Using extended Rasch models to assess validity of diagnostic tests in the presence of a reference standard

We show that extended Rasch models, built to deal with continuous latent variables, may be useful for assessing validity of medical diagnostic tests in the presence of a reference standard, particularly for chronic diseases. We derive estimates for sensitivity and specificity under the Rasch model assumptions. Our estimations can be computed conditionally on the level of potential confounding covariates, making use of a variety of extended Rasch models, namely log-linear Rasch models, to examine the association between covariates and both disease intensity and response to the tests. Also, another variety of extended Rasch models, partial credit models, can determine appropriate thresholds for quantitative diagnostic tests. As an example, we study the validity of some diagnostic tests of heart failure.