Bayesian meta-analysis of time to benefit

The clinical decisions to start a treatment for any condition require balancing short-term risks with long-term benefits. A clinically interpretable survival analysis metric in such decisions is time-to-benefit (TTB), the time at which a specific absolute risk reduction (ARR) is first obtained between two treatment arms. We describe a method for estimating TTB using Bayesian methods for meta-analysis. We first extract published survival curves using DigitizeIt and use these to reconstruct person-level time-to-event data with the Stata module ipdfc. Next, using the bayesmh command, we fit a hierarchical Bayesian model allowing for parameters of Weibull survival curves that are specific to each study and arm. We use the resulting joint posterior distribution to estimate study-specific and overall TTB for given ARR (for example, estimates and credible intervals for time until an ARR of 0.01, which is the time until an additional 1 out of 100 patients would benefit from the treatment). As a case study, the presentation shows results from a study of time-to-benefit of blood pressure medications on prevention of cardiovascular events.