Hidden population size estimation and diagnostics using two respondent-driven samples with applications in Armenia.

Estimating the size of hidden populations is essential to understand the magnitude of social and healthcare needs, risk behaviors, and disease burden. However, due to the hidden nature of these populations, they are difficult to survey, and there are no gold standard size estimation methods. Many different methods and variations exist, and diagnostic tools are needed to help researchers assess method-specific assumptions as well as compare between methods. Further, because many necessary mathematical assumptions are unrealistic for real survey implementation, assessment of how robust methods are to deviations from the stated assumptions is essential. We describe diagnostics and assess the performance of a new population size estimation method, capture-recapture with successive sampling population size estimation (CR-SS-PSE), which we apply to data from 3 years of studies from three cities and three hidden populations in Armenia. CR-SS-PSE relies on data from two sequential respondent-driven sampling surveys and extends the successive sampling population size estimation (SS-PSE) framework by using the number of individuals in the overlap between the two surveys and a model for the successive sampling process to estimate population size. We demonstrate that CR-SS-PSE is more robust to violations of successive sampling assumptions than SS-PSE. Further, we compare the CR-SS-PSE estimates to population size estimations using other common methods, including unique object and service multipliers, wisdom of the crowd, and two-source capture-recapture to illustrate volatility across estimation methods.

Estimating the size of populations at high risk for HIV using respondent-driven sampling data.

The study of hard-to-reach populations presents significant challenges. Typically, a sampling frame is not available, and population members are difficult to identify or recruit from broader sampling frames. This is especially true of populations at high risk for HIV/AIDS. Respondent-driven sampling (RDS) is often used in such settings with the primary goal of estimating the prevalence of infection. In such populations, the number of people at risk for infection and the number of people infected are of fundamental importance. This article presents a case-study of the estimation of the size of the hard-to-reach population based on data collected through RDS. We study two populations of female sex workers and men-who-have-sex-with-men in El Salvador. The approach is Bayesian and we consider different forms of prior information, including using the UNAIDS population size guidelines for this region. We show that the method is able to quantify the amount of information on population size available in RDS samples. As separate validation, we compare our results to those estimated by extrapolating from a capture-recapture study of El Salvadorian cities. The results of our case-study are largely comparable to those of the capture-recapture study when they differ from the UNAIDS guidelines. Our method is widely applicable to data from RDS studies and we provide a software package to facilitate this.

Gender Characteristics and Population Size Estimation of Transgender People: A Field-Based Study from Iran.

Purpose: We determined the size of the transgender population in Shiraz, Iran. Methods: In this cross-sectional study, the respondent-driven sampling technique was used by choosing eight seeds, three waves, and six coupons for each participant. The estimated population size was calculated by wisdom of the crowds, multiplier, and successive sampling-population size estimation (SS-PSE) methods. Pooling of results was done by an Anchored Multiplier calculator. Results: The mean age of participants (n=200) was 22.7±4 years, 197 (98.5%) were single, 86 (43%) were educated <12 years, 25 (12.5%) were not living with their families, and 52 (26%) were not financially supported by their parents. The transgender population was estimated by the wisdom of the crowds, multiplier, and SS-PSE methods to be 300 (95% confidence interval [CI]: 200-400), 677 (95% CI: 655-696), and 665 (95% CI: 624- 677), respectively. Their prevalence was found to be 0.017% (95% CI: 0.011-0.022%), 0.038% (95% CI: 0.036-0.039%), and 0.037% (95% CI: 0.034-0.038) using the same methods, respectively. Pooled results revealed that 22-37 per 100,000 general population were transgender individuals. Weighted estimation showed that trans men (56.6%) are more prevalent than trans women (43.4%), and only 17% of transgender people succeeded in gender reassignment. Conclusion: Transgender people should not be considered as marginalized groups of the community; they should be respected, heard, and valued. Establishing a standard and routine procedure for the collection of data on the status of transgender people and gender identity is necessary for policymaking and intervention programs.

Improved estimation of population variance in stratified successive sampling using calibrated weights under non-response.

This paper introduces a new method to estimate the population variance of a study variable in stratified successive sampling over two occasions, while accounting for random non-response. The method uses a logarithmic type estimator and leverages information from a highly positively correlated auxiliary variable. The paper also presents calibrated weights for the new estimator and examines its properties through numerical and simulation studies. The results indicate that the suggested estimator is more effective than the standard estimator for estimating the population variance.

Estimating the growth rate of infection during the early phase of a pandemic like COVID-19.

