Bayesian Survival Analysis With Nonproportional Hazards

Both pravastatin and aspirin are approved by the U.S. Food and Drug Administration (FDA) for secondary prevention of cardiovascular events. This article describes statistical analyses used for a successful submission to the FDA that contends that copackaging pravastatin and aspirin provides a health benefit. From the efficacy perspective this is taken to mean that the combination is more effective than either agent considered alone. We present three Bayesian hierarchical survival models and apply them to the results of five randomized clinical trials. These trials evaluated the benefit of pravastatin in the secondary-prevention setting. Aspirin use was recorded for patients in these trials, but assignment to aspirin was not randomized. We compare the effects of pravastatin and aspirin considered in combination and when given alone. We focus on time to myocardial infarction, although it was just one of several endpoints considered in the presentation to the FDA. Two of the models assume proportional hazards and the third does not. In all three models we adjust for known covariates. Our principal focus is the probability that the combination of pravastatin and aspirin is at least as effective as the agents considered separately. We also find the probability that the combination is synergistic in the sense that the effect of the combination is better than the sum of the effects of the two agents taken alone.