Mathematical predictive relationship of CD4+ lymphocytes and total leukocytes in HIV-infected patients
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Insight Group, Nacional University Hospital of Colombia, Bogotá, Colombia
Humanitas Group, Faculty of Education and Humanities, Universidad Militar Nueva Granada, Bogotá, Colombia
Services and Consulting in Infectology, Bogotá, Colombia
Clínica de Marly. Bogotá, Colombia.
Faculty of Basic and Applied Sciences, Universidad Militar Nueva Granada, Bogotá, Colombia
Faculty of Medicine, Universidad Militar Nueva Granada, Bogotá, Colombia
Submission date: 2021-09-26
Final revision date: 2022-03-06
Acceptance date: 2022-04-19
Online publication date: 2024-05-21
Corresponding author
Javier Oswaldo Rodríguez Velasquez   

Insight Group. Hospital Universitario Nacional de Colombia. Bogotá, Colombia.
HIV & AIDS Review 2024;23(2):124-129
Different parameters have been established to direct the treatment of patients with human immunodeficiency virus (HIV) infection, such as CD4+ lymphocyte values, and it is of clinical interest to have methodologies that accurately predict these values. Aim of the study was to predict the total values of leukocytes and CD4+ lymphocytes greater than 500 cells/μl3 in HIV-infected patients using the theory of probability and set theory.

Material and methods:
Starting from 7 cases with several records over time, an induction was performed establishing mathematical patterns between CD4+ lymphocyte values and total leukocyte values, while applying the probability theory to calculate predictive accuracy in 43 cases, and subsequently, sensitivity and specificity were calculated in a blinded study.

In total, 184 records were analyzed for 50 cases. The values of total leukocytes equal to or greater than 3.9 cells/mm3 were predicted to correspond to CD4+ lymphocyte values greater than 500 cells/μl3 in 100% of time, with sensitivity and specificity results of 100%.

This is the first investigation with the theory of probability, in which predictions were made from leukocyte values equal to or greater than 3.9 cells/mm3 to find CD4+ lymphocyte counts. A predictive probabilistic methodology was developed, and determined results for the calculated ranges were found.

