Generalizing some key results from "alternative weighting schemes when performing matching-adjusted indirect comparisons"

A recent paper proposed an alternative weighting scheme when performing matching-adjusted indirect comparisons. This alternative approach follows the conventional one in matching the covariate means across two studies but differs in that it maximizes the effective sample size when doing so. The appendix of this paper showed, assuming there is one covariate and negative weights are permitted, that the resulting weights are linear in the covariates. This explains how the alternative method achieves a larger effective sample size and results in a metric that quantifies the difficulty of matching on particular covariates. We explain how these key results generalize to the case where there are multiple covariates, giving rise to a new metric that can be used to quantify the impact of matching on multiple covariates.