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

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

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
Number of pages21
JournalProbability in the engineering and informational sciences
DOIs
Publication statusE-pub ahead of print/First online - 21 May 2018

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Blood Group Antigens
Blood
Likelihood
Rh-Hr Blood-Group System
Genotype
Exact Computation
Formulation
Likely
Calculate
Arbitrary
Operator

Keywords

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

Cite this

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title = "Blood group probabilities by next of kin",
abstract = "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.",
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Blood group probabilities by next of kin. / van Sambeeck, Joost H.J. (Corresponding Author); van Dijk, Nico M.; de Kort, Wim L.A.M.; Schonewille, Henk; Janssen, Mart P.

In: Probability in the engineering and informational sciences, 21.05.2018.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Blood group probabilities by next of kin

AU - van Sambeeck, Joost H.J.

AU - van Dijk, Nico M.

AU - de Kort, Wim L.A.M.

AU - Schonewille, Henk

AU - Janssen, Mart P.

N1 - Cambridge UP deal

PY - 2018/5/21

Y1 - 2018/5/21

N2 - 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.

AB - 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.

KW - UT-Hybrid-D

KW - Operations research

KW - Stochastic modeling

KW - Applied probability

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