Hierarchical multinomial processing tree models for meta-analysis of diagnostic accuracy studies

Meta-analysis represents a widely accepted approach for evaluating the accuracy of diagnostic tools in clinical and psychological investigations. This article investigates the applicability of multinomial tree models recently suggested in the literature under a fixed-effects formulation for assessing the accuracy of binary classification tools, where the study specific disease prevalences are taken into account. The model proposed in this article extends previous results to a hierarchical structure accounting for the variability between the studies included in the meta-analysis. Interestingly, by exploiting the parameter separability of the complete likelihood function, the resulting hierarchical multinomial tree model is shown to coincide, in its interest parameter component, with the well-known bivariate random-effects model under an exact within-study distribution for the number of true positives and true negatives subjects. The proposal is in line with a latent-trait approach, where inference follows a frequentist point of view. The applicability of the proposed model and its performance with respect to its fixed-effects counterpart and to the approximate bivariate random-effects model based on normality assumptions commonly used in the literature is evaluated in a series of simulation studies. Methods are applied to a real meta-analysis about the accuracy of the confusion assessment method as delirium screening tool.