Extending iterative matching methods: an approach to improving covariate balance that allows prioritisation

Comparative effectiveness studies can identify the causal effect of treatment if treatment is unconfounded with outcome conditional on a set of measured covariates. Matching aims to ensure that the covariate distributions are similar between treatment and control groups in the matched samples, and this should be done iteratively by checking and improving balance. However, an outstanding concern facing matching methods is how to prioritise competing improvements in balance across different covariates. We address this concern by developing a ‘loss function’ that an iterative matching method can minimise. Our ‘loss function’ is a transparent summary of covariate imbalance in a matched sample and follows general recommendations in prioritising balance amongst covariates. We illustrate this approach by extending Genetic Matching (GM), an automated approach to balance checking. We use the method to reanalyse a high profile comparative effectiveness study of right heart catheterisation. We find that our loss function improves covariate balance compared to a standard GM approach, and to matching on the published propensity score.