  In a bivariate meta-analysis the number of diagnostic studies involved is
often very low so that frequentist methods may result in problems. Bayesian
inference is attractive as informative priors that add small amount of
information can stabilise the analysis without overwhelming the data. However,
Bayesian analysis is often computationally demanding and the selection of the
prior for the covariance matrix of the bivariate structure is crucial with
little data. The integrated nested Laplace approximations (INLA) method
provides an efficient solution to the computational issues by avoiding any
sampling, but the important question of priors remain. We explore the penalised
complexity (PC) prior framework for specifying informative priors for the
variance parameters and the correlation parameter. PC priors facilitate model
interpretation and hyperparameter specification as expert knowledge can be
incorporated intuitively. We conduct a simulation study to compare the
properties and behaviour of differently defined PC priors to currently used
priors in the field. The simulation study shows that the use of PC priors
results in more precise estimates when specified in a sensible neighbourhood
around the truth. To investigate the usage of PC priors in practice we
reanalyse a meta-analysis using the telomerase marker for the diagnosis of
bladder cancer.
