Researchers studying hidden populations–including injection drug users, men who have sex with men, and the homeless–find that standard probability sampling methods are either inapplicable or prohibitively costly because their subjects lack a sampling frame, have privacy concerns, and constitute a small part of the general population. Therefore, researchers generally employ non-probability methods, including location sampling methods such as targeted sampling, and chain-referral methods such as snowball and respondent-driven sampling. Though nonprobability methods succeed in accessing the hidden populations, they have been insufficient for statistical inference. This paper extends the respondent-driven sampling method to show that when biases associated with chain-referral methods are analyzed in sufficient detail, a statistical theory of the sampling process can be constructed, based on which the sampling process can be redesigned to permit the derivation of indicators that are not biased and have known levels of precision. The results are based on a study of 190 injection drug users in a small Connecticut city.

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