Discrete-time closed capture-recapture models for hard-to-reach population size estimation: application to key population for HIV prevention in Rwanda

Abstract

Background: The global share of new HIV infections due to key populations (KP) and their partners is steadily rising and was estimated at 70%, with 51% in sub-Saharan Africa, in 2021.Rwanda has a heterogeneous HIV epidemic, that is widespread in the adult population (age 15-49 years), with features of a concentrated epidemic among specific population subgroups, with 35% among female sex workers (FSWs) and 6.9% among men who have sex with men (MSM).) Members of these populations are often difficult to find, and the size of these populations is largely unknown, posing a substantial challenge to calculate epidemiologic measures of the disease and to evaluate the reach and coverage of public health programs in line with progress towards the UNAIDS 95-95-95 targets. Several methods have been used so far, each presenting both strengths and weaknesses. Capture-recapture is currently being recommended due to it mathematical ground and defensible results. However, there are still some methodological limitations, including dependencies between samples, inability to reach highly hidden key population subgroups, as well as loss of marks or tags that biases produced population size estimates. With this research project, we aim at addressing list-dependency between samples and tag loss bias that arises during capture-recapture implementation and develop an extended network-tracked capture-recapture approach able to account for harder to reach KP subgroups. Methods: To achieve the research objectives, firstly, we derived and applied a Generalized capture-recapture (CRC) model for population size estimation (PSE) from Bayesian model averaging to address list-dependencies between samples; and secondly derived an extended network-tracked capture-recapture method for obtaining population size estimates from a single Respondent Driven Sampling (RDS) that addresses tag loss bias on population size estimates and able to account for usually missed KP subgroups in multiple CRCCRC studies. After derivation of the model and methods, we applied the concepts to three different national wide studies implemented in Rwanda involving FSWs aged 15 years and above and MSM aged 18 years and above, between 2021 and 2023. Data collection methods commonly used in the three studies included bio-behavioral survey (BBS), three-source capture-recapture (3S-CRC) and Respondent driven sampling was used in selecting participants. R-4.3 software was used for data analysis. Results: The Generalized capture-recapture model from Bayesian model averaging demonstrates a 71% reduction in standard errors as compared to Bayesian Latent class model. Once applied to the MSM 2021 study, the estimated MSM PSE lies within credible sets ranging from 19,347 to 22,268 with a median of 20,787 vs 18,100 median PSE ranging from 11,265 to 29,708 if the Bayesian Latent class model is used. Whereas, for FSW 2022 study, the PSE of street- and venue-based FSWs in Rwanda was estimated to be within credible sets ranging from 31,873 to 43,354 with a median of 37,647 vs a iii 35,954 median PSE ranging from 14,736 to 55,215 once Bayesian Latent class model is used. A low tag retention was observed between consecutive capture rounds in CRC implementation corresponding to 59%. The FSW 2023 study, estimated FSW PSE was 98,587 ranging from 82,978 to 114,196 once network-traced capture-recapture method is used.