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Background <p>Time to benefit (TTB) has emerged as a clinically interpretable estimand for characterizing when treatment effects become meaningful over time. Unlike conventional survival summaries, TTB is implicitly defined through marginal differences in survival probabilities and is therefore highly sensitive to modeling assumptions. In multicenter studies involving clustered time-to-event data, unobserved heterogeneity and misspecification of the baseline hazard present additional challenges for coherent TTB estimation.</p> Methods <p>We propose a unified framework for estimating TTB in clustered survival settings using marginal survival modeling with shared frailty. Specifically, TTB is defined on the marginal population scale by integrating over the frailty distribution, ensuring coherence between the estimand and its clinical interpretation. Both parametric and flexible spline-based baseline hazard models are evaluated. Uncertainty is quantified using the Delta method and Monte Carlo (MC)-based inference procedures. Extensive simulation studies are conducted to characterize estimator behavior under varying degrees of heterogeneity, censoring, and hazard misspecification. Furthermore, the framework is illustrated using data from the Systolic Blood Pressure Intervention Trial (SPRINT), a large multicenter randomized clinical trial.</p> Results <p>Simulation results indicate that ignoring latent heterogeneity or misspecifying the baseline hazard can bias TTB estimation and produce miscalibrated confidence intervals, particularly under small absolute risk reduction thresholds. Flexible hazard models combined with MC-based inference yield more stable estimates and improved coverage in the presence of model misspecification. In the SPRINT application, TTB point estimates remained relatively consistent across modeling approaches, while statistically significant frailty effects revealed meaningful between-site heterogeneity, highlighting its importance for accurate uncertainty quantification.</p> Conclusions <p>TTB is a model-sensitive implicit estimand; reliable estimation in clustered survival settings requires explicit alignment among the estimand definition, the survival model, and&#xa0;the inference strategy. The proposed framework provides a principled and practical approach to TTB estimation in multicenter studies, facilitating transparent and interpretable reporting of TTB in both clinical and real-world research contexts.</p>

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Time to benefit estimation in multicenter studies using flexible hazard shared frailty models

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月7日

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  • Mengyi Lu,
  • Zhuoyue Wu,
  • Yang Zhao,
  • Fang Shao

摘要

Background

Time to benefit (TTB) has emerged as a clinically interpretable estimand for characterizing when treatment effects become meaningful over time. Unlike conventional survival summaries, TTB is implicitly defined through marginal differences in survival probabilities and is therefore highly sensitive to modeling assumptions. In multicenter studies involving clustered time-to-event data, unobserved heterogeneity and misspecification of the baseline hazard present additional challenges for coherent TTB estimation.

Methods

We propose a unified framework for estimating TTB in clustered survival settings using marginal survival modeling with shared frailty. Specifically, TTB is defined on the marginal population scale by integrating over the frailty distribution, ensuring coherence between the estimand and its clinical interpretation. Both parametric and flexible spline-based baseline hazard models are evaluated. Uncertainty is quantified using the Delta method and Monte Carlo (MC)-based inference procedures. Extensive simulation studies are conducted to characterize estimator behavior under varying degrees of heterogeneity, censoring, and hazard misspecification. Furthermore, the framework is illustrated using data from the Systolic Blood Pressure Intervention Trial (SPRINT), a large multicenter randomized clinical trial.

Results

Simulation results indicate that ignoring latent heterogeneity or misspecifying the baseline hazard can bias TTB estimation and produce miscalibrated confidence intervals, particularly under small absolute risk reduction thresholds. Flexible hazard models combined with MC-based inference yield more stable estimates and improved coverage in the presence of model misspecification. In the SPRINT application, TTB point estimates remained relatively consistent across modeling approaches, while statistically significant frailty effects revealed meaningful between-site heterogeneity, highlighting its importance for accurate uncertainty quantification.

Conclusions

TTB is a model-sensitive implicit estimand; reliable estimation in clustered survival settings requires explicit alignment among the estimand definition, the survival model, and the inference strategy. The proposed framework provides a principled and practical approach to TTB estimation in multicenter studies, facilitating transparent and interpretable reporting of TTB in both clinical and real-world research contexts.