The use of priors for incorporating and discounting historical control data is a growing area of research. This is especially relevant when attempting to reduce the number of new patients randomized to a control arm. Unlike traditional RCTs, the results when control data are borrowed are especially sensitive to the prior. The amount of statistical research going on in this area is evidence that there is some arbitrariness in the choice of priors.

I wonder if this area of research got off on the wrong foot. A recent post on the Stan discourse site asked how to incorporate a posterior from a previous analysis as a prior in a new analysis when the posterior does not have an analytic form. One of the answers was to take advantage of Stan’s ability to fit joint models, and to include the prior data in one of the models instead of fashioning a prior from the previous analysis.

Consider that idea when the main fear of using historical data is bias in the estimate of the covariate-adjusted mean of the outcome variable. A second model for the control mean could be added to the Stan code, but include an error in measurement parameter for the control mean. So the model for the new data would have a parameter $\mu$ for the control mean, and the second model would have $\mu +\delta$ with a standard deviation of $\delta$ chosen according to the amount of trust placed in the control data. If the prior SD $\sigma =0$ then the historical data are being completely trusted and added to the trial data with equal stature to new observations. $\sigma =1000$ will result in ignoring the historical data. One could spend time specifying $\sigma$ instead of specifying priors.