Two-way capture-recapture methods with emphasis on the bootstrap

Abstract The Chapman estimator is widely used in dual system estimation for estimating the size of an elusive target population. Two independent sources are required, delivering a two-by-two table of those units identified by both sources, of those identified only by the first, and those only by the second source. Interest is in the frequency of those identified by neither source that remain hidden. While asymptotic variance estimates exist for the Chapman estimator, they often perform poorly with small sample sizes. In addition, the Chapman estimator may be biased for small sample sizes. This study explores the bias of the Chapman and a bias-corrected Chapman estimator by investigating both imputed and non-imputed (simple) bootstrap methods as alternatives for estimating variance and constructing confidence intervals. Through simulation studies, we assess the reliability of these methods by analyzing confidence interval coverage probabilities. Our findings show that the imputed bootstrap consistently delivers better performance, yielding coverage probabilities closer to the nominal level, even under moderate dependence between sources. We demonstrate the practical application of these methods with two case studies: suicide data in Cambodia and heroin use in Thailand.