Statistical Science

Structural Nested Models and G-estimation: The Partially Realized Promise

Stijn Vansteelandt and Marshall Joffe

Full-text: Open access

Abstract

Structural nested models (SNMs) and the associated method of G-estimation were first proposed by James Robins over two decades ago as approaches to modeling and estimating the joint effects of a sequence of treatments or exposures. The models and estimation methods have since been extended to dealing with a broader series of problems, and have considerable advantages over the other methods developed for estimating such joint effects. Despite these advantages, the application of these methods in applied research has been relatively infrequent; we view this as unfortunate. To remedy this, we provide an overview of the models and estimation methods as developed, primarily by Robins, over the years. We provide insight into their advantages over other methods, and consider some possible reasons for failure of the methods to be more broadly adopted, as well as possible remedies. Finally, we consider several extensions of the standard models and estimation methods.

Article information

Source
Statist. Sci. Volume 29, Number 4 (2014), 707-731.

Dates
First available in Project Euclid: 15 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.ss/1421330555

Digital Object Identifier
doi:10.1214/14-STS493

Mathematical Reviews number (MathSciNet)
MR3300367

Zentralblatt MATH identifier
1331.62208

Keywords
Causal effect confounding direct effect instrumental variable mediation time-varying confounding

Citation

Vansteelandt, Stijn; Joffe, Marshall. Structural Nested Models and G-estimation: The Partially Realized Promise. Statist. Sci. 29 (2014), no. 4, 707--731. doi:10.1214/14-STS493. https://projecteuclid.org/euclid.ss/1421330555


