trajectory that depends on two time scales: a natural time scale such as age and time to disease onset. In practice, the natural time scale often differs from time-on-study, leading to analytical challenges such as left-truncation bias. We introduce a profile kernel estimating equation approach to estimate regression coefficients and unspecified baseline mean trajectory functions. We establish the large-sample properties of the proposed estimators and conduct simulation studies to evaluate their finite-sample performance. Our method is applied to investigate brain biomarker trajectories before the onset of preclinical Alzheimer's disease. We observed a decline in cortical thickness prior to disease onset across brain regions, with APOE4 carriers showing lower levels compared to non-carriers.