At the very outbreak of a pandemic, it is very important to be able to assess the spreading rate of the disease i.e., the rate of increase of infected people in a specific locality. Combating the pandemic situation critically depends on an early and correct prediction of, to what extent the disease may possibly grow within a short period of time. This paper attempts to estimate the spreading rate by counting the total number of infected persons at times. Adaptive clustering is especially suitable for forming clusters of infected persons distributed spatially in a locality and successive sampling is used to measure the growth in number of infected persons. We have formulated a 'chain ratio to regression type estimator of population total' in two occasions adaptive cluster successive sampling and studied the properties of the estimator. The efficacy of the proposed strategy is demonstrated through simulation technique as well as real life population which is followed by suitable recommendation.

Study to Alter the Nuisance Effect of Non-Response Using Scrambled Mechanism.

INTRODUCTION: In biometric sample surveys, our objective is to get ready-made information for future planning and policy implementations related to the subject matters of highly sensitive issues. In such situations, we apply randomized response/scrambled response techniques. There are many highly sensitive issues which need to be examined over time as they may have a tendency to change. To get rid of these types of practical cases we need a scrambled response technique on successive occasions. METHODS: Using an additive and multiplicative technique, we proposed new effective scrambled response models to estimate the population mean of quantitative sensitive characteristics. Degree of privacy protection and unified measure approaches are used to examine the efficacy of the proposed models. Efficiency of the proposed models has been checked using MATLAB software. The utility of the proposed models under two occasions of successive sampling has been also explored using exponential-type estimators. Empirical and simulation studies are carried out to justify the proposition of the proposed estimators using MATLAB software. RESULTS: The percent relative efficiencies of the proposed models are always greater than 100 with respect to the well-known Bar-Lev et al model. In terms of degree of privacy protection, most of the values are greater than 0.5 and closer to 1. Similarly, the values of the proposed models are smaller with respect to the Bar-Lev et al model in terms of a unified measure approach. When the proposed scrambled response models are used on successive occasions, the percent relative efficiency is always found greater than 100 for all cases over its competitors. DISCUSSION: In this study, after deeply examining the properties of the proposed models, we found that the proposed models performed better over the well-known existing model. The proposed models may be used in human survey when we deal with highly sensitive issues. The proposed models also performed better when we utilized them in successive sampling. Hence, if sensitive characteristics change with time, the proposed estimators may be the best alternative to deal with these types of situations. MATHEMATICS SUBJECT CLASSIFICATION: 62D05.

Population Size Estimation of Female Sex Workers in Hai Phong, Vietnam: Use of Three Source Capture-Recapture Method.

INTRODUCTION: A study was conducted in three districts in Hai Phong province, Vietnam to estimate the population size of the Female Sex Workers (FSW) in June-July 2019. METHODS: The procedures included selection of three districts, compilation of a list of accessible venues where FSW congregate, distribution of first unique objects (first capture) and second unique objects (second capture) to FSW in randomly selected venues and implementation of a Mini-Respondent Driven Sampling (mRDS) Survey (third capture). Population size of the FSW was calculated based on the number of FSW in each round, number of FSW 'recaptured' during the second and the third captures. Additionally, personal network size data captured in the mRDS was used to measure the population of FSW within the three districts using Successive Sampling Population Size Estimates (SS-PSE). RESULTS: The total estimated FSWs in the three selected districts, using Three Source Capture-Recapture (3S-CRC) was 958, which is slightly lower than that estimated using SS-PSE - 1192. The 3S-CRC method yielded a provincial estimate of 1911 while the SS-PSE method resulted in a total of 2379 FSW for the province. CONCLUSION: Two techniques produced different PSE at both the district and the province levels and resulted in estimates lower than ones produced using programmatic data. For planning HIV prevention and care service needs among all FSWs, additional studies are needed to estimate the number of sex workers who are not venue-based and use social media platforms to sell services.

Kuantim mi tu ("Count me too"): Using Multiple Methods to Estimate the Number of Female Sex Workers, Men Who Have Sex With Men, and Transgender Women in Papua New Guinea in 2016 and 2017.

