Comparative performance of multiple-list estimators of key population size

Abstract

Estimates of the sizes of key populations (KPs) affected by HIV, including men who have sex with men, female sex workers and people who inject drugs, are required for targeting epidemic control efforts where they are most needed. Unfortunately, different estimators often produce discrepant results, and an objective basis for choice is lacking. This simulation study provides the first comparison of information-theoretic selection of loglinear models (LLM-AIC), Bayesian model averaging of loglinear models (LLM-BMA) and Bayesian nonparametric latent-class modeling (BLCM) for estimation of population size from multiple lists. Four hundred random samples from populations of size 1,000, 10,000 and 20,000, each including five encounter opportunities, were independently simulated using each of 30 data-generating models obtained from combinations of six patterns of variation in encounter probabilities and five expected per-list encounter probabilities, producing a total of 36,000 samples. Population size was estimated for each combination of sample and sequentially cumulative sets of 2–5 lists using LLM-AIC, LLM-BMA and BLCM. LLM-BMA and BLCM were quite robust and performed comparably in terms of root mean-squared error and bias, and outperformed LLM-AIC. All estimation methods produced uncertainty intervals which failed to achieve the nominal coverage, but LLM-BMA, as implemented in the dga R package produced the best balance of accuracy and interval coverage. The results also indicate that two-list estimation is unnecessarily vulnerable, and it is better to estimate the sizes of KPs based on at least three lists.

Key Population Size Estimation to Guide HIV Epidemic Responses in Nigeria: Bayesian Analysis of 3-Source Capture-Recapture Data

“…We used Bayesian nonparametric latent-class models to analyze the 3S-CRC data. We had several options to analyze our multiple-source capture-recapture data using empirical methods for robust estimates, such as log-linear modeling [ 24 , 35 , 46 , 47 ], Bayesian model averaging [ 48 , 49 ], and Bayesian nonparametric latent-class modeling [ 23 , 50 , 51 ]. Accounting for the heterogeneity of captures and accommodating sparse data are two of the advantages of Bayesian latent-class models over the more traditional log-linear models for analysis of multiple-source capture-recapture data.…”

“…Accounting for the heterogeneity of captures and accommodating sparse data are two of the advantages of Bayesian latent-class models over the more traditional log-linear models for analysis of multiple-source capture-recapture data. The Bayesian nonparametric latent-class models account for differences in heterogeneity from capture to capture and combine similar strata into latent classes [ 23 , 51 ]. This feature allows the models to directly estimate the joint distribution, unlike log-linear models that are based on strong assumptions about capture patterns that can result in potentially biased estimates and confidence intervals that display poor coverage.…”

“…This feature allows the models to directly estimate the joint distribution, unlike log-linear models that are based on strong assumptions about capture patterns that can result in potentially biased estimates and confidence intervals that display poor coverage. Model selection using the Akaike information criterion or the Bayesian information criterion poses the additional challenge of selecting consistent and correct models [51]. Bayesian model averaging fits all possible log-linear models, weights each model according to the posterior probability, and returns the model-probability-weighted average across many models with uncertainty [48][49][50][51].…”

“…Model selection using the Akaike information criterion or the Bayesian information criterion poses the additional challenge of selecting consistent and correct models [51]. Bayesian model averaging fits all possible log-linear models, weights each model according to the posterior probability, and returns the model-probability-weighted average across many models with uncertainty [48][49][50][51]. The Bayesian models are similar in that they inform themselves during Markov chain Monte Carlo sampling, beginning with an infinite number of probability distributions and ending with a smaller, more representative subset of those that fit the data best to produce population size estimates [23,51].…”

“…Bayesian model averaging fits all possible log-linear models, weights each model according to the posterior probability, and returns the model-probability-weighted average across many models with uncertainty [48][49][50][51]. The Bayesian models are similar in that they inform themselves during Markov chain Monte Carlo sampling, beginning with an infinite number of probability distributions and ending with a smaller, more representative subset of those that fit the data best to produce population size estimates [23,51]. In addition, the Bayesian models can accommodate sparse data (ie, when the total number of individuals with 1 of the 7 patterns of captures across 3 rounds is small or zero).…”