Methods of HRDU (PDU) population estimates

Bruno Sopko, Ph.D. 11th June 2014

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

Two population study

z

X Y

xy

Two population study

Small sample (Chapman estimator):

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 http://www.r-project.org/– http://cran.rstudio.com/– http://cran.rstudio.com/manuals.html

Required packages:– Rcapture– foreign

Rcapture installation

Data preparationSubst 2010 Needle 2010 Subst 2011 Needle 2011 Subst 2012 Frequency

[1,] 1 1 1 1 1 1520

[2,] 1 1 1 1 0 0

[3,] 1 1 1 0 1 0

[4,] 1 1 1 0 0 0

[5,] 1 1 0 1 1 0

[6,] 1 1 0 1 0 0

[7,] 1 1 0 0 1 0

[8,] 1 1 0 0 0 0

[9,] 1 0 1 1 1 0

[10,] 1 0 1 1 0 0

[11,] 1 0 1 0 1 0

[12,] 1 0 1 0 0 0

[13,] 1 0 0 1 1 0

[14,] 1 0 0 1 0 0

[15,] 1 0 0 0 1 0

[16,] 1 0 0 0 0 0

[17,] 0 1 1 1 1 284

[18,] 0 1 1 1 0 0

[19,] 0 1 1 0 1 0

[20,] 0 1 1 0 0 0

[21,] 0 1 0 1 1 10

[22,] 0 1 0 1 0 0

[23,] 0 1 0 0 1 205

[24,] 0 1 0 0 0 667

[25,] 0 0 1 1 1 0

[26,] 0 0 1 1 0 0

[27,] 0 0 1 0 1 0

[28,] 0 0 1 0 0 0

[29,] 0 0 0 1 1 0

[30,] 0 0 0 1 0 0

[31,] 0 0 0 0 1 0

Total 2686

57 % use all services

These data were wronglyconverted

Results Closed population model for every period: M0

Model fit: deviance df AICfitted model 3974.074 11 4011.492

Capture probabilities: estimate stderrperiod 1 0.9466 0.0028period 2 1.0000 0.0000

Survival probabilities: estimate stderrperiod 1 -> 2 0.6632 0.0092

Abundances: estimate stderrperiod 1 2735.2 7.7period 2 1814.0 0.1

Number of new arrivals: estimate stderrperiod 1 -> 2 0 0

Total number of units who ever inhabited the survey area: estimate stderrall periods 2735.2 7.7

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 MethodRespondent-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 http://

wiki.stat.ucla.edu/hpmrg/index.php/RDS_Analyst_Install

RDS Analyst

RDS computing – data formatIdentifikacioni broj Mreza Kupon1 Kupon2 Kupon3 Pol Godina rodjenja Godine

010000000000 20 011000000000 012000000000 013000000000 m 1978 35

030000000000 10 031000000000 032000000000 033000000000 m 1989 24

020000000000 29 021000000000 022000000000 023000000000 ž 1990 23

050000000000 30 051000000000 052000000000 053000000000 m 1985 28

040000000000 19 041000000000 042000000000 043000000000 m 1991 22

060000000000 6 061000000000 062000000000 063000000000 m 1978 35

070000000000 30 071000000000 072000000000 073000000000 ž 1978 35

032000000000 7 032100000000 032200000000 032300000000 m 1980 33

011000000000 20 011100000000 011200000000 011300000000 m 1982 31

021000000000 20 021100000000 021200000000 021300000000 m 1984 29

012000000000 10 012100000000 012200000000 012300000000 m 1985 28

013000000000 50 013100000000 013200000000 013300000000 m 1978 35

022000000000 50 022100000000 022200000000 022300000000 m 1981 32

053000000000 20 053100000000 053200000000 053300000000 m 1978 35

Video

Results – recruitment tree

RDS – convergence (theory)

RDS - result

Mean Median Mode 90% 3% 98% Prior 1935 1284 600 4422 766 2444 Posterior 360 359 359 384 325 401

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 - dataNumber of captured units: 6782 Frequency statistics: fi i = 1 3937i = 2 1360i = 3 1387i = 4 51i = 5 32i = 6 15fi: number of units captured i times

Corrected CRM - results

Year Population STD Error Arrived Left Stayed STD Error Stayed all years STD Error

2010 24169 1744

2011 20790 1500 8799 12178 11911 3244

2012 19813 1429 8817 7894 11919 2929 6355 4673