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 gcomputation formula and a collection of powerful characterizations of the gnull hypothesis of no treatment eect This is accomplished under natural continuity hypotheses concerning the conditional distributions of the outcome variable and of the covariates given the past