Standard regression methodologies for the estimation of treatment effects do not yield a sensible causal interpretation when adjusting for time-varying covariates confounded with the treatment history. In such studies, the casual null hypothesis of interest is whether subjects' responses would be the same regardless of treatment history. Under the sequential randomization assumption, the "G-computation functional" provides a representation of the expected response for a given treatment history, which is the causal quantity of interest in a longitudinal study. However, standard parameterizations of the components in the G-functional lead to false rejection of the null hypothesis in large samples. We will review derivation of the G-functional and reasons behind this null hypothesis paradox as a motivation for an alternative approach using the inverse-probability-weighted estimators of Marginal Structural Models.
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