This dissertation presents a critical examination of Respondent-Driven Sampling (RDS) from the perspective of mathematical statistics and the theory of survey sampling. RDS is a variant of snowball sampling that has gained popularity as a method for studying populations at high risk of HIV infection. Statistical estimation of population characteristics from data collected using RDS is theoretically possible provided that one makes strong assumptions about RDS as a sampling process. However, to-date there has been no review of these assumptions from the perspective of mathematical statistics. This dissertation provides such a review. The primary conclusions of this review are that (1) the model implicitly used for computing sampling probabilities and in the RDS literature can only be valid for an extremely limited class of highly interconnected populations and (2) random variation in key parameters in this model must be taken into account when carrying out supportable inference with RDS data.
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