Balancing Weights for Causal Inference in Observational Factorial Studies
Many scientific questions in biomedical research, environmental sciences, and psychology involve understanding the impact of multiple factors on an outcome of interest. Randomized factorial experiments are a popular tool for evaluating the causal effects of multiple treatments and their interactions simultaneously. However, drawing reliable causal inferences for multiple treatments in observational studies remains challenging. As the number of treatment combinations grows exponentially with the number of treatments, some treatment combinations can be rare or unobserved, posing additional difficulties in factorial effects estimation. To address these grand challenges, we propose a novel weighting approach tailored for observational studies with multiple treatments. Our approach uses weighted observational data to approximate a randomized factorial experiment, enabling us to estimate the effects of multiple treatments and their interactions simultaneously using the same set of weights. Our investigations suggest that the weights must balance the observed covariates and treatments for each contrast to provide unbiased estimates of the factorial effects of interest. Moreover, we discuss how to extend the proposed weighting method when some treatment combination groups are empty. Finally, we study the asymptotic behavior of the new weighting estimators and propose a consistent variance estimator, allowing researchers to conduct inferences for the factorial effects. Our approach is practical and widely applicable to various observational studies, providing a valuable tool for investigators interested in estimating the causal effects of multiple treatments.