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Biostatistics Advance Access published online on November 3, 2006
Biostatistics, doi:10.1093/biostatistics/kxl038
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© 2006 The Authors This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/2.0/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received June 29, 2006
Revised October 18, 2006
Accepted October 27, 2006

Article

Insights into Latent Class Analysis of Diagnostic Test Performance

Margaret Sullivan Pepe 1 * and Holly Janes 2

1 University of Washington and Fred Hutchinson Cancer Research Center, 1100 Fairview Avenue N., M2-B500, Seattle, WA 98109, USA
2 Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21205

* To whom correspondence should be addressed.
Margaret Sullivan Pepe, E-mail: mspepe{at}u.washington.edu


  Abstract

Latent class analysis is used to assess diagnostic test accuracy when a gold standard assessment of disease is not available but results of multiple imperfect tests are. We consider the simplest setting, where three tests are observed and conditional independence is assumed. Closed form expressions for maximum likelihood parameter estimates are derived. They show explicitly how observed two- and three-way associations between test results are used to infer disease prevalence and test true- and false-positive rates. Although interesting and reasonable under conditional independence, the estimators clearly have no basis when it fails. Intuition for bias induced by conditional dependence follows from the analytic expressions. Further intuition derives from an EM approach to calculating the estimates. We discuss implications of our results and related work for settings where more than three tests are available. We conclude that careful justification of assumptions about the dependence between tests in diseased and non-diseased subjects is necessary in order to ensure unbiased estimates of prevalence and test operating characteristics, and to provide these estimates clinical interpretations. Such justification must be based in part on a clear clinical definition of disease and biological knowledge about mechanisms giving rise to test results.

Keywords: imperfect reference test; errors in variables; factor analysis; item response theory; latent variables; sensitivity; specificity.
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