In an ELISA test, what reasons could there be for a positive test when you don't have the disease?

Answer 1

If the ELISA detects antibodies against a disease antigen, then it can give a positive result if you once had the disease (especially if you had it recently) - even if you have since recovered. This is because the antobodies against the disease antigen will still be in your system.

Another possible answer might be experimental error/contamination. I once hears a story about a Californian phlebotomist who balanced blood samples against each other before centrifugation by pouring blood from one tube into the other: he/she therefore constaminated all the samples with other blood, and invalidated hundreds of blood tests. Years' worth of patients who had been told they had hepatitis and HIV had to be re-tested.

Answer 2

Non-specific binding. Some hormones have similar structures, and there may be a small amount of cross-reactivity with these homologous segments.
Or an antibody present in the blood which reacts with one of the reagent antigens. Say, I had an antibody to mouse protein, and this is used in the assay, it may give a false positive.
I haven't used ELISA for a while now, but these are two that come to mind.