Antibody test kits are NOT recommended at the moment by FDA and CDC to check if your vaccine is "working".
Antibody test kits have limited antibody specificity meaning you might test positive in some, and negative in others.
There are many reasons for this.
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Most kits are not robust enough. It depends on how the kits were developed, because of the limitations (and cost), they might be tailored for certain parts of the virus or for only certain types of vaccines.
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Most serology tests detect antibodies from the spike protein, while some detect the nucleocapsid protein.
Those kits targeting the nucleocapsid will not detect antibody response from vaccines that target the spike protein (e.g. Pfizer and AZ).
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Then comes the sensitivity of the kits. If the kits are made for spike protein and the sensitivity is low, it will not detect the inactivated vaccines (e.g. Sinovac) because they produce a robust response of antibodies, not just spike protein.
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Lastly, it is the functionality of specific antibodies that can neutralise the virus that is more important rather than the level of total antibodies.
This neutralising effect is not readily deciphered by a serology test at the moment. More needs to be done on this.
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In summary, antibody tests are best left for research use only at the moment.The current consensus is that people should not rush out and get their antibody test as there is so much uncertainty on the levels required for protection, the types, and the sensitivity of the kits
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