Binary regression analysis with network structure of respondent-driven sampling data

Respondent-driven sampling (RDS) is a procedure to sample from hard-to-reach populations. It has been widely used in several countries, especially in the monitoring of HIV/AIDS and other sexually transmitted infections. Hard-to-reach populations have had a key role in the dynamics of such epidemics and must inform evidence-based initiatives aiming to curb their spread. In this paper, we present a simple test for network dependence for a binary response variable. We estimate the prevalence of the response variable. We also propose a binary regression model taking into account the RDS structure which is included in the model through a latent random effect with a correlation structure. The proposed model is illustrated in a RDS study for HIV and Syphilis in men who have sex with men implemented in Campinas (Brazil).