Abstract
Robins (1993, 1994, 1997, 1998ab) has developed a set of causal or counterfactual models, the structural nested models (SNMs). This paper describes an alternative new class of causal models — the (non-nested) marginal structural models (MSMs). We will then describe a class of semiparametric estimators for the parameters of these new models under a sequential randomization (i.e., ignorability) assumption. We then compare the strengths and weaknesses of MSMs versus SNMs for causal inference from complex longitudinal data with time-dependent treatments and confounders. Our results provide an extension to continuous treatments of propensity score estimators of an average treatment effect.
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References
Chamberlain, G., 1987, Asymptotic Efficiency in Estimation with Conditional Moment Restrictions, Journal of Econometrics, 34, 305–324.
Chamberlain, G., 1988, Efficiency bounds for semiparametric regression, Technical Report, Department of Statistics, University of Wisconsin.
Gill, R.D., Van Der Laan, M.J., and Robins, J.M., 1997, Coarsening at random: characterizations, conjectures and counterexamples, Proceedings of the First Seattle Symposium on Survival Analysis, 255–294.
Gill, R.D. and Robins, J.M., 1999, Causal inference from complex longitudinal data: The continuous case, Unpublished manuscript.
Heitjan, D.F., and Rubin, D.B., 1991, Ignorability and Coarse Data, The Annals of Statistics, 19, 2244–2253.
Holland, P., 1986, Statistics and Causal Inference, Journal of the American Statistical Association, 81, 945–961.
Lewis, D., 1973, Causation, Journal of Philosophy, 70, 556–567.
Liang, K-Y., and Zeger, S.L., 1986, Longitudinal Data Analysis Using Generalized Linear Model, Biometrika, 73, 13–22.
Lin, D.Y., Wei, L-J., 1989, The robust inference for the Cox proportional hazards model, Journal of the American Statistical Association, 84, 1074–1078.
Newey, W.K. and Mcfadden, D., 1993, Estimation in large samples, Handbook of Econometrics, Vol. 4, Eds. McFadden, D., Engler, R. Amsterdam: North Holland.
Pearl J., 1995, Causal Diagrams for Empirical Research. Biometrika, 82, 669–688.
Robins J.M., 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 Modeling, 7, 1393–1512.
Robins J.M. —, 1987, Addendum to “A new approach to causal inference in mortality studies with sustained exposure periods-Application to control of the healthy worker survivor effect”, Computers and Mathematics with Applications, 14, 923–945.
Robins J.M. —, 1993, Analytic methods for HIV treatment and cofactor effects, AIDS Epidemiology — Methodological Issues, Eds. Ostrow DG; Kessler R. Plenum Publishing, New York, 213–290.
Robins J.M. —, 1994, Correcting for non-compliance in randomized trials using structural nested mean models, Communications in Statistics, 23, 2379–2412.
Robins J.M. —, 1997, Causal inference from complex longitudinal data, In: Latent Variable Modeling and Applications to Causality, Lecture Notes in Statistics (120), M. Berkane, Editor. NY: Springer Verlag, 69–117.
Robins J.M. —, 1998a, Testing and estimation of direct effects by reparameterizing directed acyclic graphs with structural nested models, Computation, Causation, and Discovery, Eds. C. Glymour and G. Cooper, Cambridge, MA: The MIT Press, Forthcoming.
Robins J.M. —, 1998b, Structural nested failure time models, Survival Analysis, P.K. Andersen and N. Keiding, Section Editors, The Encyclopedia of Biostatistics, P. Armitage and T. Colton, Editors, Chichester, UK: John Wiley & Sons, 4372–4389.
Robins J.M. —, 1998c, Correction for non-compliance in equivalence trials, Statistics in Medicine, 17, 269–302.
Robins J.M. —, 1998d, Marginal structural models, 1997 Proceedings of the American Statistical Association, Section on Bayesian Statistical Science, 1–10.
Robins, J.M., and Greenland S., 1989, The probability of causation under a stochastic model for individual risk, Biometrics, 45, 1125–1138.
Robins, J.M., and Greenland S. —, 1994, Adjusting for differential rates of PCP prophylaxis in high-versus lowdose AZT treatment arms in an AIDS randomized trial, Journal of the American Statistical Association, 89, 737–749.
Robins, J.M., Rotnitzky, A., Zhao LP., 1994, Estimation of regression coefficients when some regressors are not always observed, Journal of the American Statistical Association, 89, 846–866.
Robins, J.M. and Ritov, Y., 1997, A curse of dimensionality appropriate (CODA) asymptotic theory for semiparametric models, Statistics in Medicine, 16, 285–319.
Robins, J.M., Rotnitzky, A., and Scharfstein, D.O., 1999, Sensitivity analysis for selection bias and unmeasured confounding in missing data and causal inference models, In: Statistical Models in Epidemiology, Halloran E., Editor, Springer-Verlag, Forthcoming.
Robins, J.M., Rotnitzky, A., and Zhao LP., 1994, Estimation of regression coefficients when some regressors are not always observed, Journal of the American Statistical Association, 89, 846–866.
Robins, J.M., and Tsiatis A.A., 1992, Semiparametric estimation of an accelerated failure time model with time-dependent covariates, Biometrika, 79, 311–319.
Robins, J.M. and Wasserman L., 1997, Estimation of Effects of Sequential Treatments by Reparameterizing Directed Acyclic Graphs, Proceedings of the Thirteenth Conference on Uncertainty in Artificial Intelligence, Providence Rhode Island, August 1-3, 1997, Dan Geiger and Prakash Shenoy (Eds.), Morgan Kaufmann, San Francisco, 409–420.
Rosenbaum, P.R. and Rubin, D.B., 1983, The Central Role of the Propensity Score in Observational Studies for Causal Effects, Biometrika, 70, 41–55.
Rubin, D.B., 1976, Inference and Missing Data, Biometrika, 63, 581–592.
Rubin, D.B. —, 1978, Bayesian Inference for Causal Effects: The Role of Randomization, The Annals of Statistics, 6, 34–58.
Sasieni, P., 1992, Information bounds for the conditional hazard ratio in a nested family of regression models, Journal of the Royal Statistical Society, Series B, 54, 617–635.
P. Spirtes, C. Glymour, and R. Scheines, 1993, Causation, Prediction, and Search, Lecture Notes in Statistics, 81, New York: Springer-Verlag.
Van Der Vaart, A.W., 1991, On differentiate functional, Annals of Statistics, 19, 178–204.
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Robins, J.M. (2000). Marginal Structural Models versus Structural nested Models as Tools for Causal inference. In: Halloran, M.E., Berry, D. (eds) Statistical Models in Epidemiology, the Environment, and Clinical Trials. The IMA Volumes in Mathematics and its Applications, vol 116. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1284-3_2
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DOI: https://doi.org/10.1007/978-1-4612-1284-3_2
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