Simultaneous Estimation of Multiple Treatment Effects from Observational Studies

Unmeasured confounding presents a significant challenge in causal inference from observational studies. Classical approaches often rely on collecting proxy variables, such as instrumental variables. However, in applications where the effects of multiple treatments are of simultaneous interest, finding a sufficient number of proxy variables for consistent estimation of treatment effects can be challenging. Various methods in the literature exploit the structure of multiple treatments to address unmeasured confounding. In this paper, we introduce a novel approach to causal inference with multiple treatments, assuming sparsity in the causal effects. Our procedure autonomously selects treatments with non-zero causal effects, thereby providing a sparse causal estimation. Comprehensive evaluations using both simulated and Genome-Wide Association Study (GWAS) datasets demonstrate the effectiveness and robustness of our method compared to alternative approaches.