Skip to main content

G-computation: Parametric Estimation of Optimal DTRs

  • Chapter
  • First Online:
Statistical Methods for Dynamic Treatment Regimes

Part of the book series: Statistics for Biology and Health ((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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 119.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • 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 

  • 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 

  • 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 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • Arjas, E., & Parner, J. (2004). Causal reasoning from longitudinal data. Scandinavian Journal of Statistics, 31, 171–187.

    Article  MathSciNet  MATH  Google Scholar 

  • Arjas, E., & Saarela, O. (2010). Optimal dynamic regimes: Presenting a case for predictive inference. The International Journal of Biostatistics, 6.

    Google Scholar 

  • Bembom, O., & Van der Laan, M. J. (2007). Statistical methods for analyzing sequentially randomized trials. Journal of the National Cancer Institute 99, 1577–1582.

    Article  Google Scholar 

  • Carlin, B. P., Kadane, J. B., & Gelfand, A. E. (1998). Approaches for optimal sequential decision analysis in clinical trials. Biometrics 54, 964–975.

    Article  MATH  Google Scholar 

  • 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 

  • 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.

    MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Davison, A. C., & Hinkley, D. V. (1997). Bootstrap methods and their application. Cambridge, UK: Cambridge University Press.

    Book  MATH  Google Scholar 

  • Dawson, R., & Lavori, P. W. (2010). Sample size calculations for evaluating treatment policies in multi-stage designs. Clinical Trials 7, 643–652.

    Article  Google Scholar 

  • Donoho, D. L., & Johnstone, I. M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika 81, 425–455.

    Article  MathSciNet  MATH  Google Scholar 

  • Huang, X., & Ning, J. (2012). Analysis of multi-stage treatments for recurrent diseases. Statistics in Medicine 31, 2805–2821.

    Article  MathSciNet  Google Scholar 

  • Kearns, M., Mansour, Y., & Ng, A.Y. (2000). Approximate planning in large POMDPs via reusable trajectories (Vol. 12). MIT.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • Lavori, P. W., & Dawson, R. (2004). Dynamic treatment regimes: Practical design considerations. Clinical Trials 1, 9–20.

    Article  Google Scholar 

  • Lavori, P. W., & Dawson, R. (2008). Adaptive treatment strategies in chronic disease. Annual Review of Medicine 59, 443–453.

    Article  Google Scholar 

  • Leeb, H., & Pötscher, B. M. (2005). Model selection and inference: Facts and fiction. Econometric Theory 21, 21–59.

    Article  MathSciNet  MATH  Google Scholar 

  • Little, R. J. A., & Rubin, D. B. (2002). Statistical analysis with missing data (2nd ed.). New York: Wiley.

    MATH  Google Scholar 

  • 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 

  • Moodie, E. E. M., Dean, N., & Sun, Y. R. (2013). Q-learning: Flexible learning about useful utilities. Statistics in Biosciences, (in press).

    Google Scholar 

  • 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 

  • 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.

    Article  MathSciNet  Google Scholar 

  • Robins, J. M. (1994). Correcting for non-compliance in randomized trials using structural nested mean models. Communications in Statistics 23, 2379–2412.

    Article  MathSciNet  MATH  Google Scholar 

  • 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 

  • Robins, J. M., Hernán, M. A., & Brumback, B. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology 11, 550–560.

    Article  Google Scholar 

  • 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 

  • 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 

  • Saarela, O., Stephens, D. A., & Moodie, E. E. M. (2013b). The role of exchangeability in causal inference (submitted).

    Google Scholar 

  • 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 

  • 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.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B 58, 267–288.

    MathSciNet  MATH  Google Scholar 

  • Watkins, C. J. C. H. (1989). Learning from delayed rewards (Dissertation, Cambridge University).

    Google Scholar 

  • WHO (1997). The World Health Report 1997: Conquering suffering, enriching humanity. Geneva: The World Health Organization.

    Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang, T. (2004). Statistical behavior and consistency of classification methods based on convex risk minimization. Annals of Statistics 32, 56–85.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Chakraborty, B., Moodie, E.E.M. (2013). G-computation: Parametric Estimation of Optimal DTRs. In: Statistical Methods for Dynamic Treatment Regimes. Statistics for Biology and Health. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7428-9_6

Download citation

Publish with us

Policies and ethics