Degree distributions in sexual networks: a framework for evaluating evidence

Abstract

Objective: We present a likelihood based statistical framework to test the fit of power-law and alternative social process models for the degree distribution, and derive the sexually transmitted infection epidemic predictions from each model.

Study design: Five surveys from the United States are analyzed. Model fit is formally compared via Akaike Information Criterion and Bayesian Information Criterion, and substantively assessed via the prediction of a generalized epidemic.

Results: Formal goodness-of-fit tests do not consistently identify any model as the best all around fit to the US data. Power-law models predict a generalized sexually transmitted infection epidemic in the United States, while most alternative models do not.

Conclusions: Power-law models do not fit the data better than alternative models, and they consistently make inaccurate epidemic predictions. Better models are needed to represent the behavioral basis of sexual networks and the structures that result, if these data are to be used for disease transmission modeling.

Fig. 1

The predicted probability mass functions from 8 models fit to the observed data from a survey of US men and women aged 20 to 39 years.

Fig. 2

The threshold transmissibility and 95% confidence intervals predicted for each of the 6 degree distributions by the best fit power-law model (top panel) and nonpower-law models (bottom panel).