Bayesian inference on the patient population size given list mismatches

A Review of Capture-recapture Methods and Its Possibilities in Ophthalmology and Vision Sciences

Epidemiological information is expected to be used to develop key aspects of eye care such as to control and minimise the impact of diseases, to allocate resources, to monitor public health actions, to determine the best treatment options and to forecast the consequence of diseases in populations. Epidemiological studies are expected to provide information about the prevalence and/or incidence of eye diseases or conditions. To determine prevalence is necessary to perform a cross-sectional screening of the population at risk to ascertain the number of cases. The aim of this review is to describe and evaluate capture-recapture methods (or models) to ascertaining the number of individuals with a disease (e.g. diabetic retinopathy) or condition (e.g. vision impairment) in the population. The review covers the fundamental aspects of capture-recapture methods that would enable non-experts in epidemiology to use it in ophthalmic studies. The review provides information about theoretical aspects of the method with examples of studies in ophthalmology in which it has been used. We also provide a problem/solution approach for limitations arising from the lists obtained from registers or other reliable sources. We concluded that capture-recapture models can be considered reliable to estimate the total number of cases with eye conditions using incomplete information from registers. Accordingly, the method may be used to maintain updated epidemiological information about eye conditions helping to tackle the lack of surveillance information in many regions of the globe.

Bayesian statistics in medicine: a 25 year review

This review examines the state of Bayesian thinking as Statistics in Medicine was launched in 1982, reflecting particularly on its applicability and uses in medical research. It then looks at each subsequent five-year epoch, with a focus on papers appearing in Statistics in Medicine, putting these in the context of major developments in Bayesian thinking and computation with reference to important books, landmark meetings and seminal papers. It charts the growth of Bayesian statistics as it is applied to medicine and makes predictions for the future. From sparse beginnings, where Bayesian statistics was barely mentioned, Bayesian statistics has now permeated all the major areas of medical statistics, including clinical trials, epidemiology, meta-analyses and evidence synthesis, spatial modelling, longitudinal modelling, survival modelling, molecular genetics and decision-making in respect of new technologies.

A Bayesian, combinatorial approach to capture-recapture

It is shown that, in the capture-recapture method, the widely used formulae of Bailey or Chapman-Seber give the most likely value for the size of the population, but systematically underestimate the probability that the population is larger than any given size. We take here a first step in a combinatorial approach which does not suffer from this flaw: formulae are given which can be used in the closed case (no birth, death or migrations between captures) when at least two animals have been recaptured and when there is homogeneity with regard to capture probability. Numerical and heuristic evidence is presented pointing to the fact that the error incurred when using the formulae of Bailey or Chapman-Seber depends asymptotically only on the number of recaptured animals, and will not diminish if the number of captured animals becomes large while the number of recaptured animals remains constant. A result that was stated and left unproven by Darroch is proven here.