Mathematical аnalysis of kidney transplant demand and availability

Aim. To analyse the dynamics of the need and availability of donor kidneys for transplantation. To construct the predictions for the number of waiting lists. To analyse the annual number of kidney transplants and the availability ofdonor kidney.

Materials and methods. Data base of Eurotransplant International Foundation 1969–2015 has been analyzed. We built a forecast of the kidney waiting list, kidney transplants quantity and availability of kidney grafts up to 2030.

Results. Random process analysis of kidney transplant recipients number has shown an increasing linear trend. Growing linear trend is due to the inability to fully meet the increasing need for a kidney transplant. Presence of a regular stochastic component is revealed that provides random fl uctuations in the number of patients waiting for kidney transplantation with a period of 35–40 years. Random process of the number of kidney transplants showed an exponential asymptotic trend growing to a certain saturation value. Estimation of its autocorrelation function showed the absence of regular stochastic components in it. Preservation of 1969–2015 dynamics for the period 2015–2030 allows to suggest a signifi cant increase in the number of people waiting for transplant and a decrease in the availability of donor kidneys.

Conclusion. The number of donor kidney transplantations tends to saturation limit, and limit is already lower than the current need for donor kidneys. The increase in the number of kidney transplantation programs and the improvement of organ donation system may lead to a limited increase in annual number of transplants and, possibly, the saturation limit, but not to a qualitative change in the dynamics of reduced availability of donor kidneys. A qualitative change in this dynamics towards increasing accessibility, is possible perhaps through activities that affect factors causing a constant increase in the number of people who need a transplant.

1. Schieppati A, Remuzzi G. Chronic renal diseases as a public health problem: epidemiology, social, and economic implications. Kidney Int. Suppl. 2005; 98: 7–10. doi:10.1111/j.1523-1755.2005.09801.x. PMID:16108976.

2. Schoolwerth AC, Engelgau MM, Hostetter TH. Chronic kidney disease: a public health problem that needs a public health action plan. Preventing Chronic Disese. 2006; 3 (2): A57.

3. Coresh J, Selvin E, Stevens LA. Prevalence of chronic kidney disease in the United States. JAMA. 2007; 298 (17): 2038–2047. doi:10.1001/jama.298.17.2038. PMID:17986697.

4. Go AS, Chertow GM, Fan D. Chronic kidney disease and the risks of death, cardiovascular events, and hospitalization. N. Engl. J. Med. 2004; 351 (13):1296–1305. doi: 10.1056/NEJMoa04103. PMID:15385656.

5. www.usrds.org [Internet].United States Renal Data System. Annual data report 2016. Available from: https:// www.usrds.org/adr.aspx.

6. Бикбов БТ, Томилина НА. Заместительная терапия больных с хронической почечной недостаточностью в Российской Федерации в 2008–2011 гг. Нефрология и диализ. 2014; 16 (1): 11–127. Renal replacement therapy for ESRD patients in Russian Federation, 1998–2011. Report of Russian RRT Registry. Part 1. Bikbov BT, Tomilina NA. Zamestitel’naya terapiya bol’nykh s khronicheskoy pochechnoy nedostatochnost’yu v Rossiyskoy Federatsii v 2008–2011 gg. Nefrologiya i dializ. 2014; 16 (1): 11–127. [English abstract].

7. Готье СВ, Хомяков СМ. Оценка потребности населения в трансплантации органов, донорского ресурса и планирование эффективной сети медицинских организаций (центров трансплантации). Вестник трансплантологии и искусственных органов. 2013; 15 (3): 11–24. Gautier SV, Khomyakov SM. Assessment of requirement of the population in the organ transplantation, the donor resource and planning of the effective network of the medical organizations (The centers of transplantation). Vestnik transplantologii i iskusstvennykh organov. 2013; 15 (3): 11–24.

8. www.eurotransplant.org [Internet]. Eurotransplant International Foundation. Available from: http://statistics. eurotransplant.org.

9. www.ont.es [Internet]. Organization Nacionale de Transplantes. Database. Available from: http://www.ont.es/infesp/Paginas/DatosdeDonacionyTrasplante.aspx.

10. Hoerger TJ, Simpson SA, Yarnoff BO. The Future Burden of CKD in the United States: A Simulation Model for the CDC CKD Initative. Am. J. Kidney Dis. 2015; 65 (3): 403–411. doi: 10.1053/j.ajkd.2014.09.023. PMI D:25468386.

11. www.aihw.gov.au [Internet]. Projection of the prevalence of treated end-stage kidney disease in Australia 2012–2020. Australian Institute of Health and Welfare, Canberra, 2014. Available from: https://www.aihw. gov.au.

12. Gilbertson DT, Liu J, Xue JL. Projecting the number of patients with end-stage renal disease in the United States to the year 2015. JASN. 2005; 16 (12): 3736–3741. doi:10.1681/ASN.2005010112. PMID:16267160.

13. Булыгин ВС, Игнатов НА. Автоматизированная система прогнозирования динамических процессов. Обеспечение качества на всех этапах жизненного цикла. Под ред. Б.В. Бойцова, Ю.Ю. Комарова. М.: МАИ-ПРИНТ, 2008: 452. Bulygin VS, Ignatov NA. Avtomatizirovannaya sistema prognozirovaniya dinamicheskikh protsessov. Obespechenie kachestva na vsekh etapakh zhiznennogo tsikla. Pod red. B.V. Boytsova, Yu.Yu. Komarova. M.: MAI-PRINT, 2008: 452.

14. Игнатов НА. Метод прогнозирования временных рядов с регулярными периодическими компонентами на основе модели периодически коррелированных случайных процессов [диссертация]. М.: Московский авиационный институт, 2011. Ignatov NA. Metod prognozirovaniya vremennykh ryadov s regulyarnymi periodicheskimi komponentami na osnove modeli periodicheski korrelirovannykh sluchaynykh protsessov [dissertatsiya]. M.: Moskovskiy aviatsionnyy institut, 2011.

15. Игнатов НА. Применение численного решения интегрального уравнения Винера в задачах прогнозирования. Современные технологии в задачах управления, автоматики и обработки информации. Труды XVII Международного научно-технического семинара. Тезисы докладов. 2008. Алушта. СПб.: ГУАП, 2008. Ignatov NA. Primenenie chislennogo resheniya integral’nogo uravneniya Vinera v zadachakh prognozirovaniya. Sovremennye tekhnologii v zadachakh upravleniya, avtomatiki i obrabotki informatsii. Trudy XVII Mezhdunarodnogo nauchno-tekhnicheskogo seminara. Tezisy dokladov. 2008. Alushta. SPb.: GUAP, 2008.

16. Игнатов НА. Прогнозирование временных рядов с регулярными циклическими компонентами с помощью модели периодически коррелированных случайных процессов. Научные труды: Институт народнохозяйственного прогнозирования РАН. 2011; 9: 461–477. Ignatov NA. Prognozirovanie vremennykh ryadov s regulyarnymi tsiklicheskimi komponentami s pomoshch’yu modeli periodicheski korrelirovannykh sluchaynykh protsessov. Nauchnye trudy: Institut narodnokhozyaystvennogo prognozirovaniya RAN. 2011; 9: 461–477.

17. Matesanz R. Factors That Infl uence the Development of an Organ Donation Program. Transplantation Proceedings. 2004; 36 (3): 739–741. doi: 10.1016/j.transproceed.2004.03.025.