To compare the accuracy of multiple diagnostic tests in a single study, three designs are commonly used (i) the multiple test comparison design; (ii) the randomized design, and (iii) the non-comparative design. Existing meta-analysis methods of diagnostic tests (MA-DT) have been focused on evaluating the performance of a single test by comparing it with a reference test. The increasing number of available diagnostic instruments for a disease condition and the different study designs being used have generated the need to develop efficient and flexible meta-analysis framework to combine all designs for simultaneous inference. In this article, we develop a missing data framework and a Bayesian hierarchical model for network MA-DT (NMA-DT) and offer important promises over traditional MA-DT: (i) It combines studies using all three designs; (ii) It pools both studies with or without a gold standard; (iii) it combines studies with different sets of candidate tests; and (iv) it accounts for heterogeneity across studies and complex correlation structure among multiple tests. We illustrate our method through a case study: network meta-analysis of deep vein thrombosis tests.