## The Annals of Applied Statistics

- Ann. Appl. Stat.
- Volume 11, Number 2 (2017), 919-948.

### Vaccines, contagion, and social networks

Elizabeth L. Ogburn and Tyler J. VanderWeele

#### Abstract

Consider the causal effect that one individual’s treatment may have on another individual’s outcome when the outcome is contagious, with specific application to the effect of vaccination on an infectious disease outcome. The effect of one individual’s vaccination on another’s outcome can be decomposed into two different causal effects, called the “infectiousness” and “contagion” effects. We present identifying assumptions and estimation or testing procedures for infectiousness and contagion effects in two different settings: (1) using data sampled from independent groups of observations, and (2) using data collected from a single interdependent social network. The methods that we propose for social network data require fitting generalized linear models (GLMs). GLMs and other statistical models that require independence across subjects have been used widely to estimate causal effects in social network data, but because the subjects in networks are presumably not independent, the use of such models is generally invalid, resulting in inference that is expected to be anticonservative. We describe a subsampling scheme that ensures that GLM errors are uncorrelated across subjects despite the fact that outcomes are nonindependent. This simultaneously demonstrates the possibility of using GLMs and related statistical models for network data and highlights their limitations.

#### Article information

**Source**

Ann. Appl. Stat., Volume 11, Number 2 (2017), 919-948.

**Dates**

Received: November 2014

Revised: February 2017

First available in Project Euclid: 20 July 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.aoas/1500537729

**Digital Object Identifier**

doi:10.1214/17-AOAS1023

**Mathematical Reviews number (MathSciNet)**

MR3693552

**Zentralblatt MATH identifier**

06775898

**Keywords**

Causal inference social networks contagion peer effects

#### Citation

Ogburn, Elizabeth L.; VanderWeele, Tyler J. Vaccines, contagion, and social networks. Ann. Appl. Stat. 11 (2017), no. 2, 919--948. doi:10.1214/17-AOAS1023. https://projecteuclid.org/euclid.aoas/1500537729

#### Supplemental materials

- Application of methods from “Vaccines, contagion, and social networks” to Harvard flu data. In the supplementary material, we describe an analysis of the Harvard flu network data using our methods.Digital Object Identifier: doi:10.1214/17-AOAS1023SUPPSupplemental files are immediately available to subscribers. Non-subscribers gain access to supplemental files with the purchase of the article.