Multivariate random effects meta-analysis of diagnostic tests with multiple thresholds

Bivariate random effects meta-analysis of diagnostic tests is becoming a well established approach when studies present one two-by-two table or one pair of sensitivity and specificity. When studies present multiple thresholds for test positivity, usually meta-analysts reduce the data to a two-by-two table or take one threshold value at a time and apply the well developed meta-analytic approaches. However, this approach does not fully exploit the data.

In this paper we generalize the bivariate random effects approach to the situation where test results are presented with k thresholds for test positivity, resulting in a 2 by (k+1) table per study. The model can be fitted with standard likelihood procedures in statistical packages such as SAS (Proc NLMIXED). We follow a multivariate random effects approach; i.e., we assume that each study estimates a study specific ROC curve that can be viewed as randomly sampled from the population of all ROC curves of such studies. In contrast to the bivariate case, where nothing can be said about the shape of study specific ROC curves without additional untestable assumptions, the multivariate model can be used to describe study specific ROC curves. The models are easily extended with study level covariates.

The method is illustrated using published meta-analysis data. The SAS NLMIXED syntax is given in the appendix.

We conclude that the multivariate random effects meta-analysis approach is an appropriate and convenient framework to meta-analyse studies with multiple threshold without losing any information by dichotomizing the test results.