Latent variable models in diagnostic medicine

In the field of infectious diseases, perfect reference tests are rare. Instead of relying on an imperfect reference test to assess the value of diagnostic test, latent variable models (LVMs) can be used. In a latent variable model, the true disease status is considered to be an unobserved, latent, variable with two possible states: diseased or not-diseased. The observed data consists of the results to one or more diagnostic tests and imperfect reference standards. These observed test result are modeled using the latent disease status as predictor. The dependence structure among the diagnostic tests is consequently used estimate the diagnostic accuracy of all tests under consideration without explicitly using any of the tests as a reference standard.
In these models, test data are routinely presented as binary results. Many diagnostic tests are however quantitative in nature. Mixture modeling, a form of LVMs, can be used to model these quantitative data directly without the need to define cut-offs and allowing uncertainty in the underlying disease status of the study participants.
As many diagnostic studies are small and give imprecise estimates of Se and Sp, systematic reviews and meta-analyses of diagnostic test accuracy studies are increasingly common. In a meta-analysis, data from different studies are combined to obtain better precision to estimate the diagnostic accuracy of a test or more power in the comparison of the accuracy of two or more tests. Again, meta-analyses of diagnostic studies are routinely performed assuming a perfect reference test is used in each study. In practice however, less than perfect reference standards which differ between studies may have been used. Also in this setting, latent variable models can be useful to correct for the use of imperfect reference standards.
Motivated by data on the diagnosis of visceral leishmaniasis (VL), a neglected tropical disease affecting up to 400,000 people annually, we assessed the use of latent variable models in diagnostic medicine. Specifically, we studied the role and interpretation of latent variable models in infectious diseases diagnostic research. In a study on the prevention of VL through the distribution of insect impregnated bednets, we incorporated quantitative test results in latent variable models in order to estimate infection rates without the need for arbitrary cut-offs to define test positive and negative results. Finally, we assessed the role of latent variable models in the meta-analysis of diagnostic test accuracy studies, while adjusting for the use of imperfect reference standards in the primary studies.