Abstract
BackgroundWhile guidance exists for obtaining population size estimates using multiplier methods with respondent-driven sampling surveys, we lack specific guidance for making sample size decisions.ObjectiveTo guide the design of multiplier method population size estimation studies using respondent-driven sampling surveys to reduce the random error around the estimate obtained.MethodsThe population size estimate is obtained by dividing the number of individuals receiving a service or the number of unique objects distributed (M) by the proportion of individuals in a representative survey who report receipt of the service or object (P). We have developed an approach to sample size calculation, interpreting methods to estimate the variance around estimates obtained using multiplier methods in conjunction with research into design effects and respondent-driven sampling. We describe an application to estimate the number of female sex workers in Harare, Zimbabwe.ResultsThere is high variance in estimates. Random error around the size estimate reflects uncertainty from M and P, particularly when the estimate of P in the respondent-driven sampling survey is low. As expected, sample size requirements are higher when the design effect of the survey is assumed to be greater.ConclusionsWe suggest a method for investigating the effects of sample size on the precision of a population size estimate obtained using multipler methods and respondent-driven sampling. Uncertainty in the size estimate is high, particularly when P is small, so balancing against other potential sources of bias, we advise researchers to consider longer service attendance reference periods and to distribute more unique objects, which is likely to result in a higher estimate of P in the respondent-driven sampling survey.
Highlights
Population size estimates (PSE) for those most at risk for human immunodeficiency virus infection are crucial to make epidemic projections, allocate funding, and monitor coverage of prevention and care programs [1,2]
We examined the relationship between sample size, P, and the width of the 95% confidence interval (CI) obtained for a population size estimate of 15,000, fixing this estimate so that M varied with P
For all values of P and M, increasing the respondent-driven sampling (RDS) survey sample size decreases the width of the CI around the PSE, Figure 2
Summary
Population size estimates (PSE) for those most at risk for human immunodeficiency virus infection are crucial to make epidemic projections, allocate funding, and monitor coverage of prevention and care programs [1,2]. One approach to obtaining a PSE is to use multiplier methods, including the service multiplier method (SMM) and the unique object multiplier method (UOM) The former uses 2 sources of data: (1) a count of program attendance or receipt of a service targeted to the population in question, and (2) a representative survey of the population in which uptake of service can be determined. Uncertainty in the size estimate is high, when P is small, so balancing against other potential sources of bias, we advise researchers to consider longer service attendance reference periods and to distribute more unique objects, which is likely to result in a higher estimate of P in the respondent-driven sampling survey
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