Estimators in capture–recapture studies with two sources |
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Authors: | Sarah Brittain Dankmar Böhning |
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Institution: | (1) Quantitative Biology and Applied Statistics, School of Biological Sciences, University of Reading, Reading, RG6 6BX, UK |
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Abstract: | This paper investigates the applications of capture–recapture methods to human populations. Capture–recapture methods are
commonly used in estimating the size of wildlife populations but can also be used in epidemiology and social sciences, for
estimating prevalence of a particular disease or the size of the homeless population in a certain area. Here we focus on estimating
the prevalence of infectious diseases. Several estimators of population size are considered: the Lincoln–Petersen estimator
and its modified version, the Chapman estimator, Chao’s lower bound estimator, the Zelterman’s estimator, McKendrick’s moment
estimator and the maximum likelihood estimator. In order to evaluate these estimators, they are applied to real, three-source,
capture-recapture data. By conditioning on each of the sources of three source data, we have been able to compare the estimators
with the true value that they are estimating. The Chapman and Chao estimators were compared in terms of their relative bias.
A variance formula derived through conditioning is suggested for Chao’s estimator, and normal 95% confidence intervals are
calculated for this and the Chapman estimator. We then compare the coverage of the respective confidence intervals. Furthermore,
a simulation study is included to compare Chao’s and Chapman’s estimator. Results indicate that Chao’s estimator is less biased
than Chapman’s estimator unless both sources are independent. Chao’s estimator has also the smaller mean squared error. Finally,
the implications and limitations of the above methods are discussed, with suggestions for further development.
We are grateful to the Medical Research Council for supporting this work. |
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Keywords: | Estimators of Chapman Chao Lincoln– Petersen McKendrick Zelterman Covariate adjustment Variance estimators |
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