A Multistate Markov Model Based on CD4 Cell Count for HIV/AIDS Patients on Antiretroviral Therapy (ART)


  • Gurprit Grover Department of Statistics, University of Delhi, Delhi, India
  • Adesh Kumar Gadpayle Ram Manohar Lohia Hospital, New Delhi, India
  • Prafulla Kumar Swain Department of Statistics, University of Delhi, Delhi, India
  • Barnali Deka Department of Statistics, University of Delhi, Delhi, India




AIDS, ART, CD4 count, Cox PH Model, Multistate Markov Model, PLHA


The main purpose of this study is to assess the impact of Antiretroviral Therapy (ART) by using a multistate Markov model to estimate transition intensities and transition probabilities among various states (transient as well as absorbing) of the AIDS patients. A total of 580 AIDS patients were included in this study who are undergoing Antiretroviral Therapy treatment in the ART centre in New Delhi during the period of April 2004 to April 2011. The patients are classified in different states on the basis of their available CD4 cell counts. The authors also estimated the mean sojourn time and total length of stay in each state before absorption, and also examined the effects of explanatory variables (i.e Age, Sex, Mode of transmission) on the rates of transition using Cox’s proportional hazard model.

Author Biographies

Gurprit Grover, Department of Statistics, University of Delhi, Delhi, India

Department of Statistics

Prafulla Kumar Swain, Department of Statistics, University of Delhi, Delhi, India

Department of Statistics


GLOBAL HIV/AIDS RESPONSE – Epidemic update and health sector progress towards Universal Access – Progress Report, 2011, [Accessed on 2012 July 28].Available from www.unaids.org/en/media/unaids/contentassets/documents/unaidspublication/2011/20111130_UA_report_en.pdf.

UNAIDS WORLD AIDS DAY REPORT 2011, [Accessed on 2012 July 28]. Available from http://www.unaids.org/en/ media/unaids/contentassets/documents/unaidspublication/2011/jc2216_worldaidsday_report_2011_en.pdf

Williams B, Lima V, Gouws E. Modelling the Impact of Antiretroviral Therapy on the Epidemic of HIV. Curr HIV Res 2011; 9(6): 367-82. http://dx.doi.org/10.2174/157016211798038533 DOI: https://doi.org/10.2174/157016211798038533

Mahy M, Stover J, Stanecki K, Stoneburner R, Tassie JM. Estimating the impact of antiretroviral therapy: regional and global estimates of life years gained among adults, Sex Transm Infect 2010; 86(Suppl 2): 67-71. http://dx.doi.org/10.1136/sti.2010.046060 DOI: https://doi.org/10.1136/sti.2010.046060

National Aids Control Organization (NACO), Annual Report, 2011-12. [Accessed on 2012 July 8].Available from http://www.nacoonline.org/upload/Publication/Annual%20Report/NACO_AR_Eng%202011-12.pdf

Kumarasamy N, Vallabhaneni S, Flanigan TP, Mayer KH, Solomon S. Clinical profile of HIV in India. Indian J Med Res 2005; 121: 377-94. DOI: https://doi.org/10.1097/01.qai.0000176591.06549.de

Palmer S, Maldarelli F, Wiegand A, et al. Low-level viremia persists for at least 7 years in patients on suppressive antiretroviral therapy. Proc Natl Acad Sci USA 2008; 105(10): 3879-84. http://dx.doi.org/10.1073/pnas.0800050105 DOI: https://doi.org/10.1073/pnas.0800050105

Mellors JW, Munoz A, Giorgi JV, et al, Plasma viral load on CD4 lymphocytes as prognostic markers of HIV-1 infection. Ann Intern Med 1997; 126(12): 946-54. http://dx.doi.org/10.7326/0003-4819-126-12-199706150-00003 DOI: https://doi.org/10.7326/0003-4819-126-12-199706150-00003

World Health Organization (WHO). ART guidelines Review 2006. Available from http://www.who.int/hiv/pub/guidelines/ paediatric020907.pdf

