Approximate Bayesian estimation of time to clinical benefit using Frequentist approaches: an application to an intensive blood pressure control trial

Background: Time to Benefit (TTB) is a critical metric in clinical practice, reflecting the duration required to achieve therapeutic goals post-treatment. Traditionally, TTB estimation has relied on Bayesian Weibull regression, which, despite its merits, can be computationally intensive. To address this, we propose and evaluate Frequentist methods as efficient alternatives to approximate Bayesian TTB estimation.

 Methods: We evaluated three Frequentist methods, parametric delta, Monte Carlo, and nonparametric bootstrap, for TTB estimation, comparing their performance with the Bayesian approach. Results: Extensive simulations demonstrated that the proposed Frequentist methods outperformed the Bayesian method in efficiency. Real-world data applications further validated these findings, with the Monte Carlo (MC) method exhibiting significantly faster computational speed compared to the nonparametric bootstrap, while the Bayesian method was the least efficient. 

Conclusions: The proposed Frequentist methods offer significant advantages to approximate the Bayesian approach for TTB estimation, particularly in efficiency and practicality. The Monte Carlo method, with its median point estimate and percentile confidence intervals, is the recommended choice for its balance of efficacy and expedience.