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Comparative Effectiveness of Dynamic Treatment Regimes: An Application of the Parametric G-Formula

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Abstract

Ideally, randomized trials would be used to compare the long-term effectiveness of dynamic treatment regimes on clinically relevant outcomes. However, because randomized trials are not always feasible or timely, we often must rely on observational data to compare dynamic treatment regimes. An example of a dynamic treatment regime is “start combined antiretroviral therapy (cART) within 6 months of CD4 cell count first dropping below x cells/mm3 or diagnosis of an AIDS-defining illness, whichever happens first” where x can take values between 200 and 500. Recently, Cain et al. (Ann. Intern. Med. 154(8):509–515, 2011) used inverse probability (IP) weighting of dynamic marginal structural models to find the x that minimizes 5-year mortality risk under similar dynamic regimes using observational data. Unlike standard methods, IP weighting can appropriately adjust for measured time-varying confounders (e.g., CD4 cell count, viral load) that are affected by prior treatment. Here we describe an alternative method to IP weighting for comparing the effectiveness of dynamic cART regimes: the parametric g-formula. The parametric g-formula naturally handles dynamic regimes and, like IP weighting, can appropriately adjust for measured time-varying confounders. However, estimators based on the parametric g-formula are more efficient than IP weighted estimators. This is often at the expense of more parametric assumptions. Here we describe how to use the parametric g-formula to estimate risk by the end of a user-specified follow-up period under dynamic treatment regimes. We describe an application of this method to answer the “when to start” question using data from the HIV-CAUSAL Collaboration.

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References

  1. Bang H, Robins JM (2005) Doubly robust estimation in missing data and causal inference models. Biometrics 61:692–972

    Article  MathSciNet  Google Scholar 

  2. Cain LE, Robins JM, Lanoy E, Logan R, Costagliola D, Hernán MA (2010) When to start treatment? A systematic approach to the comparison of dynamic regimes using observational data. Int J Biostat 6:18

    Google Scholar 

  3. Cain LE, Logan R, Robins JM, Sterne JA, Sabin C, Bansi L, Justice A, Goulet J, van Sighem A, de Wolf F, Bucher HC, von Wyl V, von Esteve A, Casabona J, del Amo J, Moreno S, Meyer L, Pérez-Hoyos S, Muga R, Lodi S, Lanoy E, Costagliola D, Hernán MA (HIV-CAUSAL Collaboration) (2011) When to initiate combined antiretroviral therapy to reduce rates of mortality and AIDS in HIV-infected individuals in developed countries. Ann Intern Med 154(8):509–515

    Google Scholar 

  4. Cameron DW, Heath-Chiozzi M, Danner S, Cohen C, Kravcik S, Maurath C, Sun E, Henry D, Rode R, Potthoff A, Leonard J (1998) Randomised placebo-controlled trial of ritonavir in advanced HIV-1 disease. The Advanced HIV Disease Ritonavir Study Group. Lancet 351(9102):543–549

    Article  Google Scholar 

  5. CDC (1992) 1993 revised classification system for HIV infection and expanded surveillance case definition for AIDS among adolescents and adults. Morb Mort Wkly Rep 41:1–19

    Google Scholar 

  6. Cole SR, Hernán MA, Robins JM, Anastos K, Chmiel J, Detels R, Ervin C, Feldman J, Greenblatt R, Kingsley L, Lai S, Young M, Cohen M, Muñoz A (2003) Effect of highly active antiretroviral therapy on time to acquired immunodeficiency syndrome or death using marginal structural models. Am J Epidemiol 158(7):687–694

    Article  Google Scholar 

  7. European AIDS Clinical Society (2009) Guidelines: clinical management and treatment of HIV infected adults in Europe. http://www.europeanaidsclinicalsociety.org/guidelinespdf/1_Treatment_of_HIV_Infected_Adults.pdf

  8. Hammer SM, Squires KE, Hughes MD, Grimes JM, Demeter LM, Currier JS, Eron JJ, Feinberg JE, Balfour HH, Deyton LR, Chodakewitz JA, Fischl MA (1997) A controlled trial of two nucleoside analogues plus indinavir in persons with human immunodeficiency virus infection and CD4 cell counts of 200 per cubic millimeter or less. AIDS Clinical Trials Group 320 Study Team. N Engl J Med 337(11):725–733

    Article  Google Scholar 

  9. Hernán MA, Lanoy E, Costagliola D, Robins JM (2006) Comparison of dynamic treatment regimes via inverse probability weighting. Basic Clin Pharmacol Toxicol 98:237–242

    Article  Google Scholar 

  10. van der Laan MJ (2010a) Targeted maximum likelihood based causal inference: Part I. Int J Biostat 6(2):2

    MathSciNet  Google Scholar 

  11. van der Laan MJ (2010b) Targeted maximum likelihood based causal inference: Part II. Int J Biostat 6(2):3

    MathSciNet  Google Scholar 

  12. van der Laan MJ, Petersen ML (2007) Causal effect models for realistic individualized treatment and intention to treat rules. Int J Biostat 3(1):3

