Advertisement

G-computation: Parametric Estimation of Optimal DTRs

  • Bibhas Chakraborty
  • Erica E. M. Moodie
Chapter
Part of the Statistics for Biology and Health book series (SBH)

Abstract

In this chapter, we present the fully parametric estimation approach of G-computation, in both frequentist and Bayesian settings. The method is illustrated using an analysis of the Promotion of Breastfeeding Intervention Trial.

Keywords

Posterior Predictive Distribution Hypothetical Population Marginal Structural Model Counterfactual Outcome Counterfactual Distribution 
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. Abbring, J. J., & Heckman, J. J. (2007). Econometric evaluation of social programs, part III: Distributional treatment effects, dynamic treatment effects, dynamic discrete choice, and general equilibrium policy evaluation. In J. J. Heckman & E. E. Leamer (Eds.), Handbook of econometrics (Vol. 6, Part B). Amsterdam: Elsevier.Google Scholar
  2. Anderson, J. W., Johnstone, B. M., & Remley, D. T. (1999). Breast-feeding and cognitive development: A meta-analysis. American Journal of Clinical Nutrition, 70, 525–535.Google Scholar
  3. Arjas, E. (2012). Causal inference from observational data: A Bayesian predictive approach. In C. Berzuini, A. P. Dawid, & L. Bernardinelli (Eds.), Causality: Statistical perspectives and applications (pp. 71–84). Chichester, West Sussex, United Kindom.Google Scholar
  4. Arjas, E., & Andreev, A. (2000). Predictive inference, causal reasoning, and model assessment in nonparametric Bayesian analysis: A case study. Lifetime Data Analysis, 6, 187–205.MathSciNetMATHCrossRefGoogle Scholar
  5. Arjas, E., & Parner, J. (2004). Causal reasoning from longitudinal data. Scandinavian Journal of Statistics, 31, 171–187.MathSciNetMATHCrossRefGoogle Scholar
  6. Arjas, E., & Saarela, O. (2010). Optimal dynamic regimes: Presenting a case for predictive inference. The International Journal of Biostatistics, 6.Google Scholar
  7. Bembom, O., & Van der Laan, M. J. (2007). Statistical methods for analyzing sequentially randomized trials. Journal of the National Cancer Institute 99, 1577–1582.CrossRefGoogle Scholar
  8. Carlin, B. P., Kadane, J. B., & Gelfand, A. E. (1998). Approaches for optimal sequential decision analysis in clinical trials. Biometrics 54, 964–975.MATHCrossRefGoogle Scholar
  9. Chakraborty, B. (2009). A study of non-regularity in dynamic treatment regimes and some design considerations for multicomponent interventions (Dissertation, University of Michigan, 2009).Google Scholar
  10. Cheung, K. Y., Lee, S. M. S., & Young, G. A. (2005). Iterating the m out of n bootstrap in nonregular smooth function models. Statistica Sinica 15, 945–967.MathSciNetMATHGoogle Scholar
  11. Daniel, R. M., Cousens, S. N., De Stavola, B. L., Kenwood, M. G., & Sterne, J. A. C. (2013). Methods for dealing with time-dependent confounding. Statistics in Medicine, 32 1584–1618.CrossRefGoogle Scholar
  12. Davison, A. C., & Hinkley, D. V. (1997). Bootstrap methods and their application. Cambridge, UK: Cambridge University Press.MATHCrossRefGoogle Scholar
  13. Dawson, R., & Lavori, P. W. (2010). Sample size calculations for evaluating treatment policies in multi-stage designs. Clinical Trials 7, 643–652.CrossRefGoogle Scholar
  14. Donoho, D. L., & Johnstone, I. M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika 81, 425–455.MathSciNetMATHCrossRefGoogle Scholar
  15. Huang, X., & Ning, J. (2012). Analysis of multi-stage treatments for recurrent diseases. Statistics in Medicine 31, 2805–2821.MathSciNetCrossRefGoogle Scholar
  16. Kearns, M., Mansour, Y., & Ng, A.Y. (2000). Approximate planning in large POMDPs via reusable trajectories (Vol. 12). MIT.Google Scholar
  17. Kramer, M. S., Aboud, F., Miranova, E., Vanilovich, I., Platt, R., Matush, L., Igumnov, S., Fombonne, E., Bogdanovich, N., Ducruet, T., Collet, J., Chalmers, B., Hodnett, E., Davidovsky, S., Skugarevsky, O., Trofimovich, O., Kozlova, L., & Shapiro, S. (2008). Breastfeeding and child cognitive development: New evidence from a large randomized trial. Archives of General Psychiatry65, 578–584.CrossRefGoogle Scholar
  18. Laber, E. B., & Murphy, S. A. (2011). Adaptive confidence intervals for the test error in classification. Journal of the American Statistical Association 106, 904–913.MathSciNetMATHCrossRefGoogle Scholar
  19. Lavori, P. W., & Dawson, R. (2004). Dynamic treatment regimes: Practical design considerations. Clinical Trials 1, 9–20.CrossRefGoogle Scholar
