Sensitivity analysis for contamination in egocentric-network randomized trials with interference

TL;DR

This paper develops a sensitivity analysis framework for contamination in egocentric-network randomized trials, addressing bias in causal effect estimation due to network edges connecting disjoint samples.

Contribution

It introduces bias-corrected estimators and a novel sensitivity analysis method to assess robustness against contamination in ENRTs.

Findings

Contamination biases cause underestimation of indirect effects.

Ignoring contamination leads to overestimation of direct effects.

Application to HIV study demonstrates the importance of accounting for contamination.

Abstract

Egocentric-Network Randomized Trials (ENRTs) are increasingly used to estimate causal effects under interference when measuring complete sociocentric network data is infeasible. ENRTs rely on egocentric network sampling, where a set of egos is first sampled, and each ego recruits a subset of its neighbors as alters. Treatments are then randomized across egos. While the observed ego-networks are disjoint by design, the underlying population network may contain edges connecting them, leading to contamination. Under a design-based framework, we show that the Horvitz-Thompson estimators of direct and indirect effects are biased whenever contamination is present. To address this, we derive bias-corrected estimators and propose a novel sensitivity analysis framework based on sensitivity parameters representing the probability or expected number of missing edges. This framework is implemented via both grid sensitivity analysis and probabilistic bias analysis, providing researchers with a flexible tool to assess the robustness of the causal estimators to contamination. We apply our methodology to the HIV Prevention Trials Network 037 study, finding that ignoring contamination may lead to underestimation of indirect effects and overestimation of direct effects.