Diagnosing diagnostic tests: evaluating the assumptions underlying the estimation of sensitivity and specificity in the absence of a gold standard

Latent class analysis to assess the sensitivity and specificity of a diagnostic test can be carried out under different assumptions. An often applied set of assumptions is known as the Hui-Walter paradigm, which essentially states that: (i) the population is divided into two or more populations in which two or more tests are evaluated under assumption that (ii) sensitivity and specificity of the tests are the same in all populations; and (iii) the tests are conditionally independent given the disease status.

This study explores the implications of these assumptions. Through simulation studies, it is shown how the size of the difference between disease prevalences within the populations influences the precision of the estimates. It is also illustrated by a simulation study how a difference in a test sensitivity between populations may result in estimates that are biased towards the sensitivity of the test in the population with highest disease prevalence, since that population estimate is supported by most of the data.

It is shown that the assumption of conditional independence between tests in general cannot be ignored in latent class models. Failure to impose conditional independence will result in a model that lacks identifiability in a way that cannot be handled by adding more tests or dividing the sample into more populations.