Using Latent Class Models to Evaluate the Performance of Diagnostic Tests in the Absence of a Gold Standard

Diagnostic tests are helpful tools for decision-making in a biomedical context. In order to determine the clinical relevance and practical utility of each test, it is critical to assess its ability to correctly distinguish diseased from non-diseased individuals. Statistical analysis has an essential role in the evaluation of diagnostic tests, since it is used to estimate performance measures of the tests, such as sensitivity and specificity. Ideally, these measures are determined by comparison with a gold standard, i.e., a reference test with perfect sensitivity and specificity.

When no gold standard is available, admitting the supposedly best available test as a reference may cause misclassifications leading to biased estimates. Alternatively, Latent Class Models (LCM) may be used to estimate diagnostic tests performance measures as well as the disease prevalence, in the absence of a gold standard. The most common LCM estimation approaches are the maximum likelihood estimation using the Expectation-Maximization algorithm and the Bayesian inference using Markov Chain Monte Carlo methods, via Gibbs sampling.

This talk illustrates the use of Bayesian Latent Class Models (BLCM) in the context of malaria and canine dirofilariosis. In each case, multiple diagnostic tests were applied to distinct subpopulations. To analyze the subpopulations simultaneously, a product multinomial distribution was considered, since the subpopulations were independent. By introducing constraints, it was possible to explore differences and similarities between subpopulations in terms of prevalence, sensitivities and specificities.

We also discuss statistical issues such as the assumption of conditional independence, model identifiability, sampling strategies and prior distribution elicitation.