World Health Organization (WHO). Antiretroviral Therapy for HIV infection in Adults and Adolescents Recommendations for public health approach revision 2010, [Accessed on 2012 July 8]. Available from http://whqlibdoc.who.int/publications/ 2010/9789241599764_eng.pdf

Longini IM, Clark WS, Byers RH, et al. Statistical analysis of the stages of HIV infection using a Markov model. Statistics Med 1989; 8: 831-43. http://dx.doi.org/10.1002/sim.4780080708 DOI: https://doi.org/10.1002/sim.4780080708

Longini IM, Clark WS, Gardner LI, Brundage JF. The Dynamic of CD4 T- Lymphocyte Decline in HIV infected

individuals: A Markov Modeling Approach. J Acquired Immune Deficiency Syndromes 1991; 4: 1141-47.

Hendriks JCM, Satten GA, Ameijden EJCV, Druten HAMV, Coutinho RA, Griensven GJPV. The incubation period to AIDS injecting drug users estimated from prevalent cohort data, accounting for death prior to an AIDS diagnosis. AIDS 1998; 12: 1537-44. http://dx.doi.org/10.1097/00002030-199812000-00017 DOI: https://doi.org/10.1097/00002030-199812000-00017

Alioum A, Leroy V, Commenges D, Dabis F, Salamon R. Effect of gender, age, transmission category, and antiretroviral therapy on the progression of HIV infection using Multistate Markov Models. Epidemiology 1998; 9: 605-12. http://dx.doi.org/10.1097/00001648-199811000-00007 DOI: https://doi.org/10.1097/00001648-199811000-00007

Reedy T. The Application of Multistate Markov Models to HIV disease progression, Master thesis, University of KwaZulu-Natal 2011.

Bwayo J, Nagelkerke N, Moses S, et al. Comparison of the declines in CD4 counts in HIV-1-seropositive female sex workers and women from the general population in Nairobi, Kenya. J Acquired Immune Deficiciency Syndromes Human Retrovirol 1995; 10: 457-61. http://dx.doi.org/10.1097/00042560-199512000-00009 DOI: https://doi.org/10.1097/00042560-199512000-00009

Jackson CH. Multistate Models for Panel Data: The msm Package for R. J Statist Software 2011; 38(8). DOI: https://doi.org/10.18637/jss.v038.i08

Kalbfleisch JD, Lawless JF. The analysis of panel data under a Markov assumption. J Am Statist Assoc 1985; 80: 863-71. http://dx.doi.org/10.1080/01621459.1985.10478195 DOI: https://doi.org/10.1080/01621459.1985.10478195

Kay R. A Markov model for analysing cancer markers and disease states in survival studies. Biometrics 1986; 42: 855-65. http://dx.doi.org/10.2307/2530699 DOI: https://doi.org/10.2307/2530699

Cox DR, Miller HD. Theory of Stochastic Processes. London: Chapman and Hall 1965.

Marshall G, Jones RH. Multistate markov models and diabetic retinopathy. Statist Med 1995; 14. DOI: https://doi.org/10.1002/sim.4780141804

Bachani D, Garg R, Rewari BB, et al. Two year treatment outcomes of patients enrolled in india’s national first-line antiretroviral therapy programme. Natl Med J India 2010; 23(1): 7-12.

Kumarasamy N, Solomon S, Chaguturu SK, et al. The safety, tolerability and effectiveness of generic antiviral drug regimens for HIV infected patients in south India. AIDS 2003; 17: 2267-69. http://dx.doi.org/10.1097/00002030-200310170-00019 DOI: https://doi.org/10.1097/00002030-200310170-00019

Pujari S, Dravid A, Gupte N, Joshi K, Bele V. Effectiveness and safety of generic fixed dose combination of tenofovir/ emitricitabine/ efavirenz in HIV 1 infected patients in western India. Medscape J Med 2008; 10: 196. DOI: https://doi.org/10.1186/1758-2652-10-8-196

Sharma A, Wanchu A, Bansal V, Singh S, Varma S. Improvements in CD4 counts in HIV positive patients treated with HAART and antitubercular drugs: An observational study from north India. Indian J Pathol Microbiol 2007; 50: 905-907.

