Variational biomarker pooling with calibration for time-to-event outcomes across multiple clinical studies

Biomarkers are widely used in oncology research to study disease progression and predict survival outcomes. Pooling biomarker data across studies can improve precision, but pooled analyses are often affected by assay heterogeneity. Many studies use calibration designs because re-assaying all biospecimens on a reference platform is impractical. In pooled analyses, calibration can be incomplete when some studies have no reference measurements. This setting can be viewed as covariate measurement error in time-to-event models. Most existing methods were developed for single-cohort designs with validation or replicate measurements, and they do not directly accommodate study-specific calibration with incomplete reference data in pooled survival analyses. In this paper, we propose Variational Inference-Based Biomarker Pooling (VIBP) for censored survival data. VIBP treats the target biomarker as latent and jointly models study-specific calibration and the survival outcome using parametric survival models. Variational inference provides scalable estimation, and uncertainty is quantified using bootstrap. Through extensive simulation studies for exponential and Weibull survival data, we find that VIBP consistently provides estimates with lower bias, smaller mean squared error, and near-nominal 95% coverage across a wide range of effect sizes and censoring rates. We further apply VIBP to a real-world dataset to evaluate the association between DJ-1 protein levels and overall survival in lung squamous cell carcinoma. The results highlight the ability of VIBP to recover meaningful survival associations under sparse and heterogeneous calibration information. The proposed method provides accurate and robust estimation in the presence of inter-study variability and partially observed reference measurements, and it remains applicable even when some studies have no reference data.