Prediction of CD4+ Cells Counts in HIV/AIDS Patients based on Sets and Probability Theories

Author(s): Javier Rodriguez* , Signed Prieto , Catalina Correa , Martha Melo , Dario Dominguez , Nancy Olarte , Daniela Suárez , Laura Aragón , Fernando Torres , Fernando Santacruz .

Journal Name: Current HIV Research

Volume 16 , Issue 6 , 2018

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Graphical Abstract:


Background: Previous studies have developed methodologies for predicting the number of CD4+ cells from the total leukocyte and lymphocytes count based on mathematical methodologies, obtaining percentages of effectiveness prediction higher than 90% with a value of less than 5000 leukocytes.

Objective: To improve the methodology probabilities prediction in 5000-9000 leukocytes ranges.

Method: from sets A, B, C and D defined in a previous study, and based on CD4+ prediction established on the total number of leukocytes and lymphocytes, induction was performed using data from 10 patients with HIV, redefining the sets A and C that describe the lymphocytes behavior relative to leukocytes. Subsequently, we evaluated with previous research prediction probabilities parameters from a sample of 100 patients, calculating the belonging probability to each sample and organized in predetermined ranges leukocytes, of each of the sets defined, their unions and intersections. Then the same procedure was performed with the new sets and the probability values obtained with the refined method were compared with respect to previously defined, by measures of sensitivity (SENS) and Negative Predictive Value (NPV) for each range.

Results: probabilities with values greater than 0.83 were found in five of the nine ranges inside the new sets. The probability for the set A∪C increased from 0.06 to 0.18 which means increases between 0.06 and 0.09 for the intersection (A∪C) ∩ (B∪D), making evident the prediction improvement with new sets defined.

Conclusion: The results show that the new defined sets achieved a higher percentage of effectiveness to predict the CD4+ value cells, which represents a useful tool that can be proposed as a substitute for clinical values obtained by the flow cytometry.

Keywords: CD4, blood count, lymphocytes, HIV/AIDS, prediction, probability.