BACKGROUND: Female sex workers (FSW), men who have sex with men (MSM), and transgender women (TGW) are at high risk of acquiring HIV in many settings, such as Papua New Guinea (PNG). An understanding of the approximate size of these populations can inform resource allocation for HIV services for FSW, MSM, and TGW. OBJECTIVE: An objective of this multi-site survey was to conduct updated population size estimations (PSE) of FSW and MSM/TGW. METHODS: Respondent-driven sampling (RDS) biobehavioral surveys of FSW and MSM/TGW were conducted in 3 major cities-(1) Port Moresby, (2) Lae, and (3) Mount Hagen-between June 2016 and December 2017. Eligibility criteria for FSW included: (1) ≥12 years of age, (2) born female, (3) could speak English or Tok Pisin (PNG Pidgin), and (4) had sold or exchanged sex with a man in the past six months. Eligibility for MSM/TGW included: (1) ≥12 years of age, (2) born male, (3) could speak English, or Tok Pisin, and (4) had engaged in oral or anal sex with another person born male in the past six months. PSE methods included unique object multiplier, service multiplier, and successive sampling-population size estimation (SS-PSE) using imputed visibility. Weighted data analyses were conducted using RDS-Analyst and Microsoft Excel. RESULTS: Sample sizes for FSW and MSM/TGW in Port Moresby, Lae, and Mount Hagen included: (1) 673 and 400, (2) 709 and 352, and (3) 709 and 111 respectively. Keychains were used for the unique object multiplier method and were distributed 1 week before the start of each RDS survey. HIV service testing data were only available in Port Moresby and Mount Hagen and SS-PSE estimates were calculated for all cities. Due to limited service provider data and uncertain prior size estimation knowledge, unique object multiplier weighted estimations were chosen for estimates. In Port Moresby, we estimate that there are 16,053 (95% CI 8232-23,874) FSW and 7487 (95% CI 3975-11,000) MSM/TGW, approximately 9.5% and 3.8% of the female and male populations respectively. In Lae, we estimate that there are 6105 (95% CI 4459-7752) FSW and 4669 (95% CI 3068-6271) MSM/TGW, approximately 14.4% and 10.1% of the female and male populations respectively. In Mount Hagen, we estimate that there are 2646 (95% CI 1655-3638) FSW and 1095 (95% CI 913-1151) MSM/TGW using service multiplier and successive sampling, respectively. This is approximately 17.1% and 6.3% of the female and male populations respectively. CONCLUSIONS: As the HIV epidemic in PNG rapidly evolves among key populations, PSE should be repeated to produce current estimates for timely comparison and future trend analysis.

Measuring a hidden population: A novel technique to estimate the population size of women with sexual violence-related pregnancies in South Kivu Province, Democratic Republic of Congo.

Successive sampling (SS)-population size estimation (PSE) is a technique used to estimate the sizes of hidden populations using data collected in respondent-driven sampling (RDS) surveys. We assess past estimations and use new data from an RDS survey to calculate a new PSE. In 2012, 852 adult women in South Kivu Province, Democratic Republic of Congo, who self-identified as survivors of sexual violence, resulting in a pregnancy, since the start of the war (in 1996) were sampled using RDS. We used imputed visibility, enrollment order, and prior estimates for PSE using SS-PSE in RDS Analyst. Prior estimates varied between Congolese local experts and researchers. We calculated the PSE of women with a sexual violence-related pregnancy in South Kivu using researchers' priors to be approximately 17,400. SS-PSE is an effective method for estimating the population sizes of hidden populations, useful for providing evidence for services and resource allocation. SS-PSE is beneficial because population sizes can be calculated after conducting the survey and do not rely on separate studies or additional data (as in network scale-up, multiplier, and capture-recapture methods).

Estimating hidden population size using Respondent-Driven Sampling data.

Respondent-Driven Sampling (RDS) is n approach to sampling design and inference in hard-to-reach human populations. It is often used in situations where the target population is rare and/or stigmatized in the larger population, so that it is prohibitively expensive to contact them through the available frames. Common examples include injecting drug users, men who have sex with men, and female sex workers. Most analysis of RDS data has focused on estimating aggregate characteristics, such as disease prevalence. However, RDS is often conducted in settings where the population size is unknown and of great independent interest. This paper presents an approach to estimating the size of a target population based on data collected through RDS. The proposed approach uses a successive sampling approximation to RDS to leverage information in the ordered sequence of observed personal network sizes. The inference uses the Bayesian framework, allowing for the incorporation of prior knowledge. A flexible class of priors for the population size is used that aids elicitation. An extensive simulation study provides insight into the performance of the method for estimating population size under a broad range of conditions. A further study shows the approach also improves estimation of aggregate characteristics. Finally, the method demonstrates sensible results when used to estimate the size of known networked populations from the National Longitudinal Study of Adolescent Health, and when used to estimate the size of a hard-to-reach population at high risk for HIV.