Degree Assortativity and Estimation of Degree Distribution in a Contact Network of People Who Inject Drugs

This dissertation analyzes data from a respondent driven sampling (RDS) study of people who inject drugs in Portland, OR. The objective was to assess assumptions for the use of weighted estimators to estimate a population physical contact (syringe sharing) network degree distribution. Visualization of degree distribution for social and physical networks, Kolmogorov-Smirnov tests of difference, and kernel tests of equivalence were used for comparison of distributions. Spearman’s rho and GAM non-parametric regression models were used to test for association and assess non-monotonic relationship. The validity of Markov chain assumptions for RDS was assessed using a transition matrix, Markov chain graphs, and convergence plots. The RDS II estimator with a visibility coefficient was used to estimate a population physical degree distribution. Results showed the social network and physical network were very different. Markov chain assumptions were met, and the sample could be expected to converge to equilibrium in three waves. The degree of assortativity observed was low, obviating concern about bias in the RDS estimators. RDS data may be used to estimate the degree distribution of a subgraph like the physical contact network with minimal bias where conditions are met. These results may inform network modeling and future RDS-based studies.