Draw out your 4/4 box.

Note that prevalence does not change specificity or sensitivity and that's why you can eliminate C and D right off the bat.

so with low prevalence, you decrease the amount of people with the disease and if you write out for formulas for PPV and NPV you can see that PPV has its variable in the numerator and denominator decrease (decrease overall) while the NPV only has its numerator in the denominator decrease. i wish I could draw it out i hate typing out math

For those not math-inclined, just think it out and forget the formulas. If TONS of people have a disease, more of the people you test will have it. So the people who test positive will probable actually have it (higher PPV).

If almost no one has it, so few of the people you test will actually have the disease. Of all the ones who test positive (for real or false negatives) not that many will really have it bc not that many of the population have it.

You can reason it out and can think through/derive the formulas without having to memorize anything!

Nothing about the test itself has changed, so sensitivity and specificity remain the same.

Switching from high to low prevalence population → ↓ TP, ↑ FP, ↓ FN, & ↑ TN

↓ PPV = ↓ TP / ( ↓ TP + ↑ FP )

↑ NPV = ↑ TN / ( ↑ TN + ↓ FN )

TP = True positive

TN = True negative

FP = False positive

FN = False negative