A Quantitative Bias Analysis Framework for Real-World Comparative-Effectiveness Studies Using Bayesian Data Augmentation and Restricted Survival

OBJECTIVES: Real-world comparative-effectiveness studies of time-to-event data are increasingly involved in supporting regulatory decision-making. Key concerns for such studies are the impact of unmeasured confounding and violation of the proportional hazards (PH) assumption, both of which can undermine the validity and interpretability of study conclusions. Quantitative bias analysis (QBA) provides a framework to assess robustness of study conclusions to unmeasured confounding. The difference in restricted mean survival (drmst) provides an interpretable analysis framework when non-proportional hazards are present. However, no QBA framework has been proposed to assess the impact of unmeasured confounding when using drmst. We propose a two-step QBA framework to assess the impact of unmeasured confounding in the presence of PH violation.

METHODS: The framework uses Bayesian data augmentation to adjust the analysis for unmeasured confounding with user-specified characteristics. The proposed framework is implementable under a wide range of data generating scenarios and allows the inclusion of prior information into analyses. We perform a simulation study to assess the precision and accuracy of the proposed framework in the presence of unmeasured confounding and a significant treatment effect, with several empirically informed simulation scenarios considered.

RESULTS: The proposed framework achieves a bias comparable in magnitude to an adjusted analysis when all confounders are measured, with the magnitude of the absolute average bias ranging from 0.0002 to 0.05 across all simulation scenarios. The actual confidence interval coverage rate was close to the nominal rate of 95% and ranged from 93% to 98% across all simulation scenarios.

CONCLUSIONS: We demonstrate a valid and flexible QBA framework to assess the robustness of treatment effect estimates to unmeasured confounding when PH is violated. The proposed framework can be easily extended to account for a range of contexts in which PH violation may arise and can be used as a key sensitivity analysis as part of evidence generation.