Population Size Estimations With Respondent Driven Sampling Lisa G. Johnston lsjohnston.global@gmail.com, www.lisagjohnston.com Some of these slides are borrowed from University of California, San Francisco, Global Health Sciences 1

Outline Multiplier methods^ Wisdom of the Crowds Size-SS Service multipliers Unique object multipliers Wisdom of the Crowds Size-SS UNAIDS/WHO Working Group on Global HIV/AIDS and STI Surveillance. (2010) Estimating the Size of Populations Most at Risk to HIV Infection: Participant Manual. http://globalhealthsciences.ucsf.edu/PPHG/assets/docs/Estimating%20_Population_Size_%20PM_April%2026_2010_Final.pdf.

Multiplier Method Two overlapping data sources specific to the population being estimated Non-duplicated counts of clients or distribution of unique objects a probability based survey (RDS).

Multiplier Assumptions No individual accounted more than once (non-duplicated data) Limited in and out migration Two data sources are independent of each other (i.e., inclusion in one is not related to inclusion in the other) The survey is representative of the hidden population

Multiplier Formula S = N / P S = size of population N = number of population accessing service/receiving unique object P = RDS weighted proportion (who reported accessing a service/receiving an object) If using RDS, you would use the weighted proportion for P. For 95% CI use those generated with the weighted proportions. Mahy’s comment: consider using a 2x2 table to describe this method.

Multiplier example Estimate the size of the YMSM population. Survey team distributes 400 special key chains to YMSM two weeks before the survey starts. In the questionnaire, respondents asked if they received a key chain and are shown an example of the object. 10% of the survey respondents reported receiving the key chain. 0.10 = (400/Total YMSM) Total YMSM = 400/0.1 = 4000 All YMSM Received unique object YMSM in survey

Wisdom of the Crowds-YPWID “What do you think is the highest of” “What do you think is the lowest number of” “What do you think is the most accurate number of” people 15 to 18 years, living in City X who are injecting illicit drugs?" (please give your best guess)

Successive Sampling – Size (SS-Size) In professional version of RDS Analyst Assumption that degree is decreasing as sampling progresses Based on successive sampling estimator Need prior PSEs Need network sizes for each participant Recommended: Entry date of each participants

SS-Size Output

Thank you!