An Iterative, Frequentist Approach for Latent Class Analysis to Evaluate Conditionally Dependent Diagnostic Tests

Abstract

Latent class analysis is a well-established method in human and veterinary medicine for evaluating the accuracy of diagnostic tests without a gold standard. An important assumption of this procedure is the conditional independence of the tests. If tests with the same biological principle are used, this assumption is no longer met. Therefore, the model has to be adapted so that the dependencies between the tests can be considered. Our approach extends the traditional latent class model with a term for the conditional dependency of the tests. This extension increases the number of parameters to be estimated and leads to negative degrees of freedom of the model, meaning that not enough information is contained in the existing data to obtain a unique estimate. As a result, there is no clear solution. Hence, an iterative algorithm was developed to keep the number of parameters to be estimated small. Given adequate starting values, our approach first estimates the conditional dependencies and then regards the resulting values as fixed to recalculate the test accuracies and the prevalence with the same method used for independent tests. Subsequently, the new values of the test accuracy and prevalence are used to recalculate the terms for the conditional dependencies. These two steps are repeated until the model converges. We simulated five application scenarios based on diagnostic tests used in veterinary medicine. The results suggest that our method and the Bayesian approach produce similar precise results. However, while the presented approach is able to calculate more accurate results than the Bayesian approach if the test accuracies are initially misjudged, the estimates of the Bayesian method are more precise when incorrect dependencies are assumed. This finding shows that our approach is a useful addition to the existing Bayesian methods, while it has the advantage of allowing simpler and more objective estimations.

An intercomparison study of ELISAs for the detection of porcine reproductive and respiratory syndrome virus – evaluating six conditionally dependent tests

“…The intercomparison of diagnostic tests was performed with the method introduced recently using a modified latent class model [ 25 ]. In a latent class analysis, it is assumed that there is a latent variable with two classes.…”

“…Let I (·) be the indicator function. Then, the likelihood of parameters γ and ρ for the observations Y can be written in the following form: where is a term for the influence of the conditional two-way to M -way dependencies of all M tests in class c on the likelihood of the respective observed response patterns as described in [ 25 ]. The conditional dependencies are expressed in terms of the conditional covariances between the test results in the two latent classes, respectively.…”

“…Estimate the dependencies of the tests in terms of their correlation (as described in [ 25 ]) based on each available source, so that these values are standardized and independent of the test accuracies: Find previous publications evaluating the diagnostic tests used in this study and use their values for conditional dependency (here, we could not find any previous publications considering a dependency of the tests, so this source did not provide any information on the conditional dependency of the tests). Ask researchers (indicated as R) from the associated laboratories (here, the Bavarian Animal Health Service) for an assessment of the dependencies of the tests used based on their experience and the biological principles of the tests used.…”

“…Adjust the standardized values of the dependencies to the selected test accuracies M, P, R and the prevalence (step 3) so that the conditional dependencies are described in terms of conditional covariances and any combination of the test results has a positive probability (see [ 25 ]). This leads to deviating values of the conditional covariances depending on the selected starting values for the test accuracies.…”

“…These methods often require some assumptions, such as a large number of diagnostic tests or accurate prior distributions. We developed a frequentist latent class approach, which takes the dependencies of the tests into account, thus no longer requiring the assumption of conditional independence [ 25 ]. In addition, this method is easily applicable in many situations even when little prior information is accessible.…”