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I am trying to find a name for the kind of study design/analysis I am working on so I can use it to look up best practices and examples of people who have done this kind of thing well.

Essentially I am trying to retrospectively compare two ways of taking biopsies of an organ. Since we are taking biopsies, we assume that the PPV of each test is 100%, so the question is simply "does biopsy method A find more cancer than biopsy method B?"

We have lots of examples of biopsy method B but only a few of A, so we would like to take patients who got biopsy type A and match them to one or more patients who got biopsy type B based on basic demographic information and risk factors for the disease before doing the comparison.

This sounds a bit like a case-control study, but it's not quite. Is there a name for what I am trying to do here? Can anyone point me to a paper that talks about or uses this kind of design?

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Do you know about 'propensity score matching'? I think it does what you want.

Here is an example https://www.researchgate.net/publication/223906464_Family_Group_Decision_Making_a_propensity_score_analysis_to_evaluate_child_and_family_services_at_baseline_and_after_36-months

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