Funnily enough, accuracy is a somewhat inaccurate term when it comes to medical testing. What we are interested in are sensitivity, specificity [0] and prevalence of the disease in the population being tested. With those three we can get positive prediction value (PPV) and negative prediction value (NPV) [1]. But PPV and NPV always depend on prevalence! That's why we don't want to test healthy people for all kinds of exotic diseases.
[0] https://en.wikipedia.org/wiki/Sensitivity_and_specificity [1] https://en.wikipedia.org/wiki/Positive_and_negative_predicti...