2019/10/23 by David Puelz, Guillaume Basse, Puelz, David +5 · 1 citation
Physics and Astronomy · Mathematics · Medicine · #Complex Network Analysis Techniques #Advanced Causal Inference Techniques #Data-Driven Disease Surveillance
paper · pdf · doi:10.48550/arxiv.1910.10862
Interference exists when a unit's outcome depends on another unit's treatment\nassignment. For example, intensive policing on one street could have a\nspillover effect on neighboring streets. Classical randomization tests\ntypically break down in this setting because many null hypotheses of interest\nare no longer sharp under interference. A promising alternative is to instead\nconstruct a conditional randomization test on a subset of units and assignments\nfor which a given null hypothesis is sharp. Finding these subsets is\nchallenging, however, and existing methods are limited to special cases or have\nlimited power. In this paper, we propose valid and easy-to-implement\nrandomization tests for a general class of null hypotheses under arbitrary\ninterference between units. Our key idea is to represent the hypothesis of\ninterest as a bipartite graph between units and assignments, and to find an\nappropriate biclique of this graph. Importantly, the null hypothesis is sharp\nwithin this biclique, enabling conditional randomization-based tests. We also\nconnect the size of the biclique to statistical power. Moreover, we can apply\noff-the-shelf graph clustering methods to find such bicliques efficiently and\nat scale. We illustrate our approach in settings with clustered interference\nand show advantages over methods designed specifically for that setting. We\nthen apply our method to a large-scale policing experiment in Medellin,\nColombia, where interference has a spatial structure.\n