### Abstract

Original language | English |
---|---|

Number of pages | 21 |

Journal | Probability in the engineering and informational sciences |

DOIs | |

Publication status | E-pub ahead of print/First online - 21 May 2018 |

### Fingerprint

### Keywords

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

### Cite this

*Probability in the engineering and informational sciences*. https://doi.org/10.1017/S0269964818000153

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*Probability in the engineering and informational sciences*. https://doi.org/10.1017/S0269964818000153

**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.

Research output: Contribution to journal › Article › Academic › peer-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

U2 - 10.1017/S0269964818000153

DO - 10.1017/S0269964818000153

M3 - Article

JO - Probability in the engineering and informational sciences

JF - Probability in the engineering and informational sciences

SN - 0269-9648

ER -