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

Nowadays, events are spread rapidly along social network. We are interested in whether people’s responses to an event are affected by their friends’ characteristics. For example, how soon will a person starts 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 data set about playing a popular mobile game from one of the largest online social network platforms.