  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.
