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December 2001 Causal Inference for Complex Longitudinal Data: The Continuous Case
Richard D. Gill, James M. Robins
Ann. Statist. 29(6): 1785-1811 (December 2001). DOI: 10.1214/aos/1015345962


We extend Robins’ theory of causal inference for complex longitudinal data to the case of continuously varying as opposed to discrete covariates and treatments. In particular we establish versions of the key results of the discrete theory: the $g$-computation formula and a collection of powerful characterizations of the $g$-null hypothesis of no treatment effect. This is accomplished under natural continuity hypotheses concerning the conditional distributions of the outcome variable and of the covariates given the past. We also show that our assumptions concerning counterfactual variables place no restriction on the joint distribution of the observed variables: thus in a precise sense, these assumptions are “for free,” or if you prefer, harmless.


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Richard D. Gill. James M. Robins. "Causal Inference for Complex Longitudinal Data: The Continuous Case." Ann. Statist. 29 (6) 1785 - 1811, December 2001.


Published: December 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1043.62094
MathSciNet: MR1891746
Digital Object Identifier: 10.1214/aos/1015345962

Primary: 62P10
Secondary: 62M99

Keywords: causality , counterfactuals , longitudinal data , observational studies

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 6 • December 2001
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