Evaluating and extending a Bayesian approach to using historical control data in an actively controlled non-inferiority clinical trial

Abstract

Obstacles sometimes limit enrollment in randomized clinical trials of an exper- imental product versus an active control, making it desirable to augment the ran- domized control group with historical control groups. However, bias between control groups with respect to the mean outcome could lead to spurious conclusions. Meth- ods are necessary that allow for the combination of control groups while controlling for bias.

Pocock (1976) developed a Bayesian test to address this need, but it requires sub- jective specification of the variance of the bias between the randomized and historical control groups and is designed to include only a single historical control group. In the context of an actively controlled non-inferiority trial, we extend his method on three fronts. First, we replace subjective specification of the variance of the bias with empirically driven estimates. Second, we develop an adaptive design that re-powers a trial based on an interim estimate of the variance of the bias using observed data. Third, we modify the test to include multiple historical control groups.

When including a single historical control group, simulations show that the true bias, if known, can be used in place of the variance of the bias, and that this estimate ivmaintains Type I Error with no loss in power as compared to using the true variance of the bias. Further, we show that using an empirical estimate of the bias to estimate the variance of bias may result in moderately inflated Type I Error, but that using a conservative estimate of the bias (the upper bound of a 90% confidence interval) maintains Type I Error. Simulations also demonstrate that using an estimate of the bias at the interim and conclusion provides designed power but may result in moder- ately inflated Type I Error. Therefore, a conservative estimate of the bias should be used at trial end when using this approach. Lastly, it is shown that if an adequate number of multiple historical control groups are available, the modified test maintains Type I Error when using bias estimates. These methods provide objective guidance on parameter estimation, but further research is necessary in order to improve power.