Based on the pattern of reactions and nonreactions shown by cells positive and negative for an antigen when tested with serum, Fisher's exact method can be used to give the probability that the pattern of reactions is due to chance and not due to specific antibody.
Antigen on Cells?
Cells React with Patient Serum?
Designation
yes
yes
A
yes
no
B
no
yes
C
no
no
D
X = (((A + B) ! ) * ((C + D) ! ) * ((A + C) ! ) * ((B + D) ! ))
Y = (((A + B + C + D) ! ) * (A ! ) * (B ! ) * (C ! ) * (D ! )
probability that the findings are due to chance
(and not due to the presence of specific antibody) =
= (X / Y)
Interpretation:
• A p value < 0.05 is the minimum value required for the interpretation that an antibody to the antigen is present to be considered statistically valid.
• If the p value is >= 0.05, then the findings could be due to another antibody and additional cells need to be tested or an alternative hypothesis considered.
Limitations:
• Harris and Hochman (next section) felt that Fisher's method is too conservative, resulting in p values that were too high (often by a factor of 2-4 fold).
• I am not sure if the use of Fisher's Exact Method is valid when cells are "ambiguous" (positive for more than one antigen) or if more than one alloantibody is present.
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