A multinomial hierarchical model for meta-analysis of diagnostic test accuracy of ordered or unordered multicategory...

Multicategory diagnostic tests are frequently utilized in clinical practice. Estimation of the predictive value of each category is an essential part of these tests, yet they are often wrongly reported due to inappropriate analysis as a proportion ignoring pretest probability or prevalence. Also, some systems do not have fully ordered categories, making meta-analysis difficult. Analyses are often performed under the assumption that data are continuous, a premise that may not be appropriate and can result in unreliable confidence or credible intervals. These shortcomings can be rectified by multinomial mixed models, which can model both categorical as well as ordinal data, and estimation of predictive values through likelihood ratios (LRs). However, such multinomial models not requiring ordering have rarely, if at all, been used as a meta-analytical tool. This study aimed to employ a multinomial hierarchical linear mixed model appropriate for both ordered as well as partially ordered categories for such an analysis.

The proposed Bayesian multinomial mixed model estimates the proportions of each diagnostic category among cases with and without disease. This model was run on data extracted from a previous meta-analysis of the Milan System for Reporting Salivary Gland Cytopathology, which only partially follows ordered categories. The model was checked for proper mixing. From the posterior draws, the proportions of each category and the LRs were estimated. Fit of the data was checked by posterior predictive checks for location and width of distribution.

The Monte Carlo Markov chains mixed well. The predictions of the model fitted the data well. From this, we could estimate the LR and predictive values, which were more informative than the previously reported Risk of Malignancy. Sensitivities and specificities could be calculated for different thresholds after ordering by the risk information derived from the LRs. Interpretation was aided by graphical examination of the predictive value to the prevalence of each category.

The proposed model is a relatively assumption free method that should be useful in meta-analysis of multicategory diagnostic tests if combined with subsequent LR estimation.