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Application Note

A three-state continuous time Markov chain model for HIV disease burden

, &
Pages 1671-1688 | Received 21 Aug 2017, Accepted 30 Nov 2018, Published online: 10 Dec 2018

References

  • O.O. Aalen, V.T. Farewell, D. de Angelis, N.E. Day, and O. Nöel Gill, A Markov model for HIV disease progression including the effect of HIV diagnosis and treatment: Application to AIDS prediction in England and Wales, Stat. Med. 16 (1997), pp. 2191–2210. doi: 10.1002/(SICI)1097-0258(19971015)16:19<2191::AID-SIM645>3.0.CO;2-5
  • A. Albert, Estimating the infinitesimal generator of a continuous time, finite state Markov process, Ann. Math. Stat. 33 (1962), pp. 727–753. doi: 10.1214/aoms/1177704594
  • A. Alioum, D. Commenges, R. Thiébaut, and F. Dabis, A multistate approach for estimating the incidence of human immunodeficiency virus by using data from a prevalent cohort study, J. R. Stat. Soc. 54 (2005), pp. 739–752. doi: 10.1111/j.1467-9876.2005.00514.x
  • G.J. Beck, Stochastic survival models with competing risks and covariates, Biometrics 35 (1979), pp. 427–438. doi: 10.2307/2530345
  • A. Begun, A. Icks, R. Waldeyer, S. Landwehr, M. Koch, and G. Giani, Identification of a multistate continuous-time nonhomogeneous Markov chain model for patients with decreased renal function, Med. Decis. Making 33 (2013), pp. 298–306. doi: 10.1177/0272989X12466731
  • S. Borg, U. Persson, T. Jess, O.Ø. Thomsen, T. Ljung, L. Riis, and P. Munkholm, A maximum likelihood estimator of a Markov model for disease activity in Crohn's disease and ulcerative colitis for annually aggregated partial observations, Med. Decis. Making 30 (2010), pp. 132–142. doi: 10.1177/0272989X09336141
  • H. Chakraborty, M. Iyer, W.A. Duffus, A.V. Samantapudi, H. Albrecht, and S. Weissman, Disparities in viral load and CD4 count trends among HIV-infected adults in South Carolina, AIDS Patient Care STDS 29 (2015), pp. 26–32. doi: 10.1089/apc.2014.0158
  • H. Chakraborty, P.K. Sen, R.W. Helms, P.L. Vernazza, S.A. Fiscus, J.J. Eron, B.K. Patterson, R.W. Coombs, J.N. Krieger, and M.S. Cohen, Viral burden in genital secretions determines male-to-female sexual transmission of HIV-1: A probabilistic empiric model, Aids 15 (2001), pp. 621–627. doi: 10.1097/00002030-200103300-00012
  • H. Chakraborty, S. Weissman, W.A. Duffus, A. Hossain, A. Varma Samantapudi, M. Iyer, and H. Albrecht, HIV community viral load trends in South Carolina, Int. J. STD AIDS 28 (2017), pp. 265–276. doi: 10.1177/0956462416642349
  • A.T.C. Collaboration, Life expectancy of individuals on combination antiretroviral therapy in high-income countries: A collaborative analysis of 14 cohort studies, Lancet 372 (2008), pp. 293–299. doi: 10.1016/S0140-6736(08)61113-7
  • D.R. Cox and H.D. Miller, The Theory of Stochastic Processes, CRC Press, New York, 1977.
  • Department of Health and Human Services, Guidelines for the use of antiretroviral agents in HIV-1-infected adults and adolescents, 2013. Available at http://aidsinfo.nih.gov/contentfiles/lvguidelines/adultandadolescentgl.pdf [Accessed: 19 May 2015].
  • W.A. Duffus, K. Weis, L. Kettinger, T. Stephens, H. Albrecht, and J.J. Gibson, Risk-based HIV testing in South Carolina health care settings failed to identify the majority of infected individuals, AIDS Patient Care STDS 23 (2009), pp. 339–345. doi: 10.1089/apc.2008.0193
  • M. Egger, M. May, G. Chêne, A.N. Phillips, B. Ledergerber, F. Dabis, D. Costagliola, A.D. Monforte, F. de Wolf, P. Reiss, and J.D. Lundgren, Prognosis of HIV-1-infected patients starting highly active antiretroviral therapy: A collaborative analysis of prospective studies, Lancet 360 (2002), pp. 119–129. doi: 10.1016/S0140-6736(02)09411-4
  • Centers for Disease Control and Prevention (CDC), Monitoring selected national HIV prevention and care objectives by using HIV surveillance data United States, and 6 US dependent areas, 2012, HIV Surveillance Supplemental Report 19, 2014.
  • J.E. Freund, A bivariate extension of the exponential distribution, J. Am. Stat. Assoc. 56 (1961), pp. 971–977. doi: 10.1080/01621459.1961.10482138
  • A.T. Goshu and Z.G. Dessie, Modelling progression of HIV/AIDS disease stages using semi-Markov processes, J. Data Sci. 11 (2013), pp. 269–280.
