Appendix 3: Detailed Statistics
We used the bivariate model for diagnostic/prognostic meta-analysis. The bivariate approach
was implemented with the hierarchical or generalized linear mixed model (GLMM) approach that
defines as between-studies model a bivariate normal distribution of pairs of true logit
sensitivities and logit 1-specificities and as within study model the true binomial distribution of
the number of subjects with a positive test among diseased subjects (“sensitivity model”) and
the number of subjects with a positive test among subjects without the disease (“specificity
model”) (1-5). We specified the bivariate model as model without intercept where the pooled
sensitivities and specificities correspond to the anti-logit of the fixed effects. The bivariate model
accounts for study size (6) and incorporates the correlation between sensitivty and 1-specificity
between studies as a latent test threshold for NP via "random effects".
We used the GLMM framework implemented with the lmer()-function in the contributed Rpackage lme4 (7-9). In a secondary approach we fitted the same models in a Bayesian
framework using Markov chain Monte Carlo (MCMC) methods implemented in the contributed R
package MCMCglmm (10). A very similar approach has recently been proposed, using
integrated nested Laplace approximations (11). The rational to extend the analyses was to
provide easily interpretable posterior distributions of the pooled sensitivity and 1-specificity and
moreover of the pooled positive predictive value (PPV) and negative predictive value (NPV). For
the Bayesian approach, we used a non-informative inverse Wishart prior for the (co)variances
and a normal prior for the fixed effects. We carefully checked the estimates of the Bayesian
approach with the standard likelihood approach.
To graphically present the results, we plotted the individual and summary points of sensitivity
and 1-specificity in a receiver operating characteristic (ROC) plane, plotting the sensitivity on the
y axis against 1-specificity (false positive rate) on the x axis. Moreover, we plotted the
distributions of these estimates derived from MCMC sampling into the ROC plane to enhance
the visualization of the accuracy parameters. We represented the uncertainty of the pooled
estimates by the 95% confidence region and plotted the posterior distribution of the same
estimates derived from the MCMC algorithm as marginal histogramms. Last, we illustrated the
posterior distribution of the pooled PPV and NPV estimates as boxplots for the different metaanalytic scenarios.
The bivariate model was fitted using R Version 2.10.1 for Windows. The code can be obtained
on request.
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