The Annals of Statistics

Causal Inference for Complex Longitudinal Data: The Continuous Case

Richard D. Gill and James M. Robins

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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.

Article information

Ann. Statist., Volume 29, Number 6 (2001), 1785-1811.

First available in Project Euclid: 5 March 2002

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Zentralblatt MATH identifier

Primary: 62P10: Applications to biology and medical sciences
Secondary: 62M99: None of the above, but in this section

Causality counterfactuals longitudinal data observational studies


Gill, Richard D.; Robins, James M. Causal Inference for Complex Longitudinal Data: The Continuous Case. Ann. Statist. 29 (2001), no. 6, 1785--1811. doi:10.1214/aos/1015345962.

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