Addressing Non‐Exchangeability in Hybrid Control Studies: A Variable Selection Approach

There is growing interest in a hybrid control design for treatment evaluation, where a randomized controlled trial is augmented with external control data from a previous trial or a real world data source. The hybrid control design has the potential to improve efficiency but also carries the risk of introducing bias. The potential bias in a hybrid control study can be mitigated by adjusting for baseline covariates that are related to the control outcome. A key assumption for this approach is that the internal and external control outcomes are exchangeable upon conditioning on a set of measured covariates. Possible violations of the exchangeability assumption can result in bias and thus need to be addressed systematically. This article proposes a variable selection approach to addressing non‐exchangeability in hybrid control studies. Under a specified outcome regression model, possible non‐exchangeability can be represented as interactions between covariates and an external control indicator, some of which may be null (with zero coefficients). Null interactions support information borrowing, while non‐null interactions require adjustment. Identifying non‐null interactions for inclusion in the model is a variable selection problem. The adaptive lasso can be used to perform variable selection and modeling fitting, and the fitted model can be substituted into a g‐computation formula. Simulation results demonstrate that, under appropriate conditions, this approach is able to improve efficiency by incorporating external control data in the absence of full exchangeability.