UNAIDS. Global Report: UNAIDS Report on the global AIDS epidemic 2012. c 2012 [citado 2012 Dic 26]. Available at:. 2012_en.pdf
Zijenah L, Kadzirange G, Madzime S, 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; 4: 33.
Brown E, Otieno P, Mbori-Ngacha D, et al. Comparison of CD4 Cell Count, Viral Load, and Other Markers for the Prediction of Mortality among HIV-1–Infected. J Infect Dis 2009; 199(9): 1292-300.
Clift IC. Diagnostic flow cytometry and the AIDS pandemic. Lab Med 2015; 46(3): e59-64.
Williams BG, Korenromp EL, Gouws E, Schmid GP, Auvert B, Dye C. HIV infection, antiretroviral therapy, and CD4+ cell count distributions in African populations. J Infect Dis 2006; 194: 1450-8.
Patrikar S, Basannar DR, Bhatti VK, Kotwal A, Gupta RM, Grewal RS. Rate of decline in CD4 count in HIV patients not on antiretroviral therapy. Med J Armed Forces India 2014; 70(2): 134-8.
Budiono W. Total lymphocyte count and hemoglobin combined to predict CD4 lymphocyte counts of less than 200 cells/mm (3) in HIV/AIDS. Acta Med Indones 2008; 40(2): 59-62.
Gitura B, Joshi MD, Lule GN, Anzala O. Total lymphocyte count as a surrogate marker for CD4+ t cell count in initiating antiretroviral therapy at Kenyatta National Hospital, Nairobi. East Afr Med J 2007; 84(10): 466-72.
Singh Y, Mars M. Support vector machines to forecast changes in CD4 count of HIV-1 positive patients. Sci Res Essays 2010; 5(17): 2384-90.
Wang Y, Li Y, Wang C, et al. Total Lymphocyte Count as a Surrogate Marker to Predict CD4 Count in Human Immunodeficiency Virus-infected Children: A Retrospective Evaluation. Pediatr Infect Dis J 2012; 31(1): 61-3.
Foulkes AS, Azzoni L, Li X, et al. Prediction based classification for longitudinal biomarkers. Ann Appl Stat 2010; 4(3): 1476-97.
Azzoni L, Foulkes A, Yan L, 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(4): e1001207. Available at:. http://www. doi/10.1371/journal.pmed.1001207
Rodríguez J, Prieto S, Bernal P, et al. Set theory applied to leukocytes, lymphocytes and CD4 in populations of HIV patients. Prediction of T-CD4 lymphocytes, for clinical application. Rev Fac Med 2011; 19(2): 148-56.
Rodríguez J, Prieto S, Bernal P, et al. T CD4 Lymphocytes Prediction Based on the Theory of Probability.Clinical application on leukocytes, lymphocytes and CD4 populations of HIV patients. Infect 2012; 16(1): 15-22.
Rodríguez J, Prieto S, Correa C, et al. Set theory applied to white cell and lymphocyte counts: prediction of CD4 T lymphocytes in patients with human immunodeficiency virus/aids. Inmunologia 2013; 32(2): 50-6.
Rodríguez J, Prieto S, Correa C, et al. Predictions of CD4 lymphocytes’ count in HIV patients from complete blood count. BMC Med Phys 2013; 13: 3. Available at: http://www.
Rodríguez J, Correa C, Ortiz L, et al. Mathematical evaluation of cardiac dynamics with the theory of probability. Rev Mex Cardiol 2009; 20(4): 183-9.
Rodríguez J, Vitery S, Puerta G, et al. Temporary probabilistic dynamics of the dengue’s epidemic in ColombiaRev Cuban Higien Epidemiol 2011; 49(1) Available at: hie/ vol49_ 1_11/hiesu111.htm
Feynman RP, Leighton RB, Sands M. Probabilidad. In: Feynman RP, Leighton RB, Sands M. Física. Vol. 1. Wilmington: Addison- Wesley Iberoamericana, S.A. 1964; pp. 6-1 - 6-16.
Obregón I. The magic and beauty of the probabilities.In: I. Obregón, editor.Magic and beauty of mathematics and some of its history. Bogotá: Intermediate Publishers; 2007; pp. 113-28.
Hrbacek KJ. Introduction to set theory. 3rd ed. Marcel Dekker, Inc.New York. 1999; pp. 1-33.
Daka D, Loha E. Relationship between total lymphocyte count (TLC) and CD4 count among peoples living with HIV, Southern Ethiopia: a retrospective evaluation. AIDS Res Ther 2008; 5: 26.
Wang Y, Liang S, Yu E, et al. Correlation analysis on total lymphocyte count and CD4 count in HIV-infected patients: a retrospective evaluation. J Huazhong Univ Sci Technolog Med Sci 2011; 31(5): 712-6.
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.
Githinji N, Maleche-Obimbo E, Nderitu M, Wamalwa DC, Mbori-Ngacha D. Utility of total lymphocyte count as a surrogate marker for CD4 counts in HIV-1 infected children in Kenya. BMC Infect Dis 2011; 30(11): 259.
Sauter R, Huang R, Ledergerber B, et al. CD4/CD8 ratio and CD8 counts predict CD4 response in HIV-1-infected drug naive and in patients on cART. Medicine 2016; 95(42): pe5094.
Shapiro NI, Karras DJ, Leech SH, et al. Absolute lymphocyte count as a predictor of CD4 count. Ann Emerg Med 1998; 32(3): 323-8.
Shoko C, Chikobvu D, Bessong PO. A Markov Model to Estimate Mortality Due to HIV/AIDS Using Viral Load Levels-Based States and CD4 Cell Counts: A Principal Component Analysis Approach. Infect Dis Ther 2018; 7(4): 457-71.
