A number of statistical approaches have been proposed for incorporating supplemental information in randomized clinical trials. Existing methods often compare the marginal treatment effects to evaluate the degree of consistency between sources. Dissimilar marginal treatment effects would either lead to increased bias or down-weighting of the supplemental data. This represents a limitation in the presence of treatment effect heterogeneity, in which case the marginal treatment effect may differ between the sources solely due to differences between the study populations. We introduce the concept of covariate-adjusted exchangeability, in which differences in the marginal treatment effect can be explained by differences in the distributions of the effect modifiers. The potential outcomes framework is used to conceptualize covariate-adjusted and marginal exchangeability. We utilize a linear model and the existing multisource exchangeability models framework to facilitate borrowing when marginal treatment effects are dissimilar but covariate-adjusted exchangeability holds. We investigate the operating characteristics of our method using simulations. We also illustrate our method using data from two clinical trials of very low nicotine content cigarettes. Our method has the ability to incorporate supplemental information in a wider variety of situations than when only marginal exchangeability is considered.

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