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A key step of the organ transplant process is matching, where blood type, leukocyte antigens, crossmatch antibodies, etc. are checked to ensure compatibility. If these tests pass, and the organ is found to be free of transmissible disease, the organ is transplanted, and the recipient typically spends the remainder of his or her life on anti-rejection drugs.

Why are these drugs necessary, if the organ is a match for the recipient? What are the factors that need to match, and why isn't this testing enough to prevent rejection?