Characterizing direct and indirect causal effects when outcomes are dependent due to treatment spillover and outcome spillover

We provide novel insight into causal inference when both treatment spillover and outcome spillover occur in connected populations, by taking advantage of recent advances in statistical network analysis. Scenarios with treatment spillover and outcome spillover are challenging, because both forms of spillover affect outcomes and therefore treatment spillover and outcome spillover are intertwined, and outcomes are dependent conditional on treatments by virtue of outcome spillover. As a result, the direct and indirect causal effects arising from spillover have remained black boxes: While the direct and indirect causal effects can be identified, it is unknown how these causal effects explicitly depend on the effects of treatment, treatment spillover, and outcome spillover. We make three contributions, facilitated by low-rank random interference graphs. First, we provide novel insight into direct and indirect causal effects by disentangling the contributions of treatment, treatment spillover, and outcome spillover. Second, we provide scalable estimators of direct and indirect causal effects. Third, we establish rates of convergence for estimators of direct and indirect causal effects. These are the first convergence rates in scenarios in which treatment spillover and outcome spillover are intertwined and outcomes are dependent conditional on treatments, and the interference graph is sparse or dense.