Latent Class Log-Linear Models for Estimating Diagnostic Test Accuracy Without a Gold Standard: A Simulation Study

In the absence of a gold standard, latent class models can be used to estimate test accuracy from a study comparing results on multiple tests. Fixed-effect and latent trait models are often used to account for conditional dependencies between tests, mitigating against biased accuracy estimates, but are difficult to implement. Latent class log-linear models are an under-evaluated alternative.

We evaluate the performance of Bayesian two-class log-linear models in estimating sensitivity, specificity, and prevalence under a variety of real-world conditional dependence structures, and the use of shrinkage priors on interaction terms when dependence structures are unknown.

Data were simulated from (i) latent trait, (ii) fixed-effect, and (iii) log-linear models, with dependence structures motivated by four real data sets and three sample sizes. We fitted conditional independence models, log-linear models incorporating the "correct" pairwise interactions, and log-linear models incorporating all interactions with shrinkage priors. We report bias, coverage, residual deviance, and DIC.

Log-linear models incorporating the correct pairwise dependencies exhibited promising but variable performance (likely due to insufficient sample sizes) across data-generating mechanisms. Improvements over conditional independence models were substantial. Shrinkage priors achieved reasonable performance when dependencies existed within a single disease class but showed poor convergence under complex dependence structures.

Latent class log-linear models offer a relatively robust alternative for estimating accuracy when the conditional dependence structure is known. When this is not the case, shrinkage priors show promise when dependencies are only within one disease state, but there are challenges related to convergence.