Ranking Treatment Saturations under Clustered Network Interference

2026-06-16

AI Summary

This study addresses the problem of ranking treatment saturation levels under clustered network interference to maximize welfare for a target population. The authors propose an Empirical Success (ES) ranking rule based on a two-stage randomized saturation experiment, which estimates welfare through pairwise comparisons of saturation levels. Innovatively integrating statistical decision theory with additively separable regret loss, the method relies solely on summary statistics of within-cluster network structures to derive a non-asymptotic upper bound on maximum regret and characterize a near-optimal first-stage saturation distribution. Theoretically, the ES rule is shown to be asymptotically optimal within the class of threshold-based rankings and effectively minimizes worst-case regret, offering a robust strategy for selecting saturation levels in practical settings.

Abstract

In this paper, we study how to rank a finite set of treatment saturations for a target population with clustered network interference. We propose an empirical success (ES) ranking rule that, for each pair of saturations, selects the saturation level with the higher estimated welfare using data from a two-stage randomized saturation design. We adopt the statistical decision theory framework with additively separable regret loss to assess the performance of the ES ranking rule. We derive non-asymptotic upper bounds on the maximum regret of the ES ranking rule that depend on the within-cluster network only through a single combinatorial summary of its dependency structure. We exploit these bounds to characterize a quasi-optimal first-stage saturation distribution within the two-stage randomized saturation design. We further show that the ES ranking rule is asymptotically optimal among threshold ranking rules in the sense of minimizing an upper bound on the worst-case regret.

Problem

• treatment saturation
• clustered network interference
• ranking
• welfare
• randomized saturation design

Innovation

• clustered network interference
• empirical success ranking
• randomized saturation design
• statistical decision theory
• non-asymptotic regret bounds