Safety monitoring of a kidney transplant study using a Bayesian time-to-event model
Jonathan L. French (1), Neal Thomas (2), Sriram Krishnaswami (3), Gary Chan (4)
(1) Global Pharmacometrics, Pfizer Inc, USA; (2) Statistical Research and Consulting Center, Pfizer Inc, USA; (3) Clinical Pharmacology-Specialty Care, Pfizer Inc, USA; (4) Specialty Care, Pfizer Inc, USA
Background: Studies to investigate new treatments to prevent kidney rejection are typically active controlled studies with a primary endpoint of Month 6 biopsy proven acute rejection (BPAR). When designing these studies, there is a strong desire to monitor the study in an on-going fashion and use formal stopping rules to stop the study quickly if the experimental treatment is clearly inferior to the active control. However, because the endpoint can be 6 months from randomization, stopping rules based on the primary endpoint can be inefficient. We desired a model and stopping rule that allowed for formal incorporation of historical control data and that does not require waiting until subjects reach the Month 6 endpoint. To this end we examined stopping criteria based on estimates from a Bayesian time to event model for BPAR.
Methods: Based on a review of the literature for the active control, we developed a Bayesian piecewise exponential time-to-event model for BPAR. We assumed that the hazard function was constant over pre-specified intervals of 0-1 week, 1-4 weeks and 4-26 weeks post-transplant and not necessarily monotonic. Through moderately informative prior distributions, we formally incorporated information about historical BPAR rates for the active control. For the experimental treatment we used weakly informative priors. This model was used to estimate risk of rejection within 6 months.
We investigated stopping rules that were based on both a comparison to active control and absolute BPAR rates. Through simulation we evaluated the operating characteristics of the proposed stopping rules and compared them to classical stopping rules based on comparing hazard rates through a log-rank test.
Results: With this approach we developed stopping rules that yielded a high probability of stopping the study very quickly if the risk of rejection is much higher than the control rate and a moderately high probability of stopping before 25% of the patients are enrolled if the BPAR rate is double the control rate. The false stopping rate was controlled at a pre-specified level. The Bayesian approach was substantially better than the classical stopping rules.
Conclusions: Bayesian time-to-event modeling of acute rejection can enable efficient early monitoring of transplant studies. By formally incorporating prior belief into the analysis, we can stop earlier than with traditional stopping methods when the risk of BPAR is high.
