Identifiability of Models for Multiple Diagnostic Testing in the Absence of a Gold Standard
Article first published online: 17 SEP 2009
© 2009, The International Biometric Society
Volume 66, Issue 3, pages 855–863, September 2010
How to Cite
Jones, G., Johnson, W. O., Hanson, T. E. and Christensen, R. (2010), Identifiability of Models for Multiple Diagnostic Testing in the Absence of a Gold Standard. Biometrics, 66: 855–863. doi: 10.1111/j.1541-0420.2009.01330.x
- Issue published online: 17 SEP 2009
- Article first published online: 17 SEP 2009
- Received November 2008. Revised July 2009. Accepted July 2009.
- Correlated tests;
- Latent class model;
Summary We discuss the issue of identifiability of models for multiple dichotomous diagnostic tests in the absence of a gold standard (GS) test. Data arise as multinomial or product-multinomial counts depending upon the number of populations sampled. Models are generally posited in terms of population prevalences, test sensitivities and specificities, and test dependence terms. It is commonly believed that if the degrees of freedom in the data meet or exceed the number of parameters in a fitted model then the model is identifiable. Goodman (1974, Biometrika 61, 215–231) established that this was not the case a long time ago. We discuss currently available models for multiple tests and argue in favor of an extension of a model that was developed by Dendukuri and Joseph (2001, Biometrics 57, 158–167). Subsequently, we further develop Goodman's technique, and make geometric arguments to give further insight into the nature of models that lack identifiability. We present illustrations using simulated and real data.