New methods for analysing generalised linear models with applications to epidemiology

Abstract

The aim of capture-recapture methods in epidemiology is to accurately estimate the total number of people who have a specific disease. These methods were first developed by ecologists interested in estimating the total population size of various animal species. Capture-recapture methods have a relatively short history, at least in terms of application to epidemiological data sets. If applied correctly they can be of great benefit, and are invaluable for planning and resource allocation. The aim of this thesis is to enhance the existing methods used in epidemiological capture-recapture problems. This research explores new methods for analysing generalised linear models, within the capture-recapture framework, with applications to epidemiology. In particular, we critically examine two New Zealand data sets. We compare two small sample adjustments for capture-recapture methods, and find that the Evans and Bonett adjustment can be a useful tool for sparse data. We employ stratified capture-recapture analyses to alleviate problems with heterogeneity and reporting patterns. In addition, we consider a type of cost-benefit analysis for the reporting sources. Two proposed methods of internal validity analysis are scrutinised. We find that one of these is counter-intuitive and of no use, however, the other method may be of some use in at least indicating the direction of any bias in the capture-recapture estimates. We use simulation to explore the effects of errors on patient records, and find that even relatively small percentages of errors can affect estimates dramatically. We conclude with a study of the optimal number of sources to use in epidemiological capture-recapture analyses. We argue that using three sources is not necessarily optimal, and that using four sources is also entirely manageable. This thesis outlines a strategy for analysing epidemiological data sets using capture-recapture methods, and includes aspects of model fitting and selection, cost-benefit analysis, diagnostic checking through simulations of the effects of record errors, and the effects of collapsing lists, as well as a critical check of the capture-recapture assumptions. This investigation demonstrates the potential of capture-recapture methods to provide accurate estimates of the size of various disease populations.