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As the pretest probability (prevalence, more or less) increases, the positive predictive value of a test increases. As the pretest probability declines, the PPV declines.
Positive predictive value is the number of true disease (true positive) over the number of predicted disease (positive results). In other words, of all the positive test results, what percentage were true positives?
If we increase the pretest probability the disease is more common, so true positives would rise (numerator), but the number of positive tests doesn't really change, since we aren't adjusting how the test works (it's threshold is the same). The ratio (PPV) has increased. The same logic works for decreasing the prevalence; our test still functions the same (threshold is unchanged), but the disease is more rare, so fewer positive test results will be true positives (indicating a lower PPV with lower prevalence).
