Performance and robustness of single-source capture-recapture population size estimators with covariate information and potential one-inflation

Abstract Capture-recapture methods for estimating the total size of elusive populations are widely-used, however, due to the choice of estimator impacting upon the results and conclusions made, the question of performance of each estimator is raised. Motivated by an application of the estimators which allow covariate information to meta-analytic data focused on the prevalence rate of completed suicide after bariatric surgery, where studies with no completed suicides did not occur, this paper explores the performance of the estimators through use of a simulation study. The simulation study addresses the performance of the Horvitz–Thompson, generalised Chao and generalised Zelterman estimators, and develops a novel, generalised, form of the modified Chao estimator to account for both covariate information and one-inflation. In addition, the performance of the analytical approach to variance computation is addressed. Given that the estimators vary in their dependence on distributional assumptions, additional simulations are utilised to address the question of the impact outliers have on performance and inference.