Time-to-Event Analysis with Unknown Time Origins via Longitudinal Biomarker Registration

In observational studies, the time origin of interest for time-to-event analysis is often unknown, such as the time of disease onset. Existing approaches to estimating the time origins are commonly built on extrapolating a parametric longitudinal model, which rely on rigid assumptions that can lead to biased inferences. In this paper, we introduce a flexible semiparametric curve registration model. It assumes the longitudinal trajectories follow a flexible common shape function with person-specific disease progression pattern characterized by a random curve registration function, which is further used to model the unknown time origin as a random start time. This random time is used as a link to jointly model the longitudinal and survival data where the unknown time origins are integrated out in the joint likelihood function, which facilitates unbiased and consistent estimation. Since the disease progression pattern naturally predicts time-to-event, we further propose a new functional survival model using the registration function as a predictor of the time-to-event. The asymptotic consistency and semiparametric efficiency of the proposed models are proved. Simulation studies and two real data applications demonstrate the effectiveness of this new approach. for this article are available online.

Automated summary

In this paper, a flexible semiparametric curve registration model is introduced to estimate the time origin in observational studies. The model assumes a flexible common shape function for the longitudinal trajectories, characterized by a random curve registration function that represents person-specific disease progression patterns. The unknown time origin is modeled as a random start time, which is used to jointly model the longitudinal and survival data. The proposed models are proved to be asymptotically consistent and semiparametrically efficient. Simulation studies and real data applications demonstrate the effectiveness of this new approach.