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Biostatistics (2004), 5, 3, pp. 361-380
Biostatistics Vol. 5 No. 3 © Oxford University Press 2004; all rights reserved.

Analysis of longitudinal marginal structural models

Jenny Bryan

Statistics Department and Biotechnology Lab., University of British Columbia, 333-6356 Agricultural Road, Vancouver, BC V6T 1Z2, Canada
jenny{at}stat.ubc.ca

Zhuo Yu and Mark J. van der Laan

Division of Biostatistics, University of California, Earl Warren Hall 7360, Berkeley, CA 94720-7360 USA

In this article we construct and study estimators of the causal effect of a time-dependent treatment on survival in longitudinal studies. We employ a particular marginal structural model (MSM), proposed by Robins (2000; Statistical models in Epidemiology, the Environment, and Clinical Trials, 95–133), and follow a general methodology for constructing estimating functions in censored data models. The inverse probability of treatment weighted (IPTW) estimator of Robins et al. (2000; Epidemiology, 11, 550–560) is used as an initial estimator and forms the basis for an improved, one-step estimator that is consistent and asymptotically linear when the treatment mechanism is consistently estimated. We extend these methods to handle informative censoring. The proposed methodology is employed to estimate the causal effect of exercise on mortality in a longitudinal study of seniors in Sonoma County. A simulation study demonstrates the bias of naive estimators in the presence of time-dependent confounders and also shows the efficiency gain of the IPTW estimator, even in the absence such confounding. The efficiency gain of the improved, one-step estimator is demonstrated through simulation.

Keywords: Causal inference; Counterfactual; Estimating function; IPTW estimator; Marginal structural model; One-step estimator; Propensity score; Sequential randomization


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