Blood group probabilities by next of kin

Joost H.J. van Sambeeck (Corresponding Author), Nico M. van Dijk, Wim L.A.M. de Kort, Henk Schonewille, Mart P. Janssen

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For rare blood groups the recruitment of donor relatives, for example siblings, is expected to be effective, since the probability of a similar rare blood group is likely. However, the likelihood differs between blood groups and is not commonly available. This paper provides a unified mathematical formulation to calculate such likelihoods. From a mathematical and probabilistic point of view, it is shown that these likelihoods can be obtained from the computation of a stationary genotype distribution. This, in turn, can be brought down to a system of quadratic stochastic operators. A generic mathematical approach is presented which directly leads to a stationary genotype distribution for arbitrary blood groups. The approach enables an exact computation for the effectiveness of recruiting next of kin for blood donorship. Next to an illustration of computations for ‘standard’ ABO and Rhesus-D blood groups, it is particularly illustrated for the extended Rhesus blood group system. Also other applications requiring next of kin blood group associations can be solved directly by using the unified mathematical formulation.
Original languageEnglish
Pages (from-to)343-363
Number of pages21
JournalProbability in the engineering and informational sciences
Issue number3
Early online date21 May 2018
Publication statusPublished - Jul 2020


  • UT-Hybrid-D
  • Operations research
  • Stochastic modeling
  • Applied probability


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