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References

  • Achy-Brou, A. C., Frangakis, C. E. and Griswold, M. (2010). Estimating treatment effects of longitudinal designs using regression models on propensity scores. Biometrics 66 824–833.
  • Almirall, D., Ten Have, T. and Murphy, S. A. (2010). Structural nested mean models for assessing time-varying effect moderation. Biometrics 66 131–139.
  • Bowden, J. and Vansteelandt, S. (2011). Mendelian randomization analysis of case-control data using structural mean models. Stat. Med. 30 678–694.
  • Cain, L. E., Logan, R., Robins, J. M., Sterne, J. A. C., Sabin, C., Bansi, L., Justice, A., Goulet, J., van Sighem, A., de Wolf, F., Bucher, H. C., von Wyl, V., Esteve, A., Casabona, J., del Amo, J., Moreno, S., Seng, R., Meyer, L., Perez-Hoyos, S., Muga, R., Lodi, S., Lanoy, E., Costagliola, D. and Hernan, M. A. (2011). When to initiate combined antiretroviral therapy to reduce mortality and AIDS-defining illness in HIV-infected persons in developed countries: An observational study. Ann. Intern. Med. 154 509–W173.
  • Chamberlain, G. (1987). Asymptotic efficiency in estimation with conditional moment restrictions. J. Econometrics 34 305–334.
  • Frangakis, C. E. and Rubin, D. B. (2002). Principal stratification in causal inference. Biometrics 58 21–29.
  • Goetgeluk, S., Vansteelandt, S. and Goetghebeur, E. (2008). Estimation of controlled direct effects. J. R. Stat. Soc. Ser. B Stat. Methodol. 70 1049–1066.
  • Greenland, S. and Robins, J. M. (1986). Identifiability, exchangeability, and epidemiological confounding. Int. J. Epidemiol. 15 412–418.
  • Greenland, S., Robins, J. and Pearl, J. (1999). Confounding and collapsibility in causal inference. Statist. Sci. 14 29–46.
  • Henderson, R., Ansell, P. and Alshibani, D. (2010). Regret-regression for optimal dynamic treatment regimes. Biometrics 66 1192–1201.
  • Hernán, M. A. (2010). The hazards of hazard ratios. Epidemiology 21 13–15.
  • Hernán, M. A. and Robins, J. M. (2006). Instruments for causal inference: An epidemiologist’s dream? Epidemiology 17 360–372.
  • Joffe, M. M., Small, D. and Hsu, C.-Y. (2007). Defining and estimating intervention effects for groups that will develop an auxiliary outcome. Statist. Sci. 22 74–97.
  • Joffe, M. M., Yang, W. P. and Feldman, H. I. (2010). Selective ignorability assumptions in causal inference. Int. J. Biostat. 6 Art. 11, 25.
  • Joffe, M. M., Yang, W. P. and Feldman, H. (2012). G-estimation and artificial censoring: Problems, challenges, and applications. Biometrics 68 275–286.
  • Mark, S. D. and Robins, J. M. (1993). A method for the analysis of randomized trials with compliance information: An application to the multiple risk factor intervention trial. Contr. Clin. Trials 14 79–97.
  • Martinussen, T., Vansteelandt, S., Gerster, M. and von Bornemann Hjelmborg, J. (2011). Estimation of direct effects for survival data by using the Aalen additive hazards model. J. R. Stat. Soc. Ser. B Stat. Methodol. 73 773–788.
  • Murphy, S. A. (2003). Optimal dynamic treatment regimes. J. R. Stat. Soc. Ser. B Stat. Methodol. 65 331–366.
  • Newey, W. K. (1990). Semiparametric efficiency bounds. J. Appl. Econometrics 5 99–135.
  • Okui, R., Small, D. S., Tan, Z. and Robins, J. M. (2012). Doubly robust instrumental variable regression. Statist. Sinica 22 173–205.
  • Pearl, J. (1995). Causal diagrams for empirical research. Biometrika 82 669–710.
  • Pearl, J. (2001). Direct and indirect effects. In Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence 411–420. Morgan Kaufmann, San Francisco, CA.
  • Picciotto, S., Hernán, M. A., Page, J. H., Young, J. G. and Robins, J. M. (2012). Structural nested cumulative failure time models to estimate the effects of interventions. J. Amer. Statist. Assoc. 107 886–900.
  • 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 models in medicine: Diseases and epidemics. Part 2. Math. Modelling 7 1393–1512.
  • Robins, J. M. (1989). The analysis of randomized and non-randomized AIDS treatment trials using a new approach to causal inference in longitudinal studies. In Health Service Research Methodology: A Focus on AIDS (L. Sechrest, H. Freeman and A. Mulley, eds.) 113–159. U.S. Public Health Service, National Center for Health Services Research, Washington, DC.
  • Robins, J. (1992). Estimation of the time-dependent accelerated failure time model in the presence of confounding factors. Biometrika 79 321–334.
  • Robins, J. M. (1994). Correcting for non-compliance in randomized trials using structural nested mean models. Comm. Statist. Theory Methods 23 2379–2412.
  • Robins, J. M. (1997). Causal inference from complex longitudinal data. In Latent Variable Modeling and Applications to Causality (Los Angeles, CA, 1994). Lecture Notes in Statist. 120 69–117. Springer, New York.
  • Robins, J. M. (1999). Testing and estimation of direct effects by reparameterizing directed acyclic graphs with structural nested models. In Computation, Causation, and Discovery (C. Glymour and G. Cooper, eds.) 349–405. AAAI Press, Menlo Park, CA.
  • Robins, J. M. (2000). Marginal structural models versus structural nested models as tools for causal inference. In Statistical Models in Epidemiology, the Environment, and Clinical Trials (Minneapolis, MN, 1997) (M. Halloran and D. Berry, eds.). IMA Vol. Math. Appl. 116 95–133. Springer, New York.
  • Robins, J. M. (2004). Optimal structural nested models for optimal sequential decisions. In Proceedings of the Second Seattle Symposium in Biostatistics. Lecture Notes in Statist. 179 189–326. Springer, New York.
  • Robins, J. M. and Greenland, S. (1992). Identifiability and exchangeability for direct and indirect effects. Epidemiology 3 143–155.
  • Robins, J. M. and Greenland, S. (1994). Adjusting for differential rates of prophylaxis therapy for PCP in high- versus low-dose AZT treatment arms in an AIDS randomized trial. J. Amer. Statist. Assoc. 89 737–749.
