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I want to perform a meta-analysis of multiple diagnostic test at once. Outcomes are sensitivity, specificity, positive predictive value and negative predictive value. All the test have the same reference standard.

For example:

Study 1 - Biomarker 1 for detecting hepatic cancer
Study 2 - Biomarker 2 for detecting hepatic cancer
Study 3 - Biomarker 2 for detecting hepatic cancer
Study 4 - Biomarker 2 for detecting hepatic cancer
Study 5 - Biomarker 3 for detecting hepatic cancer
Study 6 - Biomarker 3 for detecting hepatic cancer
Study 7 - Biomarker 4 for detecting hepatic cancer
Study 8 - Biomarker 5 for detecting hepatic cancer
Study 9 - Biomarker 5 for detecting hepatic cancer

Do I need to make a meta-analysis of all studies comparing biomarker 2 (2-4) first, and then finally compare the pooled results with the pooled results of other biomarkers, or is there a way to do it all at once? Is there a tool in R capable of doing this (mada)?

I've read about network meta-analysis, but it seems that it's only applicable to treatments and such.

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You can do a meta-regression of diagnostic test studies. You would use biomarker as a factor. You do not have many repetitions of some of them in your example dataset so your ability to tell the biomarkers apart may be limited.

It is certainly possible to do this with mada and there is an example in the vignette in section 6.2

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