Kamalanand K, Jawahar PM. Prediction of Human Immunodeficiency Virus-1 Viral Load from CD4 Cell Count Using Artificial Neural Networks. J Med Imaging Health Inform 2015; 5(3): 641-6.
Martins L, Barcellos M, Brindeiro R, Fonseca F. Probabilistic Neural Network for Predicting Resistance to HIV-Protease Inhibitor Nelfinavir. Bioinformatics 2014; 2014: 17-23.
Kebede M, Zegeye DT, Zeleke BM. Predicting CD4 count changes among patients on antiretroviral treatment: Application of data mining techniques. Comput Methods Programs Biomed 2017; 152: 149-57.
Vélez N, Torrealdea J. >Modeling in systems dynamics of the immune response to HIV-1 infection. Ini Inv 2006; 1: 1-9. Available at:. article/view/240
Altman A, Däumer M, Beerenwinkel N, et al. Predicting the Response to Combination Antiretroviral Therapy: Retrospective Validation of geno2pheno-THEO on a Large Clinical Database. JID 199: 999-1006
Altmann A, Rosen-Zvi M, Prosperi M, et al. Comparison of Classifier Fusion Methods for Predicting Response to Anti HIV-1 Therapy. PLoS One 2008; 3(10): e3470.
Wang D, DeGruttola V, Hammer S, et al. A Collaborative HIV Resistance Response Database Initiative: Predicting Virological Response Using Neural Network Models. Poster presentation at: The XI International HIV Drug Resistance Workshop. Seville. 2002.
Larder B, Wang D, Revell A, et al. The development of artificial neural networks to predict virological response to combination HIV therapy. Antivir Ther 12(1): 15-24.
Pirzada Y, Khuder S, Donabedian H. Predicting AIDS-related events using CD4 percentage or CD4 absolute counts. AIDS Res Ther 2006; 3: 20.
Hansen S, Kronborg G, Benfield T. Prediction of liver disease, AIDS and mortality based on discordant absolute and relative peripheral CD4 T lymphocytes in HIV/HCV co-infected individuals. AIDS Res Hum Retroviruses 2018. [Epub ahead of print].
Operskalski EA, Kovacs A. HIV/HCV co-infection: pathogenesis, clinical complications, treatment, and new therapeutic technologies. Curr HIV/AIDS Rep 2011; 8(1): 12-22.
McGovern BH, Golan Y, Lopez M, et al. The impact of cirrhosis on CD4+ T cell counts in HIV-seronegative patients. Clin Infect Dis 2007; 44(3): 431-7.
Mandorfer M, Reiberger T, Payer BA, et al. Vienna HIV & Liver Study Group. The influence of portal pressure on the discordance between absolute CD4+ cell count and CD4+ cell percentage in HIV/hepatitis C virus-coinfected patients. Clin Infect Dis 2013; 56(6): 904-5.
Lewden C, Gabillard D, Minga A, et al. CD4-specific mortality rates among HIV-infected adults with high CD4 counts and no antiretroviral treatment in West Africa. J Acquir Immune Defic Syndr 2012; 59(2): 213-9.
The Opportunistic Infections Project Team of the Collaboration of Observational HIV Epidemiological Research in Europe (COHERE) in EuroCoord. CD4 Cell Count and the Risk of AIDS or Death in HIV-Infected Adults on Combination Antiretroviral Therapy with a Suppressed Viral Load: A Longitudinal Cohort Study from COHERE. PLoS Med 2012; 9(3): e1001194.
May MT, Vehreschild JJ, Trickey A, et al. Mortality According to CD4 Count at Start of Combination Antiretroviral Therapy Among HIV-infected Patients Followed for up to 15 Years After Start of Treatment: Collaborative Cohort Study. Clin Infect Dis 2016; 62(12): 1571-7.
Ying R, Granich RM, Gupta S, Williams BG. CD4 Cell Count: Declining Value for Antiretroviral Therapy Eligibility. Clin Infect Dis 2016; 62(8): 1022-8.
Maduna PH, Dolan M, Kondlo L, et al. Morbidity and Mortality According to Latest CD4+ Cell Count among HIV Positive Individuals in South Africa Who Enrolled in Project Phidisa. PLoS One 2015; 10(4): e0121843.
Masiira B, Baisley K, Mayanja BN, et al. Mortality and its predictors among antiretroviral therapy naïve HIV-infected individuals with CD4 cell count ≥350 cells/mm3 compared to the general population: data from a population-based prospective HIV cohort in Uganda. Glob Health Action 2014; 7: 21843.
Tang ZZ, Pan SW, Ruan Y, et al. Effects of high CD4 cell counts on death and attrition among HIV patients receiving antiretroviral treatment: an observational cohort study. Sci Rep 2017; 7: 3129.
Mermin J, Ekwaru JP, Were W, et al. Utility of routine viral load, CD4 cell count, and clinical monitoring among adults with HIV receiving antiretroviral therapy in Uganda: randomised trial. BMJ 2011; 343: d6792.
Gabillard D, Lewden C, Ndoye I, et al. Mortality, AIDS-Morbidity, and Loss to Follow-up by Current CD4 Cell Count Among HIV-1–Infected Adults Receiving Antiretroviral Therapy in Africa and Asia: Data From the ANRS 12222 Collaboration. J Acquir Immune Defic Syndr 2013; 62(5): 555-61.
