A valid formulation of the analysis of noninferiority trials under random effects meta-analysis

A noninferiority (NI) trial is sometimes employed to show efficacy of a new treatment when it is unethical to randomize current patients to placebo because of the established efficacy of a standard treatment. Under this framework, if the NI trial determines that the treatment advantage of the standard to the new drug (i.e. S-N) is less than the historic advantage of the standard to placebo (S-P), then the efficacy of the new treatment (N-P) is established indirectly. We explicitly combine information from the NI trial with estimates from a random effects model, allowing study-to-study variability in k historic trials. Existing methods under random effects, such as the synthesis method, fail to account for the variability of the true standard versus placebo effect in the NI trial. Our method effectively uses a prediction interval for the missing standard versus placebo effect rather than a confidence interval of the mean. The consequences are to increase the variance of the synthesis method by incorporating a prediction variance term and to approximate the null distribution of the new statistic with a t with k-1 degrees of freedom instead of the standard normal. Thus, it is harder to conclude NI of the new to (predicted) placebo, compared with traditional methods, especially when k is small or when between study variability is large. When the between study variances are nonzero, we demonstrate substantial Type I error rate inflation with conventional approaches; simulations suggest that the new procedure has only modest inflation, and it is very conservative when between study variances are zero. An example is used to illustrate practical issues.