Comparative performance of multiple-list estimators of key population size

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.