Methods of HRDU (PDU) population estimates

1. Methods of HRDU (PDU) population estimates Bruno Sopko, Ph.D. 11th June 2014

2. Content • Capture-recapturemethod • Multipliermethod(overview) • RDS method

3. Two population study

4. Two population study Small sample (Chapman estimator):

5. Two population – non coded clients

6. Three and more samples • R – statistical program • R add-ons (Rcapture) • Log-linear estimation (Poisson, Chao, AIC) • Data preparation

7. Robust design

8. R-project • http://www.r-project.org/ • http://cran.rstudio.com/ • http://cran.rstudio.com/manuals.html • Required packages: • Rcapture • foreign

10. Rcapture installation

11. Data preparation These data were wrongly converted 57 % use all services

12. Closedpopulation model forevery period: M0 Model fit: deviancedf AIC fitted model 3974.074 11 4011.492 Captureprobabilities: estimatestderr period 1 0.9466 0.0028 period 2 1.0000 0.0000 Survivalprobabilities: estimatestderr period 1 -> 2 0.6632 0.0092 Abundances: estimatestderr period 1 2735.2 7.7 period 2 1814.0 0.1 Numberofnewarrivals: estimatestderr period 1 -> 2 0 0 Totalnumberofunitswhoeverinhabitedthesurvey area: estimatestderr allperiods 2735.2 7.7 Totalnumberofcapturedunits: 2686 Results

13. Multiplier method • Network size reliability • Statistical weight • Standard errorofweightedmean – SPSS x “rest of the world”

14. Response driven sampling Method Respondent-driven sampling (RDS), combines “snowball sampling" (getting individuals to refer those they know, these individuals in turn refer those they know and so on) with a mathematical model that weights the sample to compensate for the fact that the sample was collected in a non-random way.

15. RDS – essential information • Personal Network Size (Degree) - Number of people the respondent knows within the target population. • Respondent's Serial Number - Serial number of the coupon the respondent was recruited with. • Respondent's Recruiting Serial Numbers - Serial numbers from the coupons the respondent is given to recruit others.

16. RDS - program • http://wiki.stat.ucla.edu/hpmrg/index.php/RDS_Analyst_Install

17. RDS Analyst

18. RDS computing – data format

19. Video

20. Results – recruitment tree

22. RDS – convergence (theory)

23. RDS - result SummaryofPopulationSizeEstimation

24. RDS – convergence results

25. Thank you for your attention

26. Corrected CRM – preliminary biasobservation • The codes supplied were from Syringe exchange program and from Substitution treatment program • These programs are mutually exclusive – therefore negatively biased • The data were collected over three years, therefore data from the same program have been positively biased • The data from Syringe exchange program for year 2012 were incomplete

27. Corrected CRM - method • Due to the previously described bias problems, the classical robust design method (robustd.0 or robustd.t functions in R) could not be deployed. • The capture-recapture method with bias correction over all years have been used (closedp.mX function in R), the total number of estimated PDU has been broken into years values by the corresponding code counts.

28. Corrected CRM - data Number of captured units: 6782 Frequency statistics: fi i = 1 3937 i = 2 1360 i = 3 1387 i = 4 51 i = 5 32 i = 6 15 fi: number of units captured i times

29. Corrected CRM - results