Assessing Bias in Population Size Estimates Among Hidden Populations When Using the Service Multiplier Method Combined With Respondent-Driven Sampling Surveys: Survey Study

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Abstract
Background: Population size estimates (PSEs) for hidden populations at increased risk of HIV, including female sex workers (FSWs), are important to inform public health policy and resource allocation. The service multiplier method (SMM) is commonly used to estimate the sizes of hidden populations. We used this method to obtain PSEs for FSWs at 9 sites in Zimbabwe and explored methods for assessing potential biases that could arise in using this approach. Objective: This study aimed to guide the assessment of biases that arise when estimating the population sizes of hidden populations using the SMM combined with respondent-driven sampling (RDS) surveys. Methods: We conducted RDS surveys at 9 sites in late 2013, where the Sisters with a Voice program (the program), which collects program visit data of FSWs, was also present. Using the SMM, we obtained PSEs for FSWs at each site by dividing the number of FSWs who attended the program, based on program records, by the RDS-II weighted proportion of FSWs who reported attending this program in the previous 6 months in the RDS surveys. Both the RDS weighting and SMM make a number of assumptions, potentially leading to biases if the assumptions are not met. To test these assumptions, we used convergence and bottleneck plots to assess seed dependence of RDS-II proportion estimates, chi-square tests to assess if there was an association between the characteristics of FSWs and their knowledge of program existence, and logistic regression to compare the characteristics of FSWs attending the program with those recruited to RDS surveys. Results: The PSEs ranged from 194 (95% CI 62-325) to 805 (95% CI 456-1142) across 9 sites from May to November 2013. The 95% CIs for the majority of sites were wide. In some sites, the RDS-II proportion of women who reported program use in the RDS surveys may have been influenced by the characteristics of selected seeds, and we also observed bottlenecks in some sites. There was no evidence of association between characteristics of FSWs and knowledge of program existence, and in the majority of sites, there was no evidence that the characteristics of the populations differed between RDS and program data. Conclusions: We used a series of rigorous methods to explore potential biases in our PSEs. We were able to identify the biases and their potential direction, but we could not determine the ultimate direction of these biases in our PSEs. We have evidence that the PSEs in most sites may be biased and a suggestion that the bias is toward underestimation, and this should be considered if the PSEs are to be used. These tests for bias should be included when undertaking population size estimation using the SMM combined with RDS surveys.

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