G-estimation for Accelerated Failure Time Models

  • Kate Tilling
  • Jonathan A. C. Sterne
  • Vanessa Didelez
Chapter

Abstract

In this chapter we examine the problem of time-varying confounding, and one method (structural nested accelerated failure time models, estimated using and also known as g-estimation) which may be used to overcome it. A practical example is given, and the methodology demonstrated. Cautions as to the use of g-estimation are provided, and alternative methods suggested. Much of the material in this chapter has been published as an application to analysis of a longitudinal study (Tilling et al. Am J Epidemiol 155:710–718, 2002) and as a description of the implementation of these methods in standard statistical software (Sterne and Tilling, Stata J 2:164–182, 2002). The material is used here with permission from the Stata Journal and the American Journal of Epidemiology (Oxford University Press and the Society for Epidemiologic Research).

Keywords

Failure Time Unmeasured Confound Past Exposure Accelerate Failure Time Model Introduce Selection Bias 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Amuzu, A., Carson, C., Watt, H. C., Lawlor, D. A., & Ebrahim, S. (2009). Influence of area and individual lifecourse deprivation on health behaviours: Findings from the British Women's Heart and Health Study. European Journal of Cardiovascular Prevention and Rehabilitation, 16(2), 169–173.PubMedCrossRefGoogle Scholar
  2. Ben-Shlomo, Y. (2007). Rising to the challenges and opportunities of life course epidemiology. International Journal of Epidemiology, 36(3), 481–483.PubMedCrossRefGoogle Scholar
  3. Ben-Shlomo, Y., & Kuh, D. (2002). A life course approach to chronic disease epidemiology: Conceptual models, empirical challenges and interdisciplinary perspectives. International Journal of Epidemiology, 31(2), 285–293.PubMedCrossRefGoogle Scholar
  4. Dawid, A. P., & Didelez, V. (2010). Identifying the consequences of dynamic treatment strategies: A decision theoretic overview. Statistics Surveys, 4, 184–231.CrossRefGoogle Scholar
  5. Glymour, M. M., Avendano, M., Haas, S., & Berkman, L. F. (2008). Lifecourse social conditions and racial disparities in incidence of first stroke. Annals of Epidemiology, 18(12), 904–912.PubMedCrossRefGoogle Scholar
  6. Goetgeluk, S., Vansteelandt, S., & Goetghebeur, E. (2008). Estimation of controlled direct effects. Journal of the Royal Statistical Society Series B-Statistical Methodology, 70, 1049–1066.CrossRefGoogle Scholar
  7. Hernan, M. A., Brumback, B., & Robins, J. M. (2000). Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men. Epidemiology, 11(5), 561–570.PubMedCrossRefGoogle Scholar
  8. Hernan, M. A., Brumback, B., & Robins, J. M. (2001). Marginal structural models to estimate the joint causal effect of nonrandomized treatments. Journal of the American Statistical Association, 96(454), 440–448.CrossRefGoogle Scholar
  9. Hernan, M. A., Brumback, B. A., & Robins, J. M. (2002). Estimating the causal effect of zidovudine on CD4 count with a marginal structural model for repeated measures. Statistics in Medicine, 21(12), 1689–1709.PubMedCrossRefGoogle Scholar
  10. Hernan, M. A., Hernandez-Diaz, S., & Robins, J. M. (2004). A structural approach to selection bias. Epidemiology, 15(5), 615–625.PubMedCrossRefGoogle Scholar
  11. Hernan, M. A., Cole, S. R., Margolick, J., Cohen, M., & Robins, J. M. (2005). Structural accelerated failure time models for survival analysis in studies with time-varying treatments. Pharmacoepidemiology and Drug Safety, 14(7), 477–491.PubMedCrossRefGoogle Scholar
  12. Hernan, M. A., Lanoy, E., Costagliola, D., & Robins, J. M. (2006). Comparison of dynamic treatment regimes via inverse probability weighting. Basic & Clinical Pharmacology & Toxicology, 98(3), 237–242.CrossRefGoogle Scholar
