In medical diagnosis, I prefer to think in terms of probabilities than in terms of formulas. For example, one could remember the formula, sensitivity = tp/(tp + fn).

However, it’s easier to understand that sensitivity is the probability of a test being positive given that a disease is positive: sens = p(test+|dz+) and tp/(tp+fn) is just a way to use data to estimate this quantity.

In particular, p(test+|dz+)=p(test+,dz+)/p(dz+), and if there are n people in the 2×2 table, one can estimate p(test+,dz+) with tp/n, and p(dz+) = p(dz+,test+) + p(dz+,test-) with (tp+fn)/n. Stack these, the n cancel, and we get the first formula for sensitivity.

Although I can write these probabilities in terms of tp, fn, etc, I don’t need to. I can just compute them directly from a table, which is easier than remembering formulas that depend on tp, fn.

Maybe more importantly, the probabilistic way of thinking shows us the link between PPV and risk scores, which I will discuss next.