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.