## The Annals of Applied Statistics

- Ann. Appl. Stat.
- Volume 11, Number 4 (2017), 1912-1947.

### Estimating average causal effects under general interference, with application to a social network experiment

Peter M. Aronow and Cyrus Samii

#### Abstract

This paper presents a randomization-based framework for estimating causal effects under interference between units motivated by challenges that arise in analyzing experiments on social networks. The framework integrates three components: (i) an experimental design that defines the probability distribution of treatment assignments, (ii) a mapping that relates experimental treatment assignments to exposures received by units in the experiment, and (iii) estimands that make use of the experiment to answer questions of substantive interest. We develop the case of estimating average unit-level causal effects from a randomized experiment with interference of arbitrary but known form. The resulting estimators are based on inverse probability weighting. We provide randomization-based variance estimators that account for the complex clustering that can occur when interference is present. We also establish consistency and asymptotic normality under local dependence assumptions. We discuss refinements including covariate-adjusted effect estimators and ratio estimation. We evaluate empirical performance in realistic settings with a naturalistic simulation using social network data from American schools. We then present results from a field experiment on the spread of anti-conflict norms and behavior among school students.

#### Article information

**Source**

Ann. Appl. Stat., Volume 11, Number 4 (2017), 1912-1947.

**Dates**

Received: January 2016

Revised: November 2016

First available in Project Euclid: 28 December 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.aoas/1514430272

**Digital Object Identifier**

doi:10.1214/16-AOAS1005

**Mathematical Reviews number (MathSciNet)**

MR3743283

**Zentralblatt MATH identifier**

1383.62329

**Keywords**

Interference potential outcomes causal inference randomization inference SUTVA networks

#### Citation

Aronow, Peter M.; Samii, Cyrus. Estimating average causal effects under general interference, with application to a social network experiment. Ann. Appl. Stat. 11 (2017), no. 4, 1912--1947. doi:10.1214/16-AOAS1005. https://projecteuclid.org/euclid.aoas/1514430272