Testing and Estimation of Social Network Dependence With Time to Event Data

Abstract

Nowadays, events are spread rapidly along social networks. We are interested in whether people’s responses to an event are affected by their friends’ characteristics. For example, how soon will a person start playing a game given that his/her friends like it? Studying social network dependence is an emerging research area. In this work, we propose a novel latent spatial autocorrelation Cox model to study social network dependence with time-to-event data. The proposed model introduces a latent indicator to characterize whether a person’s survival time might be affected by his or her friends’ features. We first propose a score-type test for detecting the existence of social network dependence. If it exists, we further develop an EM-type algorithm to estimate the model parameters. The performance of the proposed test and estimators are illustrated by simulation studies and an application to a time-to-event dataset about playing a popular mobile game from one of the largest online social network platforms. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Keywords:

• Cox model
• EM algorithm
• Social network dependence
• Time-to-event data

Acknowledgments

The authors thank an associate editor and referees for their thoughtful and constructive comments that help to improve the work.

Additional information

Funding

This work was partly supported by a NIH grant P01 CA142538 and a NSF grant DMS 1555244.