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Respondent-Driven Sampling is a widely-used method for sampling hard-to-reach human populations by link-tracing over their social networks. Inference from such data requires specialized techniques because the sampling process is both partially beyond the control of the researcher, and partially implicitly defined. Therefore, it is not generally possible to directly compute the sampling weights for traditional design-based inference, and likelihood inference requires modeling the complex sampling process. As an alternative, we introduce a model-assisted approach, resulting in a design-based estimator leveraging a working network model. We derive a new class of estimators for population means and a corresponding bootstrap standard error estimator. We demonstrate improved performance compared to existing estimators, including adjustment for an initial convenience sample. We also apply the method and an extension to the estimation of HIV prevalence in a high-risk population.