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BLOOD GROUP PROBABILITIES BY NEXT OF KIN

Published online by Cambridge University Press:  21 May 2018

Joost H. J. van Sambeeck ,
Nico M. van Dijk ,
Wim L. A. M. de Kort ,
Henk Schonewille  and
Mart P. Janssen
Joost H. J. van Sambeeck
Affiliation:
Department of Transfusion Technology Assessment, Sanquin, Amsterdam, The Netherlands and Centre for Healthcare Operations Improvement & Research, University of Twente, Enschede, The Netherlands E-mail: [email protected]
Nico M. van Dijk
Affiliation:
Department of Stochastic Operations Research, University of Twente, Enschede, The Netherlands and Centre for Healthcare Operations Improvement & Research, University of Twente, Enschede, The Netherlands E-mail: [email protected]
Wim L. A. M. de Kort
Affiliation:
Department of Donor Studies, Sanquin, Amsterdam, The Netherlands and Department of Social Medicine, Academic Medical Center, Amsterdam, The Netherlands E-mail: [email protected]
Henk Schonewille
Affiliation:
Department of Experimental Immunohematology, Sanquin, Amsterdam, The Netherlands E-mail: [email protected]
Mart P. Janssen
Affiliation:
Department of Transfusion Technology Assessment, Sanquin, Amsterdam, The Netherlands and Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Utrecht, The Netherlands E-mail: [email protected]
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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.

Keywords

applied probabilityoperations researchstochastic modeling
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 34 , Special Issue 3: Analytic Methods in Health Care and in Clinical Trials In Honor and Memory of Lycourgos (Lee) Papayanopoulos , July 2020 , pp. 343 - 363
Copyright
Copyright © Cambridge University Press 2018

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