Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-25T02:20:08.648Z Has data issue: false hasContentIssue false
  • English
  • Français

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: j.vansambeeck@sanquin.nl
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: n.m.vandijk@utwente.nl
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: w.dekort@sanquin.nl
Henk Schonewille
Affiliation:
Department of Experimental Immunohematology, Sanquin, Amsterdam, The Netherlands E-mail: h.schonewille@sanquin.nl
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: m.janssen@sanquin.nl
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Bernstein, S. (1924). Solution of a mathematical problem related to the theory of inheritance. Uch. Zap. n.-i. kaf. Ukrainy 1: 83–115.Google Scholar
2.Brousseau, D.C., Panepinto, A.J., Nimmer, M., & Hoffmann, R.G. (2010). The number of people with sickle-cell disease in the united states: national and state estimates. American Journal of Hematology 85(1): 77–78.Google ScholarPubMed
3.Carter, M.C., Wilson, J., Redpath, G.S., Hayes, P., & Mitchell, C. (2011). Donor recruitment in the 21st century: challenges and lessons learned in the first decade. Transfusion and Apheresis Science 45(1): 31–43.CrossRefGoogle ScholarPubMed
4.Casas, J., Ladra, M., Omirov, B., & Turdibaev, R. (2016). On the algebraic properties of the human abo-blood group inheritance pattern. The ANZIAM Journal 58(1): 78–95.CrossRefGoogle Scholar
5.Davey, R.J. (2004). Recruiting blood donors: challenges and opportunities. Transfusion 44(4): 597–600.CrossRefGoogle ScholarPubMed
6.Elston, R.C., Satagopan, J.M., & Sun, S. (2012). Genetic terminology. In Statistical Human Genetics. New York, NY, USA: Humana Press, pp. 1–9.CrossRefGoogle Scholar
7.Ganikhodjaev, N., Daoud, J., & Usmanova, M. (2010a). Linear and nonlinear models of heredity for blood groups and rhesus factor. Journal of Applied Sciences 10(16): 1748–1754.Google Scholar
8.Ganikhodjaev, N., Jamal Ibrahim, D., & Usmanova, M. (2010b). Stochastic models of heredity rhesus factor. Australian Journal of Basic and Applied Sciences 4(8): 3306–3310.Google Scholar
9.Ganikhodjaev, N., Saburov, M., & Jamilov, U. (2013). Mendelian and non-mendelian quadratic operators. Applied Mathematics & Information Sciences 7(5): 1721–1729.CrossRefGoogle Scholar
10.Ganikhodzhaev, R., Mukhamedov, F., & Rozikov, U. (2011). Quadratic stochastic operators and processes: results and open problems. Infinite Dimensional Analysis, Quantum Probability and Related Topics 14(2): 279–335.CrossRefGoogle Scholar
11.Guo, S.W. & Thompson, E.A. (1992). Performing the exact test of hardy-weinberg proportion for multiple alleles. Biometrics 48(2): 361–372.CrossRefGoogle ScholarPubMed
12.International Society of Blood Transfusion (2014). Table of blood group systems v4.0. http://www.isbtweb.org/working-parties/red-cell-immunogenetics-and-blood-group-terminology/ [Accessed: January 2017].Google Scholar
13.Reid, M.E., Lomas-Francis, C., & Olsson, M.L. (2012). The blood group antigen factsbook. Waltham, Massachusetts, USA: Academic Press.Google Scholar
14.Sadykov, T. (2017). Polynomial dynamics of human blood genotypes frequencies. Journal of Symbolic Computation 79: 342–355.CrossRefGoogle Scholar
15.Trefethen, L.N. & Bau, D. III (1997). Numerical linear algebra. Philadelphia, Pennsylvania, USA: Siam.CrossRefGoogle Scholar
16.Williamson, L.M. & Devine, D.V. (2013). Challenges in the management of the blood supply. The Lancet 381(9880): 1866–1875.CrossRefGoogle ScholarPubMed