Gnedenko BV, Khintchine A. Introducción a la teoría de las probabilidades. Barcelona: Montaner y Simon, S.A.; 1968, p. 175-176.
Spiegel M. Estadística, serie Schaum. México: Mc Graw Hill; 1980.
Feynman R, Leighton RB, Sands M. Física. Vol. 1. Chapter 6. México: Addison Wesley; 1998.
Obregón I. La magia y belleza de las probabilidades. In: Obregón I. Magia y belleza de las matemáticas y algo de su historia. Colombia: Intermedio Ed.; 2007, p. 116.
UNAIDS. Global HIV & AIDS statistics – 2018 fact sheet. 2018. Available at: (Accessed: 26.05.2019).
De Oliveira M, Bastos M, Martins E, de Lima NA, Leite AJ, Kallas E, et al. Acute HIV infection with rapid progression to AIDS. Braz J Infect Dis 2010; 14: 291-293.
Noda AL, Vidal LA, Pérez JE, Cañete R. Interpretación clínica del conteo de linfocitos T CD4 positivos en la infección por VIH. Rev Cubana Med 2013; 52: 118-127.
Clift IC. Diagnostic flow cytometry and the AIDS pandemic. Lab Med 2015; 46: e59-e64. DOI: 10.1309/LMKHW2C86ZJDRTFE.
Zijenah L, Kadzirange G, Madzime S, Borok M, Mudiwa C, Tobai­wa O, et al. Affordable flow cytometry for enumeration of absolute CD4+ T-lymphocytes to identify subtype C HIV-1 infected adults requiring antiretroviral therapy (ART) and monitoring response to ART in a resource-limited setting. J Transl Med 2006; 14: 33. DOI: 10.1186/1479-5876-4-33.
Brown ER, Otieno P, Mbori DA, Farquhar C, Obimbo EM, Nduati R, et al. Comparison of CD4 cell count, viral load, and other markers for the prediction of mortality among HIV-1-infected Kenyan pregnant women. J Infect Dis 2009; 199: 1292-1300.
Azzoni L, Foulkes A, Liu Y, Li X, Johnson M, Smith C, et al. Prioritizing CD4 count monitoring in response to ART in resource-constrained settings: a retrospective application of prediction-based classification. PLoS Med 2012; 9: e1001207. doi: 10.1371/journal.pmed.1001207.
Gitura B, Joshi MD, Lule GN, Anzala O. Total lymphocyte count as a surrogate marker for CD4+ T cell count in initiaing antiretroviral therapy at Kenyatta National Hospital, Nairobi. East Afr Med J 2007; 84: 466-472.
Sing Y, Mars M. Support vector machines to forecast changes in CD4 count of HIV-1 positive patients. Sci Res Essays 2010; 5: 2384-2390.
Foulkes AS, Azzoni L, Li X, Johnson MA, Mounzer K, Montaner LJ. Prediction based classification for longitudinal biomarkers. Ann Appl Stat 2010; 4: 1476-1497.
Rodríguez JO, Prieto SE, Correa C, Pérez CE, Mora JT, Bravo J, et al. Predictions of CD4 lymphocytes’ count in HIV patients from complete blood count. BMC Med Phys 2013; 13: 3: doi: 10.1186/1756-6649-13-3.
Rodríguez J, Prieto S, Correa C, Melo M, Dominguez D, Olarte N, Suárez D, et al. Prediction of CD4+ cells counts in HIV/AIDS patients based on sets and probability theories. Curr HIV Res 2018; 16: 416-424.
Asociación Médica Mundial. Declaración de Helsinki. Fortaleza, Brasil. 2013. Available at: (Accessed: 26.05.2019).
Ministerio de Salud. Resolución Número 8430 de 1993. Bogotá, Colombia. 1993. Available at: (Accessed: 26.05.2019).
Obirikorang C, Quaye L, Acheampong I. Total lymphocyte count as a surrogate marker for CD4 count in resource-limited settings. BMC Infect Dis 2012; 12: 128. DOI: 10.1186/1471-2334-12-128.
Chen J, Li W, Huang X, Guo C, Zou R, Yang Q, et al. Evaluating total lymphocyte count as a surrogate marker for CD4 cell count in the management of HIV-infected patients in resource-limited settings: a study from China. PLoS One 2013; 8: e69704. doi: 10.1371/journal.pone.0069704.
Shapiro NI, Karras DJ, Leech SH, Heilpern KL. Absolute lymphocyte count as a predictor of CD4 count. Ann Emerg Med 1998; 32: 323-328.
Sauter R, Huang R, Ledergerber B, Battegay M, Bernasconi E, Cavassini M, et al. CD4/CD8 ratio and CD8 counts predict CD4 response in HIV-1-infected drug naive and in patients on cART. Medicine (Baltimore) 2016; 95: e5094. doi: 10.1097/MD.0000000000005094.
Kidd PG, Cheng SC, Paxton H, Landay A, Gelman R. Prediction of CD4 count from CD4 percentage: experience from three laboratories. AIDS 1993; 7: 933-940.
Kebede M, Zegey DT, Zeleke BM. Predicting CD4 count changes among patients on antiretroviral treatment: application of data mining techniques. Comput Methods Programs Biomed 2017; 152: 149-157.
Einstein A, Infeld L. La evolución de la física. Barcelona: Salvat; 1986.
Rodríguez J. Dynamical systems applied to dynamic variables of patients from the intensive care unit (ICU): physical and mathematical mortality predictions on ICU. J Med Med Sci 2015; 6: 209-220.
Rodríguez J. Spatio-temporal probabilistic prediction of appearance and duration of malaria outbreaks in municipalities of Colombia. J Phys Conf Ser 2019; 1160: 012018. DOI 10.1088/1742-6596/1160/1/012018.
Rodríguez J. Teoría de unión al HLA clase II, teoría de probabilidad combinatoria y entropía aplicadas a secuencias peptídicas. Inmunología 2008; 27: 151-166.
Rodríguez J, Prieto SE, Dominguez D, Correa C, Melo M, Pardo J, et al. Application of the chaotic power law to cardiac dynamics in patients with arrhythmias. Rev Fac Med 2014; 62: 539-546.
Rodríguez J, Prieto S, Ramírez LJ. A novel heart rate attractor for the prediction of cardiovascular disease. Informatics in Medicine Unlocked 2019; 15: 100174. DOI:
Prieto SE, Rodríguez JO, Correa SC, Soracipa MY. Diagnosis of cervical cells based on fractal and Euclidian geometrical measurements: Intrinsic Geometric Cellular Organization. BMC Med Phys 2014; 14: 2. DOI: 10.1186/1756-6649-14-2.
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