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{1015345962,
author = {Gill, Richard D. and Robins, James M.},
title = {Causal Inference for Complex Longitudinal Data: The Continuous
Case},
journal = {Ann. Statist.},
volume = {29},
number = {2},
year = {2001},
pages = { 1785-1811},
language = {en},
url = {http://dml.mathdoc.fr/item/1015345962}
}
Gill, Richard D.; Robins, James M. Causal Inference for Complex Longitudinal Data: The Continuous
Case. Ann. Statist., Tome 29 (2001) no. 2, pp. 1785-1811. http://gdmltest.u-ga.fr/item/1015345962/