Ford N, Shubber Z, Jarvis JN, et al. CD4 Cell Count Threshold for Cryptococcal Antigen Screening of HIV-Infected Individuals: A Systematic Review and Meta-analysis. CID 2018; 66: S152-9.
Maskew M, Brennan AT, Westreich D, et al. Gender Differences in Mortality and CD4 Count Response Among HIV-Positive Patients Virally Suppressed Within 6 Months of Antiretroviral Therapy Initiation. J Womens Health 2013; 22: 1-9.
Biset M. Mortality and Its Predictors among HIV Infected Patients Taking Antiretroviral Treatment in Ethiopia: A Systematic Review. Aids Res Treat 2017; 5415298.
The Antiretroviral Therapy Cohort Collaboration. Survival of HIV-positive patients starting antiretroviral therapy between 1996 and 2013: a collaborative analysis of cohort studies. Lancet HIV 2017; 4: e349-56.
Shen Z, Zhu Q, Tang Z, et al. Effects of CD4 Cell Counts and Viral Load Testing on Mortality Rates in Patients with HIV Infection Receiving Antiretroviral Treatment: An Observational Cohort Study in Rural Southwest China. Clin Infect Dis 2016; 63(1): 108-14.
Nakagawa F, May M, Phillips A. Life expectancy living with HIV: recent estimates and future implications. Curr Opin Infect Dis 2013; 26: 17-25.
Trickey A, May MT, Vehreschild J, et al. Cause-Specific Mortality in HIV-Positive Patients Who Survived Ten Years after Starting Antiretroviral Therapy. PLoS One 2016; 11(8): e0160460.
Eyawo O, Franco C, Hull MW, et al. Changes in mortality rates and causes of death in a population-based cohort of persons living with and without HIV from 1996 to 2012. BMC Infect Dis 2017; 17: 174.
Saavedra A, Campinha N, Hajjar M, et al. Causes of death and factors associated with early mortality of HIV-infected adults admitted to Korle-Bu Teaching Hospital. Pan Afr Med J 2017; 27: 48.
Hoffmann CJ, Schomaker M, Fox MP, et al. CD4 count slope and mortality in HIV-infected patients on antiretroviral therapy: multi-cohort analysis from South Africa. J Acquir Immune Defic Syndr 2013; 63(1): 34-4.
Yin DE, Warshaw MG, Miller WC, et al. Using CD4 Percentage and Age to Optimize Pediatric Antiretroviral Therapy Initiation. Pediatrics 2014; 134(4): e1104-16.
Kabue MM, Buck WC, Wanless SR, et al. Mortality and Clinical Outcomes in HIV-Infected Children on Antiretroviral Therapy in Malawi, Lesotho, and Swaziland. Pediatrics 2012; 130(3): e591-9.
Ademola E, Adedeji S. Mortality in a Cohort of HIV-Infected Children: A 12-Month Outcome of Antiretroviral Therapy in Makurdi, Nigeria. Adv Med 2018; 6409134.
Moreira SF, Zandonade E, Miranda AE. Mortality in children and adolescents vertically infected by HIV receiving care at a referral hospital in Vitoria, Brazil. BMC Infect Dis 2015; 15: 155.
Shoko C, Chikobvu D. A superiority of viral load over CD4 cell count when predicting mortality in HIV patients on therapy. BMC Infect Dis 2019; 19: 169.
Rodríguez J, Bernal P, Prieto P, et al. Plasmodium falciparum binding peptides prediction to HLA class IIProbability, combinatory and entropy applied to MSP-5 and MSP-6 proteinsArchivos de alergia e Immunol Clin 2013; 44(1): 7-14
Rodríguez J. New physical and mathematicaldiagnosis of fetal monitoring: Clinicalapplication prediction. Mom Rev Física 2012; 44: 49-65.
Rodríguez J, Prieto S, Melo M, et al. Proportional entropy of cardiac dynamics applied to the diagnosis of patients in the intensive care unit. Med 2013; 35(100): 17-28.
Rodríguez J, Prieto S, Domínguez D, et al. Mathematical-physical prediction of cardiac dynamics using the proportional entropy of dynamic systems. J Med Med Sci 2013; 4(8): 370-81.
Rodríguez J, Prieto S, Correa C, et al. Fractal and euclidean geometric generalization of normal and restenosed arteries: fractal and euclidean geometric generalization of arteries. J Med Med Sci 2013; 4(4): 174-80.
Rodríguez J, Prieto S, Correa C, et al. Fractal generalization of pre-neoplasic cervical epithelial cells for clinical application. Rev Fac Med 2010; 18(2): 33-41.
Correa C, Rodríguez J, Prieto S, et al. Geometric diagnosis of erythrocyte morphophysiology. J Med Med Sci 2012; 3(11): 715-20.
Rodríguez J. Spatio-temporal probabilistic prediction of appearance and duration of malaria outbreak in municipalities of Colombia. J Phys Conf Ser 2019; 1160: 1-7.
Rodríguez J, Correa C. Temporal prediction of the dengue epidemic in Colombia: The epidemic’s probabilistic dynamics. Rev Salud Publica 2009; 11(3): 443-53.
Ministry of Health. Resolution Number 8430 of 1993. Bogotá, Colombia [Internet]. 1993. Available at: . https://www.minsalud.

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Year: 2018
Page: [416 - 424]
Pages: 9
DOI: 10.2174/1570162X17666190306125819
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