All tests give false positives and negatives, and doctors rarely know the difference.
Example: for a test with a 99% accuracy (for both positives and negatives), for a disease with a 1% incidence in the population, if your patient tests positive what is the chance they have the disease? 50%. Only 10% of docs get this question right. The more rare the disease, the more likely a false positive (as the disease incidence approaches the error rate).
Saw an article about this recently regarding a surge in early pregnancy genetic testing. Since these tests test for highly rare diseases, even accurate tests throw out way more false positives than true positives.
For your question, such tests should be used as a screening tool only, and probably only if you are only marginally at risk (otherwise skip straight to the better test). Useful to know if you should follow up with a more invasive or expensive test. So long as the false negative rate is low.
Yes, in your scenario a positive test would give you a 50% chance of being positive, while a negative test would give you a 98% chance of being negative.
If you tested 100 people and you assume the group matches statistical averages, then only 1 of those people would be positive. But 1 other person would return a false positive. So you would have 2 positive tests but only 1 positive person, meaning a 50% chance of infection in both people.
The other 98 people test negative, and I guess there is a 1% chance one of them is actually positive? Not sure of the math on that one.
So, If you test positive, go to the doctor for more tests. If you test negative but have symptoms, go see a doctor. If you test negative and have no symptoms, you are probably okay.