  • Robins, J. M. and Hernán, M. A. (2009). Estimation of the causal effects of time-varying exposures. In Longitudinal Data Analysis (G. Fitzmaurice, M. Davidian, G. Verbeke and G. Molenberghs, eds.) 553–599. CRC Press, Boca Raton, FL.
  • Robins, J. M., Hernán, M. A. and Brumback, B. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology 11 550–560.
  • Robins, J. M., Mark, S. D. and Newey, W. K. (1992). Estimating exposure effects by modelling the expectation of exposure conditional on confounders. Biometrics 48 479–495.
  • Robins, J. M. and Ritov, Y. (1997). Toward a curse of dimensionality appropriate (CODA) asymptotic theory for semi-parametric models. Stat. Med. 16 285–319.
  • Robins, J. M. and Rotnitzky, A. (2001). Comment on “Inference for semiparametric models: Some questions and an answer,” by P. J. Bickel and J. Kwon. Statist. Sinica 11 920–936.
  • Robins, J. and Rotnitzky, A. (2004). Estimation of treatment effects in randomised trials with non-compliance and a dichotomous outcome using structural mean models. Biometrika 91 763–783.
  • Robins, J. M., Rotnitzky, A. and Scharfstein, D. O. (2000). Sensitivity analysis for selection bias and unmeasured confounding in missing data and causal inference models. In Statistical Models in Epidemiology, the Environment, and Clinical Trials (Minneapolis, MN, 1997) (M. Halloran and D. Berry, eds.). IMA Vol. Math. Appl. 116 1–94. Springer, New York.
  • Robins, J. M., Rotnitzky, A. and Zhao, L. P. (1994). Estimation of regression coefficients when some regressors are not always observed. J. Amer. Statist. Assoc. 89 846–866.
  • Robins, J. M. and Tsiatis, A. A. (1991). Correcting for noncompliance in randomized trials using rank preserving structural failure time models. Comm. Statist. Theory Methods 20 2609–2631.
  • Robins, J. M. and Wasserman, L. (1997). Estimation of Effects of Sequential Treatments by Reparameterizing Directed Acyclic Graphs. In Proceedings of the Thirteenth Conference on Uncertainty in Artificial Intelligence (D. Geiger and P. Shenoy, eds.) 409–420. Morgan Kaufmann, San Francisco, CA.
  • Robins, J. M., Blevins, D., Ritter, G. and Wulfsohn, M. (1992). G-estimation of the effect of prophylaxis therapy for pneumocystic carinii pneumonia on the survival of AIDS patients. Epidemiology 3 319–336.
  • Rosenbaum, P. R. (1984). The consequences of adjustment for a concomitant variable that has been affected by the treatment. J. Roy. Statist. Soc. Ser. A 147 656–666.
  • Rosenbaum, P. R. and Rubin, D. B. (1984). Reducing bias in observational studies using subclassification on the propensity score. J. Amer. Statist. Assoc. 79 516–524.
  • Rubin, D. B. (1978). Bayesian inference for causal effects: The role of randomization. Ann. Statist. 6 34–58.
  • Stephens, A., Keele, L. and Joffe, M. (2013). Estimating post-treatment effect modification with generalized structural mean models. Submitted.
  • Tchetgen Tchetgen, E. J. (2012). Multiple-robust estimation of an odds ratio interaction. Harvard Univ. Biostatistics working paper series. Working Paper 142. Available at http://biostats.bepress.com/harvardbiostat/paper142.
  • Tchetgen Tchetgen, E. J. and Robins, J. (2010). The semiparametric case-only estimator. Biometrics 66 1138–1144.
  • Tchetgen Tchetgen, E. J., Robins, J. M. and Rotnitzky, A. (2010). On doubly robust estimation in a semiparametric odds ratio model. Biometrika 97 171–180.
  • Tchetgen Tchetgen, E. J. and Rotnitzky, A. (2011). Double-robust estimation of an exposure-outcome odds ratio adjusting for confounding in cohort and case-control studies. Stat. Med. 30 335–347.
  • Tchetgen Tchetgen, E. J. and Shpitser, I. (2014). Estimation of a semiparametric natural direct effect model incorporating baseline covariates. Biometrika 101 849–864.
  • Ten Have, T. R., Joffe, M. M., Lynch, K. G., Brown, G. K., Maisto, S. A. and Beck, A. T. (2007). Causal mediation analyses with rank preserving models. Biometrics 63 926–934.
  • Vansteelandt, S. (2010). Estimation of controlled direct effects on a dichotomous outcome using logistic structural direct effect models. Biometrika 97 921–934.
  • Vansteelandt, S., Bekaert, M. and Claeskens, G. (2012). On model selection and model misspecification in causal inference. Stat. Methods Med. Res. 21 7–30.
  • Vansteelandt, S. and Daniel, R. M. (2014). On regression adjustment for the propensity score. Stat. Med. 33 4053–4072.
  • Vansteelandt, S. and Goetghebeur, E. (2003). Causal inference with generalized structural mean models. J. R. Stat. Soc. Ser. B Stat. Methodol. 65 817–835.
  • Vansteelandt, S., VanderWeele, T., Tchetgen, E. J. and Robins, J. M. (2008a). Semiparametric inference for statistical interactions. J. Amer. Statist. Assoc. 103 1693–1704.
  • Vansteelandt, S., DeMeo, D. L., Lasky-Su, J. et al. (2008b). Testing and estimating gene-environment interactions in family-based association studies. Biometrics 64 458–467, 666.
  • Vansteelandt, S., Bowden, J., Babanezhad, M. and Goetghebeur, E. (2011). On instrumental variables estimation of causal odds ratios. Statist. Sci. 26 403–422.
  • van der Laan, M. J., Hubbard, A. and Jewell, N. P. (2007). Estimation of treatment effects in randomized trials with non-compliance and a dichotomous outcome. J. R. Stat. Soc. Ser. B Stat. Methodol. 69 463–482.
  • van der Laan, M. J. and Petersen, M. L. (2008). Direct effect models. Int. J. Biostat. 4 1–27.
  • Vock, D. M., Tsiatis, A. A., Davidian, M., Laber, E. B., Tsuang, W. M., Finlen Copeland, C. A. and Palmer, S. M. (2013). Assessing the causal effect of organ transplantation on the distribution of residual lifetime. Biometrics 69 820–829.
  • Wei, L. J. (1992). The accelerated failure time model: A useful alternative to the Cox regression model in survival analysis. Stat. Med. 11 1871–1879.
  • Zhang, M., Joffe, M. M. and Small, D. S. (2011). Causal inference for continuous-time processes when covariates are observed only at discrete times. Ann. Statist. 39 131–173.