  20. Lavori, P. W., & Dawson, R. (2008). Adaptive treatment strategies in chronic disease. Annual Review of Medicine 59, 443–453.CrossRefGoogle Scholar
  21. Leeb, H., & Pötscher, B. M. (2005). Model selection and inference: Facts and fiction. Econometric Theory 21, 21–59.MathSciNetMATHCrossRefGoogle Scholar
  22. Little, R. J. A., & Rubin, D. B. (2002). Statistical analysis with missing data (2nd ed.). New York: Wiley.MATHGoogle Scholar
  23. Lizotte, D., Bowling, M., & Murphy, S. A. (2010). Efficient reinforcement learning with multiple reward functions for randomized clinical trial analysis. In Twenty-seventh international conference on machine learning (ICML), Haifa (pp. 695–702). Omnipress.Google Scholar
  24. Moodie, E. E. M., Dean, N., & Sun, Y. R. (2013). Q-learning: Flexible learning about useful utilities. Statistics in Biosciences, (in press).Google Scholar
  25. Neugebauer, R., Silverberg, M. J., & Van der Laan, M. J. (2010). Observational study and individualized antiretroviral therapy initiation rules for reducing cancer incidence in HIV-infected patients (Technical report). U.C. Berkeley Division of Biostatistics Working Paper Series.Google Scholar
  26. Petersen, M. L., Deeks, S. G., & Van der Laan, M. J. (2007). Individualized treatment rules: Generating candidate clinical trials. Statistics in Medicine 26, 4578–4601.MathSciNetCrossRefGoogle Scholar
  27. Robins, J. M. (1994). Correcting for non-compliance in randomized trials using structural nested mean models. Communications in Statistics 23, 2379–2412.MathSciNetMATHCrossRefGoogle Scholar
  28. Robins, J. M., & Wasserman, L. (1997). Estimation of effects of sequential treatments by reparameterizing directed acyclic graphs. In D. Geiger & P. Shenoy (Eds.), Proceedings of the thirteenth conference on uncertainty in artificial intelligence (pp. 409–430). Providence.Google Scholar
  29. Robins, J. M., Hernán, M. A., & Brumback, B. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology 11, 550–560.CrossRefGoogle Scholar
  30. Rubin, D. B. (1980). Discussion of “randomized analysis of experimental data: The Fisher randomization test” by D. Basu. Journal of the American Statistical Association 75, 591–593.Google Scholar
  31. Rubin, D. B., & van der Laan, M. J. (2012). Statistical issues and limitations in personalized medicine research with clinical trials. International Journal of Biostatistics 8.Google Scholar
  32. Saarela, O., Stephens, D. A., & Moodie, E. E. M. (2013b). The role of exchangeability in causal inference (submitted).Google Scholar
  33. Schneider, L. S., Tariot, P. N., Lyketsos, C. G., Dagerman, K. S., Davis, K. L., & Davis, S. (2001). National Institute of Mental Health Clinical Antipsychotic Trials of Intervention Effectiveness (CATIE): Alzheimer disease trial methodology. American Journal of Geriatric Psychiatry 9, 346–360.Google Scholar
  34. Thall, P. F., & Wathen, J. K. (2005). Covariate-adjusted adaptive randomization in a sarcoma trial with multi-stage treatments. Statistics in Medicine 24, 1947–1964.MathSciNetCrossRefGoogle Scholar
  35. Thall, P. F., Wooten, L. H., Logothetis, C. J., Millikan, R. E., & Tannir, N. M. (2007a). Bayesian and frequentist two-stage treatment strategies based on sequential failure times subject to interval censoring. Statistics in Medicine 26, 4687–4702.MathSciNetCrossRefGoogle Scholar
  36. Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B 58, 267–288.MathSciNetMATHGoogle Scholar
  37. Watkins, C. J. C. H. (1989). Learning from delayed rewards (Dissertation, Cambridge University).Google Scholar
  38. WHO (1997). The World Health Report 1997: Conquering suffering, enriching humanity. Geneva: The World Health Organization.Google Scholar
  39. Zajonc, T. (2012). Bayesian inference for dynamic treatment regimes: Mobility, equity, and efficiency in student tracking. Journal of the American Statistical Association 107, 80–92.MathSciNetMATHCrossRefGoogle Scholar
  40. Zhang, T. (2004). Statistical behavior and consistency of classification methods based on convex risk minimization. Annals of Statistics 32, 56–85.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Bibhas Chakraborty
    • 1
  • Erica E. M. Moodie
    • 2
  1. 1.Department of BiostatisticsColumbia UniversityNew YorkUSA
  2. 2.Department of Epidemiology, Biostatistics, and Occupational HealthMcGill UniversityMontrealCanada

Personalised recommendations