How does disease prevalence affect the positive predictive value of a test?

• A. Higher disease prevalence decreases positive predictive value.
• B. The positive predictive value is independent of disease prevalence.
• C. Higher disease prevalence increases positive predictive value.
• D. Lower disease prevalence increases positive predictive value.

Answer: (C)

The key idea is that positive predictive value (PPV) depends on how common the disease is in the population. PPV is the probability that a person truly has the disease given they tested positive, and with a fixed test performance (sensitivity and specificity), PPV rises as disease prevalence increases. When disease is more common, a positive result is more likely to be a true positive rather than a false positive.

This relationship can be seen in the formula: PPV = (sensitivity × prevalence) / [(sensitivity × prevalence) + ((1 − specificity) × (1 − prevalence))]. As prevalence increases, the numerator grows and the denominator shifts in a way that increases the overall value of PPV. For example, with sensitivity of 90% and specificity of 95%, PPV moves from roughly 15% at 1% prevalence to about 67% at 10% prevalence, and over 94% when prevalence is 50%.

So, higher disease prevalence increases the positive predictive value because positives are more likely to reflect true disease rather than false positives. When disease is rare, many positives are false positives, lowering PPV, and when disease is common, positives are more likely true positives, raising PPV.