Is it better to improve sensitivity or specificity?

Here’s a slightly unusual exercise on the topic of Bayes’ Theorem for those of you teaching or studying introductory probability. Imagine that you’re developing a diagnostic test for a disease. The test is very simple: it either comes back positive or negative. You have a choice between slightly increasing either your test’s sensitivity or its specificity . If your goal is to maximize the positive predictive value (PPV) of your test, i.e. the probability that a patient has the disease given that