Inferring bivariate associations with continuous data from studies using respondent-driven sampling

Respondent-driven sampling (RDS) is a link-tracing sampling design that was developed to sample from hidden populations. Although associations between variables are of great interest in epidemiological research, there has been little statistical work on inference on relationships between variables collected through RDS. The link-tracing design, combined with homophily, the tendency for people to connect to others with whom they share characteristics, induces similarity between linked individuals. This dependence inflates the Type 1 error of conventional statistical methods (e.g. t-tests, regression, etc.). A semiparametric randomization test for bivariate association was developed to test for association between two categorical variables. We directly extend this work and propose a semiparametric randomization test for relationships between two variables, when one or both are continuous. We apply our method to variables that are important for understanding tuberculosis epidemiology among people who smoke illicit drugs in Worcester, South Africa.