Uni-list capture-recapture approaches, with uncertainty quantification, performance analysis and a meta-analytic application

Abstract

Meta-analysis is a powerful tool for evaluating numerous studies focused on the same or similar research question and integrating the results to identify a common parameter.
This well-established methodology is prone to bias, so this thesis proposes the use of model-based meta-analytic and uni-list capture-recapture approaches, to compute more reliable estimates, with a focus on count data systematically missing zero counts.
For the meta-analytic approach, traditional methodologies do not adequately address zero-truncated count data. This thesis develops a model-based approach with zero-truncated count models which appropriately account for the missing zeroes and an exposure variable if applicable. From these models, a maximum likelihood approach is taken with the expectation-maximisation algorithm, used to compute less biased parameter estimates. Following these approaches, both observed and unobserved heterogeneity are addressed through covariate modelling and overdispersion modelling respectively.
As for the uni-list capture-recapture approach, the Horvitz-Thompson, generalised Chao’s and generalised Zelterman’s estimators are used for population size estimation, allowing for the inclusion of covariate information and an exposure variable.
Also explored is the uncertainty that arises from these estimation methods, with both approximation-based variance estimation methods and the bootstrap algorithm addressed. Various approaches to the bootstrap algorithm and methods for accounting for model uncertainty are developed, in addition to alternative methods of confidence interval construction. The last focus of the thesis addresses the estimators under the presence of one-inflation, and given the poor performance of many of the existing estimators, the generalised-modified Chao’s estimator is developed to account for zero-truncation, one-inflation and covariate information.
The methodologies discussed in this thesis are demonstrated through the use of real-life case study data, and assessed through a series of simulation studies.

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Identifiers

ORCID for Layna Charlie Dennett: orcid.org/0000-0002-3357-3636

ORCID for Dankmar Böhning: orcid.org/0000-0003-0638-7106

ORCID for Antony Overstall: orcid.org/0000-0003-0638-8635

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