Abstract

Consider a population of individuals and a  network that encodes social connections among them.   We are interested in making inference on super-population estimands that are a function of both individuals' responses and of the network, from a sample. Neither the sampling frame nor the network are available. However, the sampling mechanism implicitly leverages the network to recruit individuals, thus partially revealing social interactions among the individuals in the sample, as well as their responses.   This is a common setting that arises, for instance, in epidemiology and healthcare, where samples from hard-to-reach populations are collected using link-tracing mechanisms, including respondent-driven sampling. Contrary to random sampling, the probability models of these network sampling mechanisms carry information about the estimands of interest, such as the incidence of certain diseases in the target population.   In this work, we study statistical properties of popular network sampling mechanisms. We formulate the estimation problem in terms of Rubin's inferential framework to explicitly   account for social network structure. We then identify key modeling elements that lead to inferences with good frequentist properties when dealing with data collected through non-ignorable network sampling mechanisms.   We demonstrate these methods on a study of the  incidence of HIV in Brazil.   Joint work with Edoardo Airoldi