tables. Each cell in Table \[2times2T\] provides the cell frequency corresponding to a combination of index test and disease outcomes in study $i$ for test $t$. We assume that the gold standard is the same for the $T$ tests, i.e. $y_{i+01}=\cdots=y_{i+0T}$ and $y_{i+11}=\cdots=y_{i+1T}$.

  ------------ -- ------------ ------------ ---------- -------------- -- ------------ ------------ ---------- -------------- -- ------------ ------------ -- -- -- --
                                                                                                                                                                   
  [Test 1]{}          $-$          $+$       $\ldots$   [Test $t$]{}     $-$              $+$       $\ldots$   [Test $T$]{}     $-$          $+$                   
  $-$              $y_{i001}$   $y_{i011}$   $\ldots$       $-$          $y_{i00t}$    $y_{i01t}$   $\ldots$       $-$          $y_{i00T}$   $y_{i01T}$            
  $+$              $y_{i101}$   $y_{i111}$   $\ldots$       $+$          $y_{i10t}$    $y_{i11t}$   $\ldots$       $+$          $y_{i10T}$   $y_{i11T}$            
  Total            $y_{i+01}$   $y_{i+11}$   $\ldots$      Total         $y_{i+0t}$    $y_{i+1t}$   $\ldots$      Total         $y_{i+0T}$   $y_{i+1T}$            
  ------------ -- ------------ ------------ ---------- -------------- -- ------------ ------------ ---------- -------------- -- ------------ ------------ -- -- -- --

  : \[2times2T\] Data from an individual study in a $2\times 2T$ table.

The within-study model assumes that the number of true positives $Y_{i11t}$ and true negatives $Y_{i00t}$ for $t=1,\ldots,T$ are conditionally independent and binomially distributed given $(\X_{1t},\X_{0t})=(\x_{1t},\x_{0t})$, where $\X_t=(X_{1t},X_{0t})$ denotes the bivariate latent pair of (transformed) sensitivity and specificity for the test $t$. That is $$\begin{aligned}
\label{withinBinom}
Y_{i11t}|X_{1t}=x_{1t}&\sim& \mbox{Binomial}\Bigl(y_{i+1t},l^{-1}(x_{1t})\Bigr);\nonumber\\
Y_{i00t}|X_{0t}=x_{0t}&\sim& \mbox{Binomial}\Bigl(y_{i+0t},l^{-1}(x_{0t})\Bigr),\end{aligned}$$ for $t=1,\ldots, T$, where $l(\cdot)$ is a link function.

The stochastic representation of 