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International Journal of Epidemiology 2003;32:1072-1078
© International Epidemiological Association 2003

Theory and Methods

Efficiency of two-phase designs for prevalence estimation

R McNamee

Biostatistics Group, School of Epidemiology and Health Sciences, University of Manchester, Oxford Road, Manchester M13 9PT, UK. E-mail: rmcnamee{at}man.ac.uk

Background Unbiased estimation of the prevalence of diseases and other conditions is important but can be expensive, especially for conditions which do not necessarily lead to contact with health services. A two-phase population survey may seem an attractive option when there is a relatively cheap, although fallible, test for disease status available: the test is used in the first phase of the survey but in the second, only a subsample are classified by the relatively expensive, gold standard. Previously the cost efficiency of such studies compared with simple, one-phase random sample designs was investigated empirically and some questions remain unclear.

Methods A simple formula for the maximum reduction in cost or standard error that can be achieved by two-phase sampling compared with simple random sampling is derived mathematically. A formula for the minimum reduction is also given and the influence of prevalence on efficiency explained.

Results The main result shows that the sensitivity and specificity of the first stage test set an absolute limit on the efficiency of two-phase designs; in particular, two-phase sampling can never be justified on efficiency grounds alone if the test is not accurate enough.

Keywords Two-phase designs, double sampling, two-stage designs, prevalence estimation, survey design, epidemiology, cost efficiency, statistical efficiency

Accepted 7 May 2003


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