On efficient covariate adjustment selection in causal effect estimation

In order to achieve unbiased and efficient estimators of causal effects from observational data, covariate selection for confounding adjustment becomes an important task in causal inference. Despite recent advancements in graphical criterion for constructing valid and efficient adjustment sets, these methods often rely on assumptions that may not hold in practice. We examine the properties of existing graph-free covariate selection methods with respect to both validity and efficiency, highlighting the potential dangers of producing invalid adjustment sets when hidden variables are present. To address this issue, we propose a novel graph-free method, referred to as CMIO, adapted from Mixed Integer Optimization (MIO) with a set of causal constraints. Our results demonstrate that CMIO outperforms existing state-of-the-art methods and provides theoretically sound outputs. Furthermore, we present a revised version of CMIO capable of handling the scenario in the absence of causal sufficiency and graphical information, offering efficient and valid covariate adjustments for causal inference.