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

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

Two population study

Two population – non coded clients

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

Robust design

R-project  – –  Required packages: – Rcapture – foreign

Rcapture installation

Data preparation Subst 2010Needle 2010Subst 2011Needle 2011Subst 2012Frequency [1,] [2,] [3,] [4,] [5,] [6,] [7,] [8,] [9,] [10,] [11,] [12,] [13,] [14,] [15,] [16,] [17,] [18,] [19,] [20,] [21,] [22,] [23,] [24,] [25,] [26,] [27,] [28,] [29,] [30,] [31,] Total % use all services These data were wrongly converted

Results Closed population model for every period: M0 Model fit: deviance df AIC fitted model Capture probabilities: estimate stderr period period Survival probabilities: estimate stderr period 1 -> Abundances: estimate stderr period period Number of new arrivals: estimate stderr period 1 -> Total number of units who ever inhabited the survey area: estimate stderr all periods Total number of captured units: 2686

Multiplier method  Network size reliability  Statistical weight  Standard error of weighted mean – SPSS x “rest of the world”

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.

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.

RDS - program  Analyst_Install Analyst_Install

RDS Analyst

RDS computing – data format Identifikacioni brojMrezaKupon1Kupon2Kupon3PolGodina rodjenjaGodine m m ž m m m ž m m m m m m m197835

Video

Results – recruitment tree

RDS – convergence (theory)

RDS - result MeanMedianMode90%3%98% Prior Posterior Summary of Population Size Estimation

RDS – convergence results

Thank you for your attention

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

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.

Corrected CRM - data Number of captured units: 6782 Frequency statistics: fi i = i = i = i = 4 51 i = 5 32 i = 6 15 fi: number of units captured i times

Corrected CRM - results YearPopulationSTD ErrorArrivedLeftStayedSTD Error Stayed all years STD Error