  13. Joffe, M. M., Hoover, D. R., Jacobson, L. P., Kingsley, L., Chmiel, J. S., & Visscher, B. R. (1997). Effect of treatment with zidovudine on subsequent incidence of Kaposi’s sarcoma. Clinical Infectious Diseases, 25(5), 1125–1133.PubMedCrossRefGoogle Scholar
  14. Joffe, M. K., Hoover, D. R., Jacobson, L. P., Kingsley, L., Chmiel, J. S., Visscher, B. R., & Robins, J. M. (1998). Estimating the effect of zidovudine on Kaposi’s sarcoma from observational data using a rank preserving structural failure-time model. Statistics in Medicine, 17, 1073–1102.PubMedCrossRefGoogle Scholar
  15. Keiding, N., Filiberti, M., Esbjerg, S., Robins, J. M., & Jacobsen, N. (1999). The graft versus leukemia effect after bone marrow transplantation: A case study using structural nested failure time models. Biometrics, 55(1), 23–28.PubMedCrossRefGoogle Scholar
  16. Korhonen, P. A., Laird, N. M., & Palmgren, J. (1999). Correcting for non-compliance in randomized trials: An application to the ATBC Study. Statistics in Medicine, 18(21), 2879–2897.PubMedCrossRefGoogle Scholar
  17. Little, R. J. A., & Rubin, D. B. (2002). Statistical analysis with missing data (2nd ed.). Hoboken: Wiley.Google Scholar
  18. Lok, J., Gill, R., van der Vaart, A., & Robins, J. (2004). Estimating the causal effect of a time-varying treatment on time-to-event using structural nested failure time models. Statistica Neerlandica, 58(3), 271–295.CrossRefGoogle Scholar
  19. Mark, S. D., & Robins, J. M. (1993). Estimating the causal effect of smoking cessation in the presence of confounding factors using a rank preserving structural failure time model. Statistics in Medicine, 12(17), 1605–1628.PubMedCrossRefGoogle Scholar
  20. Robins, J. (1986). A new approach to causal inference in mortality studies with a sustained exposure period – application to control of the healthy worker survivor effect. Mathematical Modelling, 7(9–12), 1393–1512.CrossRefGoogle Scholar
  21. Robins, J. M. (1992). Estimation of the time-dependent accelerated failure time model in the presence of confounding factors. Biometrika, 79(2), 321–334.CrossRefGoogle Scholar
  22. Robins, J. M. (2004). Optimal structural nested models for optimal sequential decisions. In D. Y. Lin & P. Heagerty (Eds.), Proceedings of the Second Seattle Symposium on Biostatistics (pp. 189–326). New York: Springer.Google Scholar
  23. Robins, J. M. (2008). Causal models for estimating the effects of weight gain on mortality. International Journal of Obesity, 32(Suppl 3), S15–S41.PubMedCrossRefGoogle Scholar
  24. Robins, J. M., Blevins, D., Ritter, G., & Wulfsohn, M. (1992a). G-estimation of the effect of prophylaxis therapy for Pneumocystis carinii pneumonia on the survival of AIDS patients. Epidemiology, 3(4), 319–336.PubMedCrossRefGoogle Scholar
  25. Robins, J. M., Mark, S. D., & Newey, W. K. (1992b). Estimating exposure effects by modelling the expectation of exposure conditional on confounders. Biometrics, 48(2), 479–495.PubMedCrossRefGoogle Scholar
  26. Robins, J. M., Greenland, S., & Hu, F. C. (1999). Estimation of the causal effect of a time-varying exposure on the marginal mean of a repeated binary outcome. Journal of the American Statistical Association, 94(447), 687–700.CrossRefGoogle Scholar
  27. Robins, J. M., Hernan, M. A., & Brumback, B. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology, 11(5), 550–560.PubMedCrossRefGoogle Scholar
  28. Robins, J. M., Hernan, M. A., & Rotnitzky, A. (2007). Effect modification by time-varying covariates. American Journal of Epidemiology, 166(9), 994–1002.PubMedCrossRefGoogle Scholar
