A positive recipient can receive either a positive or negative blood-type organ, as long as the ABO is the same (with the exception that anyone can receive O type blood/organs). A negative recipient cannot receive a blood type positive organ.
There is also HLA typing done; they check for 6 different antibodies. When you are on the transplant list, you have blood taken for this once a month. It’s then stored for that amount of time, and if you are in line for a specific kidney, they then will check it against the potential donor’s blood for compatibility. This is not done for livers, hearts, etc to the best of my knowledge.
If the recipient has had a previous transplant or blood transfusion, it’s harder to match the donor, as there are most likely antibodies that could cause rejection.
As for the HLA antibodies, it used to be that the higher number of matches indicated a lower likelihood of rejection. However, with the newer immunosuppressive regimens, this isn’t an issue anymore. My transplant was a 5/6 “mismatch”; in other words, I only matched 1 antibody to my donor’s, but so far, no rejection (since May 2008). I also received a CMV + kidney, and I’m CMV negative (even 17 months afterwards)
As an aside, a kidney that is a 6/6 match (0/6 mismatch) will bump a recipient to first spot on the list for that specific kidney, irregardless of wait time on the list. It’s the transplant equivalent to hitting the Powerball.
Thanks for clarifying that. I went to a transplant orientation, and they didn’t tell us any of that. They only said the blood types had to be an exact match, which is misleading since Rh positive and negative can be a match.