Ghate M, Deshpande S, Tripathy S, et al. Mortality in HIV infected individuals in Pune, India. Indian J Med Res 2011; 133: 414-20.

Touloumi G, Hatzakis A, Rosenberg PS, O’Brien TR, Goedert JJ. Effects of age at seroconversion and baseline HIV RNA level on the loss of CD4 cells among persons with hemophilia. AIDS 1998; 12(13): 1691-97. http://dx.doi.org/10.1097/00002030-199813000-00018 DOI: https://doi.org/10.1097/00002030-199813000-00018

Darby SC, Ewart DW, Giangrande PLF, Spooner RJD, Rizza CR. Importance of age at infection with HIV-1 for survival and development of AIDS in UK hemophilia population. Lancet 1996; 347(9015): 1573-79. http://dx.doi.org/10.1016/S0140-6736(96)91073-9 DOI: https://doi.org/10.1016/S0140-6736(96)91073-9

Geskus RB, Meyer L, Hubert JB, et al. Causal pathways of the effects of age and the CCR5-Delta32, CCR2-641 and SDF-13’ A alleles on AIDS development. J AIDS 2005; 39(3): 321-26. http://dx.doi.org/10.1097/01.qai.0000142017.25897.06 DOI: https://doi.org/10.1097/01.qai.0000142017.25897.06

CASCADE collaboration, Porter K, Babiker AG, et al. Determinants of survival following HIV1 seroconversion after the introduction of HAART. Lancet 2003; 362(9392): 1267-74. http://dx.doi.org/10.1016/S0140-6736(03)14570-9 DOI: https://doi.org/10.1016/S0140-6736(03)14570-9

Sterling TR, Vlahov D, Astemborski J, Hoover DR, Margolick JB, Quinn TC. Initial plasma HIV1 RNA levels and progression to AIDS in women and men. N Engl J Med 2001; 344(10): 720-25. http://dx.doi.org/10.1056/NEJM200103083441003 DOI: https://doi.org/10.1056/NEJM200103083441003

Farzadegan H, Hoover DR, Astemborski J, et al. Sex differences in HIV1 viral load and progression to AIDS. Lancet 1998; 352: 1510-14. http://dx.doi.org/10.1016/S0140-6736(98)02372-1 DOI: https://doi.org/10.1016/S0140-6736(98)02372-1

Donnelly CA, Bartley LM, Ghani AC, et al. Gender differences in HIV1 RNA viral loads. HIV Med 2005; 6(3): 170-78. http://dx.doi.org/10.1111/j.1468-1293.2005.00285.x DOI: https://doi.org/10.1111/j.1468-1293.2005.00285.x

Sterling TR, Chaisson RE, Moore RD. HIV1 RNA, CD4 T-lymphocytes, and clinical response to highly active antiretroviral therapy. AIDS 2001; 15(17): 2251-57. http://dx.doi.org/10.1097/00002030-200111230-00006 DOI: https://doi.org/10.1097/00002030-200111230-00006

Carre N, Deveau C, Belenger F, et al. Effect of age and exposure group on the onset of AIDS in heterosexual and homosexual HIV infected patients. AIDS 1994; 8(6): 797-802. http://dx.doi.org/10.1097/00002030-199406000-00012 DOI: https://doi.org/10.1097/00002030-199406000-00012

Prins M, Veugelers PJ. Comparison of progression and non progression in injecting drug users and homosexual men with documented dates of HIV 1 seroconversion. AIDS 1997; 11(5): 621-31. http://dx.doi.org/10.1097/00002030-199705000-00010 DOI: https://doi.org/10.1097/00002030-199705000-00010




How to Cite

Grover, G., Gadpayle, A. K., Swain, P. K., & Deka, B. . (2013). A Multistate Markov Model Based on CD4 Cell Count for HIV/AIDS Patients on Antiretroviral Therapy (ART). International Journal of Statistics in Medical Research, 2(2), 144–151. https://doi.org/10.6000/1929-6029.2013.02.02.08



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