## The Annals of Statistics

### Causal Inference for Complex Longitudinal Data: The Continuous Case

#### Abstract

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

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

Dates
First available in Project Euclid: 5 March 2002

https://projecteuclid.org/euclid.aos/1015345962

Digital Object Identifier
doi:10.1214/aos/1015345962

Mathematical Reviews number (MathSciNet)
MR1891746

Zentralblatt MATH identifier
1043.62094

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

#### Citation

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. https://projecteuclid.org/euclid.aos/1015345962

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