Positive Predictive Value
You should calculate the positive predictive value (PPV) to determine the likelihood that you actually have this virus given your positive test result. 1
Why PPV is the Correct Answer
When you receive a positive test result, you need to know the posterior probability—the actual chance you have the disease after testing positive. This is precisely what PPV tells you. 1
PPV is defined as the probability that a person has the disease given a positive test result. 1 In your scenario with 10% prevalence and 30% false-positive rate (meaning 70% specificity), the PPV will tell you what proportion of positive test results are true positives versus false positives.
Understanding the Clinical Context
The ESCMID guidelines explicitly state: "The posterior probability of a positive test result (PPV) is the probability that a person has the disease, given the positive result." 1
With a relatively low prevalence of 10% and a concerning false-positive rate of 30%, your PPV will be substantially reduced. The guidelines demonstrate that "in a tested population with a low prior probability for the disease, a positive test result will only be proof of the disease if the test is free of false positives (specificity of 100%). Otherwise the posterior probability (PPV) will be only 50%, even in the case of a high sensitivity." 1
Why Not the Other Options?
- Negative predictive value (NPV): This tells you the probability of not having the disease when you test negative—irrelevant since you tested positive
- Sensitivity: This is the probability of testing positive if you have the disease—but you need the reverse calculation
- Specificity: This is the probability of testing negative if you don't have the disease—again, the wrong direction
- Odds ratio: This is a measure of association used in epidemiological studies, not for individual test interpretation
The Mathematical Relationship
PPV depends on three factors:
- Prevalence (your pre-test probability): 10%
- Sensitivity (not provided, but needed)
- Specificity: 70% (derived from 30% false-positive rate)
The formula incorporates all three to give you the actual probability of infection given your positive result. 1
Clinical Implications
A low PPV means many positive test results are false positives, leading to unnecessary treatment and anxiety. 1 The ESCMID guidelines emphasize that at low prevalences (5-10%), even tests with high specificity can have unacceptably low PPVs, and they recommend a two-step testing approach with confirmatory testing for positive results. 1
In your case, with 10% prevalence and 70% specificity, you should expect a moderate PPV—meaning a substantial proportion of positive results will be false positives, making confirmatory testing advisable.