A covariate adjustment for zero-truncated approaches to estimating the size of hidden and elusive populations

摘要

In this paper we consider the estimation of population size from one-sourcecapture--recapture data, that is, a list in which individuals can potentiallybe found repeatedly and where the question is how many individuals are missedby the list. As a typical example, we provide data from a drug user study inBangkok from 2001 where the list consists of drug users who repeatedly contacttreatment institutions. Drug users with 1, 2, 3$,...$ contacts occur, but drugusers with zero contacts are not present, requiring the size of this group tobe estimated. Statistically, these data can be considered as stemming from azero-truncated count distribution. We revisit an estimator for the populationsize suggested by Zelterman that is known to be robust under potentialunobserved heterogeneity. We demonstrate that the Zelterman estimator can beviewed as a maximum likelihood estimator for a locally truncated Poissonlikelihood which is equivalent to a binomial likelihood. This result allows theextension of the Zelterman estimator by means of logistic regression to includeobserved heterogeneity in the form of covariates. We also review an estimatorproposed by Chao and explain why we are not able to obtain similar results forthis estimator. The Zelterman estimator is applied in two case studies, thefirst a drug user study from Bangkok, the second an illegal immigrant study inthe Netherlands. Our results suggest the new estimator should be used, inparticular, if substantial unobserved heterogeneity is present.