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Commentary on “On the robustness of latent class models for diagnostic testing with no gold‐standard” by Schofield et al.

For many diseases or medical conditions, there is no perfect diagnostic test. Common examples can be found among infectious diseases including, for example, Chlamydia trachomatis,1 pediatric pulmonary tuberculosis,2 and more recently COVID-19.3 The absence of a perfect diagnostic test complicates disease diagnosis in individuals, for example, imperfect sensitivity of the best available test may mean individuals with the disease may be missed and left untreated. It also complicates evaluation of a new diagnostic test for the disease, as it is unknown whether an individual with a positive result on the new test and a negative result on the best available test is a true positive or a false positive. Latent class models (LCMs) or finite mixture models have been described in the statistics literature to address this problem.4-6 They model an individual subject’s probability of having the disease (the latent variable). They provide estimates for the prevalence of the latent variable and the accuracy of the observed tests with respect to the latent variable. Though applications of LCMs in diagnostic accuracy research have been described since the 1980s, the statistical literature has repeatedly brought up concerns with these models inhibiting their widespread application.7 Schofield et al.8 present their experience of applying a “two-state latent class model” for estimating the diagnostic accuracy of four tests for leptospirosis, a disease for which there is no perfect diagnostic test. The authors describe this as the “simplest possible LCM”. The simplest possible LCM assumes the observed results arise from a mixture of two latent classes (or states) labeled “disease” and “disease free” within which the four observed tests are independent. The resulting estimates did not match the authors’ expectations—they found the estimate for sensitivity of the imperfect reference test, MAT, was implausibly low at 27% (90% credible interval roughly from 15% to 45% from their Figure 1) and lower than the sensitivity of the three rapid tests (Test-It Leptospira, Leptocheck, and Leptocheck WB). However, standard statistical goodness-of-fit measures did not indicate anything was amiss. This led the authors to carry out a simulation exercise with the goal of studying the consequences of the model misspecification that occurs when the true number of latent classes is three but is incorrectly assumed to be two. They defined simulation settings for two different LCMs—one with two latent classes and the other with three latent classes-such that both would result in the same observed frequency of the four tests even though the sensitivity and specificity of the tests under each model was different. The simulations showed that incorrectly fitting an LCM with two classes when in fact the true model had three classes, would result in biased sensitivity and specificity estimates, yet the lack of fit is detected with a probability 0.07 when the sample size is 225 and with probability 0.23 when N is 1000. The bias is lowered somewhat when considering two of the three latent classes correspond to “true disease,” rather than only one of the three.