    MathSciNet  Google Scholar 

  13. Mocroft A, Phillips AN, Gatell J, Ledergerber B, Fisher M, Clumeck N, Losso M, Lazzarin A, Fatkenheuer G, Lundgren JD (EuroSIDA study group) (2007) Normalisation of CD4 counts in patients with HIV-1 infection and maximum virological suppression who are taking combination antiretroviral therapy: an observational cohort study. Lancet 370(9585):407–413

    Article  Google Scholar 

  14. Murphy SA, van der Laan MJ, Robins JM (2001) Marginal mean models for dynamic regimes. J Am Stat Assoc 96(456):1410–1423

    Article  MATH  Google Scholar 

  15. NIH (2009) Early antiretroviral treatment and/or early isoniazid prophylaxis against tuberculosis in HIV-infected adults (ANRS 12136 TEMPRANO). Vol 2009

  16. Orellana L, Rotnitzky A, Robins JM (2010a) Dynamic regime marginal structural mean models for estimation of optimal dynamic treatment regimes. Part I: Main content. Int J Biostat 6:7

    Google Scholar 

  17. Orellana L, Rotnitzky A, Robins JM (2010b) Dynamic regime marginal structural mean models for estimation of optimal dynamic treatment regimes. Part II: Proofs and additional results. Int J Biostat 6:8

    MathSciNet  Google Scholar 

  18. Panel on Antiretroviral Guidelines for Adults and Adolescents (2009) Guidelines for the use of antiretroviral agents in HIV-1 infected adults and adolescents. http://www.aidsinfo.nih.gov/ContentFiles/AdultandAdolescentGL.pdf

  19. Petersen ML, Deeks SJ, van der Laan MJ (2007) Individualized treatment rules: Generating candidate clinical trials. Stat Med 26(25):4578–4601

    Article  MathSciNet  Google Scholar 

  20. Petersen ML, Porter KE, Gruber S, Wang Y, van der Laan MJ (2010, in print) Diagnosing and responding to violations in the positivity assumption. Stat Methods Med Res

  21. Ray M, Logan R, Sterne J, Hernández-Díaz S, Robins J, Sabin C, Bansi L, van Sighem A, de Wolf F, Costagliola D, Lanoy E, Bucher H, von Wyl V, Esteve A, Casbona J, del Amo J, Moreno S, Justice A, Goulet J, Lodi S, Phillips A, Seng R, Meyer L, Pérez-Hoyos S, Garcia de Olalla P, Hernán MA (The HIV-CAUSAL Collaboration PG) (2010) The effect of combined antiretroviral therapy on the overall mortality of HIV-infected individuals. AIDS 24(1):123–137

    Article  Google Scholar 

  22. Robins JM (1986) A new approach to causal inference in mortality studies with a sustained exposure period: application to the healthy worker survivor effect. Math Model 7:1393–1512 [Errata (1987) in Comput Math Appl 14:917–921. Addendum (1987) in Comput Math Appl 14:923–945. Errata (1987) to addendum in Comput Math Appl 18:477.]

    Article  MathSciNet  MATH  Google Scholar 

  23. Robins JM (1997) Causal inference from complex longitudinal data. In: Berkane M (ed) Latent variable modeling and applications to causality. Lecture notes in statistics, vol 120. Springer, Berlin, pp 69–117

    Chapter  Google Scholar 

  24. Robins JM, Hernán MA (2009) Estimation of the causal effects of time-varying exposures. In: Fitzmaurice G, Davidian M, Verbeke G, Molenberghs G (eds) Advances in longitudinal data analysis. Chapman and Hall/CRC Press, Boca Raton, pp 553–599

    Google Scholar 

  25. Robins JM, Hernán MA, Siebert U (2004) Effects of multiple interventions. In: Ezzati M, Lopez AD, Rodgers A, Murray CJL (eds) Comparative quantification of health risks: global and regional burden of disease attributable to selected major risk factors. World Health Organization, Geneva

    Google Scholar 

  26. Taubman SL, Robins JM, Mittleman MA, Hernán MA (2009) Intervening on risk factors for coronary heart disease: an application of the parametric g-formula. Int J Epidemiol 38(6):1599–1611

    Article  Google Scholar 

  27. Thompson MA, Aberg JA, Cahn P, Montaner JS, Rizzardini G, Telenti A, Gatell JM, Günthard HF, Hammer SM, Hirsch MS, Jacobsen DM, Reiss P, Richman DD, Volberding PA, Yeni P, Schooley RT (2010) Antiretroviral treatment of adult HIV infection: 2010 recommendations of the International AIDS Society-USA panel. J Am Med Assoc 304(3):321–333

    Article  Google Scholar 

  28. World Health Organization (2009) Rapid advice: antiretroviral therapy for HIV infection in adults and adolescents. http://www.who.int/hiv/pub/arv/rapid_advice_art.pdf

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Correspondence to Jessica G. Young.

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Contributors to the HIV-CAUSAL Collaboration (PDF 88.7 KB)

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Young, J.G., Cain, L.E., Robins, J.M. et al. Comparative Effectiveness of Dynamic Treatment Regimes: An Application of the Parametric G-Formula. Stat Biosci 3, 119–143 (2011). https://doi.org/10.1007/s12561-011-9040-7

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