Improving Randomization Tests under Interference Based on Power Analysis

TL;DR

This paper enhances the power of randomization tests under interference by refining subset selection based on power analysis, leading to more effective hypothesis testing in causal inference with interference effects.

Contribution

It introduces a new method to improve biclique tests by explicitly evaluating and optimizing the power of the randomization test through subset selection.

Findings

Proposed method increases test power in interference settings.

Simulation confirms higher power compared to existing methods.

Explicit power expression guides subset selection for better testing performance.

Abstract

In causal inference, we can consider a situation in which treatment on one unit affects others, i.e., interference exists. In the presence of interference, we cannot perform a classical randomization test directly because a null hypothesis is not sharp. Instead, we need to perform the randomization test restricted to a subset of units and assignments that makes the null hypothesis sharp. A previous study constructed a useful testing method, a biclique test, by reducing the selection of the appropriate subsets to searching for bicliques in a bipartite graph. However, since the power depends on the features of selected subsets, there is still room to improve the power by refining the selection procedure. In this paper, we propose a method to improve the biclique test based on a power evaluation of the randomization test. We explicitly derived an expression for the power of the randomization test under several assumptions and found that a certain quantity calculated from a given assignment set characterizes the power. Based on this fact, we propose a method to improve the power of the biclique test by modifying the selection rule for subsets of units and assignments. Through a simulation with a spatial interference setting, we confirm that the proposed method has higher power than the existing method.