A general framework for comparative Bayesian meta-analysis of diagnostic studies

Joris Menten, Emmanuel Lesaffre

Selecting the most effective diagnostic method is essential for patient management and public health interventions. This requires evidence of the relative performance of alternative tests or diagnostic algorithms. Consequently, there is a need for diagnostic test accuracy meta-analyses allowing the comparison of the accuracy of two or more competing tests. The meta-analyses are however complicated by the paucity of studies that directly compare the performance of diagnostic tests. A second complication is that the diagnostic accuracy of the tests is usually determined through the comparison of the index test results with those of a reference standard. These reference standards are presumed to be perfect, i.e. allowing the classification of diseased and non-diseased subjects without error. In practice, this assumption is however rarely valid and most reference standards show false positive or false negative results. When an imperfect reference standard is used, the estimated accuracy of the tests of interest may be biased, as well as the comparisons between these tests. We propose a model that allows for the comparison of the accuracy of two diagnostic tests using direct (head-to-head) comparisons as well as indirect comparisons through a third test. In addition, the model allows and corrects for imperfect reference tests. The model is inspired by mixed-treatment comparison meta-analyses that have been developed for the meta-analysis of randomized controlled trials. As the model is estimated using Bayesian methods, it can incorporate prior knowledge on the diagnostic accuracy of the reference tests used. We show the bias that can result from using inappropriate methods in the meta-analysis of diagnostic tests and how our method provides more correct estimates of the difference in diagnostic accuracy between two tests. As an illustration, we apply this model to a dataset on visceral leishmaniasis diagnostic tests, comparing the accuracy of the RK39 dipstick with that of the direct agglutination test. Our proposed meta-analytic model can improve the comparison of the diagnostic accuracy of competing tests in a systematic review. This is however only true if the studies and especially information on the reference tests used are sufficiently detailed. More specifically, the type and exact procedures used as reference tests are needed, including any cut-offs used and the number of subjects excluded from full reference test assessment. If this information is lacking, it may be better to limit the meta-analysis to direct comparisons.