Weighted Euclidean balancing for a matrix exposure in estimating causal effect

With the increasing complexity of data, researchers in various fields have become increasingly interested in estimating the causal effect of a matrix exposure, which involves complex multivariate treatments, on an outcome. Balancing covariates for the matrix exposure is essential to achieve this goal. While exact balancing and approximate balancing methods have been proposed for multiple balancing constraints, dealing with a matrix treatment introduces a large number of constraints, making it challenging to achieve exact balance or select suitable threshold parameters for approximate balancing methods. To address this challenge, the weighted Euclidean balancing method is proposed, which offers an approximate balance of covariates from an overall perspective. In this study, both parametric and nonparametric methods for estimating the causal effect of a matrix treatment is proposed, along with providing theoretical properties of the two estimations. To validate the effectiveness of our approach, extensive simulation results demonstrate that the proposed method outperforms alternative approaches across various scenarios. Finally, we apply the method to analyze the causal impact of the omics variables on the drug sensitivity of Vandetanib. The results indicate that EGFR CNV has a significant positive causal effect on Vandetanib efficacy, whereas EGFR methylation exerts a significant negative causal effect.