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

Abstract

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. Supplementary materials for this article are available online.

Keywords:

• Accelerated failure time
• Curve registration
• Joint modeling
• Left censoring
• Sieve estimation

Supplementary Material

Supplementary material provides the working assumption for outcome-dependent follow-up and proofs of model identifiability and the theorems.

Acknowledgments

The authors are grateful to the Editor, Associate Editor, and three referees for their insightful comments that greatly improved the paper.

Additional information

Funding

This research was supported by National Institutes of Health grants R01–GM104470 and R01–DK117208.