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Standard methods for the meta-analysis of medical tests without a goldstandard are limited to dichotomous data. Multivariate probit models are usedto analyze correlated binary data, and can be extended to multivariate orderedprobit models to model ordinal data. Within the context of an imperfect goldstandard, they have previously been used for the analysis of dichotomous andordinal tests in a single study, and for the meta-analysis of dichotomoustests. In this paper, we developed a hierarchical, latent class multivariateprobit model for the simultaneous meta-analysis of ordinal and dichotomoustests without assuming a gold standard. The model can accommodate ahierarchical partial pooling model on the conditional within-studycorrelations, enabling one to obtain summary estimates of joint test accuracy.Dichotomous tests use probit regression likelihoods and ordinal tests useordered probit regression likelihoods. We fitted the models using Stan, whichuses a state-of-the-art Hamiltonian Monte Carlo algorithm. We applied themodels to a dataset in which studies evaluated the accuracy of tests, and testcombinations, for deep vein thrombosis. We first demonstrated the issues withdichotomising test accuracy data a priori without a gold standard by fittingmodels which dichotomised the ordinal test data, and then we applied modelswhich do not dichotomise the data. Furthermore, we fitted and compared avariety of other models, including those which assumed conditional independenceand dependence between tests, and those assuming perfect and an imperfect goldstandard.

Meta-analysis of dichotomous and ordinal tests without a gold standard