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

2. Content  Capture-recapture method  Multiplier method (overview)  RDS method

3. Two population study

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://www.r-project.org/ – http://cran.rstudio.com/ http://cran.rstudio.com/ – http://cran.rstudio.com/manuals.html http://cran.rstudio.com/manuals.html  Required packages: – Rcapture – foreign

10. Rcapture installation

11. Data preparation Subst 2010Needle 2010Subst 2011Needle 2011Subst 2012Frequency [1,]111111520 [2,]111100 [3,]111010 [4,]111000 [5,]110110 [6,]110100 [7,]110010 [8,]110000 [9,]101110 [10,]101100 [11,]101010 [12,]101000 [13,]100110 [14,]100100 [15,]100010 [16,]100000 [17,]01111284 [18,]011100 [19,]011010 [20,]011000 [21,]0101110 [22,]010100 [23,]01001205 [24,]01000667 [25,]001110 [26,]001100 [27,]001010 [28,]001000 [29,]000110 [30,]000100 [31,]000010 Total2686 57 % use all services These data were wrongly converted

12. Results Closed population model for every period: M0 Model fit: deviance df AIC fitted model 3974.074 11 4011.492 Capture probabilities: estimate stderr period 1 0.9466 0.0028 period 2 1.0000 0.0000 Survival probabilities: estimate stderr period 1 -> 2 0.6632 0.0092 Abundances: estimate stderr period 1 2735.2 7.7 period 2 1814.0 0.1 Number of new arrivals: estimate stderr period 1 -> 2 0 0 Total number of units who ever inhabited the survey area: estimate stderr all periods 2735.2 7.7 Total number of captured units: 2686

13. Multiplier method  Network size reliability  Statistical weight  Standard error of weighted mean – 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 http://wiki.stat.ucla.edu/hpmrg/index.php/RDS_ Analyst_Install

17. RDS Analyst

18. RDS computing – data format Identifikacioni brojMrezaKupon1Kupon2Kupon3PolGodina rodjenjaGodine 01000000000020011000000000012000000000013000000000m197835 03000000000010031000000000032000000000033000000000m198924 02000000000029021000000000022000000000023000000000ž199023 05000000000030051000000000052000000000053000000000m198528 04000000000019041000000000042000000000043000000000m199122 0600000000006061000000000062000000000063000000000m197835 07000000000030071000000000072000000000073000000000ž197835 0320000000007032100000000032200000000032300000000m198033 01100000000020011100000000011200000000011300000000m198231 02100000000020021100000000021200000000021300000000m198429 01200000000010012100000000012200000000012300000000m198528 01300000000050013100000000013200000000013300000000m197835 02200000000050022100000000022200000000022300000000m198132 05300000000020053100000000053200000000053300000000m197835

19. Video

20. Results – recruitment tree

22. RDS – convergence (theory)

23. RDS - result MeanMedianMode90%3%98% Prior1935128460044227662444 Posterior360359 384325401 Summary of Population Size Estimation

24. RDS – convergence results

25. Thank you for your attention

26. Corrected CRM – preliminary bias observation  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 YearPopulationSTD ErrorArrivedLeftStayedSTD Error Stayed all years STD Error 2010241691744 2011207901500879912178119113244 20121981314298817789411919292963554673