Meta-analysis of dichotomous and polytomous diagnostic tests without a gold standard
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Standard methods for the meta-analysis of diagnostic tests without a gold standard are limited to dichotomous data. Multivariate probit models are used to analyze correlated binary data, and can be extended to multivariate ordered probit models to model polytomous (i.e. non-binary) data. Within the context of an imperfect gold standard, they have previously been used for the analysis of dichotomous and polytomous diagnostic tests in a single study, and for the meta-analysis of dichotomous tests. In this paper, we developed a hierarchical, latent class multivariate probit model for the meta-analysis of polytomous and dichotomous diagnostic tests without a gold standard. The model can accommodate a hierarchical partial pooling model on the conditional within-study correlations, which allow us to obtain summary estimates of joint test accuracy. Dichotomous tests use probit regression likelihoods and polytomous tests use ordinal probit regression likelihoods. We fitted the models using Stan, which uses a state-of-the-art Hamiltonian Monte Carlo algorithm. We applied the models to a dataset in which studies evaluated the accuracy of tests, and combinations of tests, for deep vein thrombosis. We first demonstrate the issues with dichotomising test accuracy data a priori without a gold standard, and then we apply a model which does not dichotomise the data. We fitted models assuming conditional independence and dependence between tests, as well as models assuming a perfect gold standard, and compared model fit and summary estimates.
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