  29. Snowden, J. M., Rose, S., & Mortimer, K. M. (2011). Implementation of G-computation on a simulated data set: Demonstration of a causal inference technique. American Journal of Epidemiology, 173(7), 731–738.PubMedCrossRefGoogle Scholar
  30. Stata Corporation. (2007). College Station, Texas.Google Scholar
  31. Sterne, J., & Tilling, K. (2002). G-estimation of causal effects, allowing for time-varying confounding. The Stata Journal, 2(2), 164–182.Google Scholar
  32. Sterne, J. A., Hernan, M. A., Ledergerber, B., Tilling, K., Weber, R., Sendi, P., Rickenbach, M., Robins, J. M., & Egger, M. (2005). Long-term effectiveness of potent antiretroviral therapy in preventing AIDS and death: A prospective cohort study. The Lancet, 366(9483), 378–384.CrossRefGoogle Scholar
  33. Tanaka, Y., Matsuyama, Y., & Ohashi, Y. (2008). Estimation of treatment effect adjusting for treatment changes using the intensity score method: Application to a large primary prevention study for coronary events (MEGA study). Statistics in Medicine, 27(10), 1718–1733.PubMedCrossRefGoogle Scholar
  34. Taubman, S. L., Robins, J. M., Mittleman, M. A., & Hernan, M. A. (2009). Intervening on risk factors for coronary heart disease: An application of the parametric g-formula. International Journal of Epidemiology, 38(6), 1599–1611.PubMedCrossRefGoogle Scholar
  35. Tehranifar, P., Liao, Y., Ferris, J. S., & Terry, M. B. (2009). Life course socioeconomic conditions, passive tobacco exposures and cigarette smoking in a multiethnic birth cohort of U.S. women. Cancer Causes & Control, 20(6), 867–876.CrossRefGoogle Scholar
  36. Tennant, P. W., Gibson, G. J., & Pearce, M. S. (2008). Lifecourse predictors of adult respiratory function: Results from the Newcastle Thousand Families Study. Thorax, 63(9), 823–830.PubMedCrossRefGoogle Scholar
  37. Tilling, K., Sterne, J. A., & Szklo, M. (2002). Estimating the effect of cardiovascular risk factors on all-cause mortality and incidence of coronary heart disease using G-estimation: The atherosclerosis risk in communities study. American Journal of Epidemiology, 155(8), 710–718.PubMedCrossRefGoogle Scholar
  38. Toh, S., & Hernan, M. A. (2008). Causal inference from longitudinal studies with baseline randomization. The International Journal of Biostatistics, 4(1), Article 22.Google Scholar
  39. Vansteelandt, S., Goetgeluk, S., Lutz, S., Waldman, I., Lyon, H., Schadt, E. E., Weiss, S. T., & Lange, C. (2009). On the adjustment for covariates in genetic association analysis: A novel, simple principle to infer direct causal effects. Genetic Epidemiology, 33(5), 394–405.PubMedCrossRefGoogle Scholar
  40. Witteman, J. C., D’Agostino, R. B., Stijnen, T., Kannel, W. B., Cobb, J. C., de Ridder, M. A., Hofman, A., & Robins, J. M. (1998). G-estimation of causal effects: Isolated systolic hypertension and cardiovascular death in the Framingham Heart Study. American Journal of Epidemiology, 148(4), 390–401.PubMedCrossRefGoogle Scholar
  41. Yamaguchi, T., & Ohashi, Y. (2004). Adjusting for differential proportions of second-line treatment in cancer clinical trials. Part I: Structural nested models and marginal structural models to test and estimate treatment arm effects. Statistics in Medicine, 23(13), 1991–2003.PubMedCrossRefGoogle Scholar
  42. Young, J. G., Hernan, M. A., Picciotto, S., & Robins, J. M. (2010). Relation between three classes of structural models for the effect of a time-varying exposure on survival. Lifetime Data Analysis, 16(1), 71–84.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Kate Tilling
    • 1
  • Jonathan A. C. Sterne
    • 1
  • Vanessa Didelez
    • 2
  1. 1.School of Social and Community MedicineUniversity of BristolBristolUK
  2. 2.School of MathematicsUniversity of BristolBristolUK

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