each bivariate margin. With an one-factor copula, dimension reduction is achieved as the dependence among the latent sensitivities and specificities is explained by one other latent variable/factor. Hence, the proposed model has $2T$ dependence parameters instead of $\binom{T}{2}$, but more importantly its derivation requires bi-dimensional instead of $2T$-dimensional integration.

The remainder of the paper proceeds as follows. Section \[copula-mixed-model-sec\] introduces the one-factor copula mixed model for the comparison of multiple diagnostic tests and discusses its relationship with existing models. Section \[miss-section\] contains small-sample efficiency calculations to investigate the effect of misspecifying the random effects distribution on parameter estimators and standard errors. Section \[app-sec\] illustrates our methodology. We conclude with some discussion in Section \[discussion\].

\[copula-mixed-model-sec\]The one-factor copula mixed model 
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We first introduce the notation used in this paper. The data are $y_{ijkt},\, i = 1, . . . ,N,\, j=0,1,\,k=0,1,\,t=1,\ldots,T$, where $i$ is an index for the individual studies, $j$ is an index for the test outcome (0:negative; 1:positive), $k$ is an index for the disease outcome (0: non-diseased; 1: diseased) and $t$ is an index for the diagnostic test. The “classic" $2\times 2$ table is extended to a $2\times 2T$ table (Table \[2times2T\]), that is $T$ $2\times 2$ 