  • J.C. Hendriks, G.A. Satten, I.M. Longini, H.A. van Druten, P.T.A. Schellekens, R.A. Coutinho, and G.J. van Griensven, Use of immunological markers and continuous-time Markov models to estimate progression of HIV infection in homosexual men, AIDS 10 (1996), pp. 649–656. doi: 10.1097/00002030-199606000-00011
  • R.S. Hogg, M.V. O'Shaughnessy, N. Gataric, B. Yip, K. Craib, M.T. Schechter, and J.S. Montaner, Decline in deaths from AIDS due to new antiretrovirals, Lancet 349 (1997), pp. 1294. doi: 10.1016/S0140-6736(05)62505-6
  • C.H. Jackson, L.D. Sharples, S.G. Thompson, S.W. Duffy, and E. Couto, Multistate Markov models for disease progression with classification error, J. R. Stat. Soc. 52 (2003), pp. 193–209. doi: 10.1111/1467-9884.00351
  • J. Kalbfleisch and J.F. Lawless, The analysis of panel data under a Markov assumption, J. Am. Stat. Assoc. 80 (1985), pp. 863–871. doi: 10.1080/01621459.1985.10478195
  • R. Kay, A Markov model for analysing cancer markers and disease states in survival studies, Biometrics 42 (1986), pp. 855–865. doi: 10.2307/2530699
  • J.P. Klein, J.H. Klotz, and M.R. Grever, A biological marker model for predicting disease transitions, Biometrics (1984), pp. 927–936. doi: 10.2307/2531144
  • S.W. Lagakos, A stochastic model for censored-survival data in the presence of an auxiliary variable, Biometrics 32 (1976), pp. 551–559. doi: 10.2307/2529744
  • S. Lee, J. Ko, X. Tan, I. Patel, R. Balkrishnan, and J. Chang, Markov chain modelling analysis of HIV/AIDS progression: A race-based forecast in the United States, Indian J. Pharm. Sci. 76 (2014), pp. 107.
  • I.M. Longini, W.S. Clark, R.H. Byers, J.W. Ward, W.W. Darrow, G.F. Lemp, and H.W. Hethcote, Statistical analysis of the stages of HIV infection using a Markov model, Stat. Med. 8 (1989), pp. 831–843. doi: 10.1002/sim.4780080708
  • I.M. Longini Jr, W.S. Clark, L.I. Gardner, and J.F. Brundage, The dynamics of CD4+ t-lymphocyte decline in HIV-infected individuals: A Markov modeling approach, J. Acquir. Immune Defic. Syndr. 4 (1991), pp. 1141–1147.
  • E.L. Murphy, A.C. Collier, L.A. Kalish, S.F. Assmann, M.F. Para, T.P. Flanigan, P.N. Kumar, L. Mintz, F.R. Wallach, and G.J. Nemo, Highly active antiretroviral therapy decreases mortality and morbidity in patients with advanced HIV disease, Ann. Intern. Med. 135 (2001), pp. 17–26. doi: 10.7326/0003-4819-135-1-200107030-00005
  • C.L. Smith and G.E. Stein, Viral load as a surrogate end point in HIV disease, Ann. Pharmacother. 36 (2002), pp. 280–287. doi: 10.1345/aph.1A118
  • C. Sommen, A. Alioum, and D. Commenges, A multistate approach for estimating the incidence of human immunodeficiency virus by using HIV and AIDS French surveillance data, Stat. Med. 28 (2009), pp. 1554–1568. doi: 10.1002/sim.3570
  • South Carolina Department of Health and Environmental Control, South Carolina's STD/HIV/AIDS data, 2012. Available at https://scdhec.gov/sites/default/files/docs/Health/docs/stdhiv/data/SR2012.pdf [Accessed: 14 Sep 2018].
  • The Centers for Disease Control and Prevention (CDC), Guidance on community viral load: A family of measures, definitions, and method for calculation, 2011. Available at https://stacks.cdc.gov/view/cdc/28147/cdc_28147_DS1.pdf [Accessed: 14 Sep 2018].
  • S. Wasserman, Analyzing social networks as stochastic processes, J. Am. Stat. Assoc. 75 (1980), pp. 280–294. doi: 10.1080/01621459.1980.10477465
  • K.E. Weis, A.D. Liese, J. Hussey, J.J. Gibson, and W.A. Duffus, Associations of rural residence with timing of HIV diagnosis and stage of disease at diagnosis, South Carolina 2001–2005, J. Rural Health 26 (2010), pp. 105–112. doi: 10.1111/j.1748-0361.2010.00271.x
  • G.H. Weiss and M. Zelen, A semi-Markov model for clinical trials, J. Appl. Probab. 2 (1965), pp. 269–285. doi: 10.2307/3212194
  • S. Weissman, W.A. Duffus, M. Iyer, H. Chakraborty, A.V. Samantapudi, and H. Albrecht, Rural-urban differences in HIV viral loads and progression to AIDS among new HIV cases, South. Med. J. 108 (2015), pp. 180–188. doi: 10.14423/SMJ.0000000000000255
  • World Health Organization (WHO), Global health observatory (GHO) data: HIV/AIDS – size of the epidemic, 2018. Available at http://www.who.int/gho/hiv/epidemic_status/en/ [Accessed: 14 Sep 2018].

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