In point treatment marginal structural models with treatment A, outcome Y and covariates W, causal parameters can be estimated under the assumption of no unobserved confounders. Three estimates can be used: the G-computation, Inverse Probability of Treatment Weighted (IPTW) or Double Robust (DR) estimates. The properties of the IPTW and DR estimates are known under an assumption on the treatment mechanism that we name "Experimental Treatment Assignment" (ETA) assumption. We show that the DR estimating function is unbiased when the ETA assumption is violated if the model used to regress Y on A and W is correctly specified. The practical consequence is that the IPTW estimate is biased at finite sample size when the ETA assumption is approximately or theoretically violated, whereas the finite sample bias for the DR estimate is negligible if the model used to regress Y on A and W is correctly specified. This result also implies that estimating point treatment causal parameters using a DR estimating function is more robust than using the G-computation formula. We conclude with a methodology to construct DR estimates for a general data structure and prove that such DR estimates are more robust than their corresponding maximum likelihood estimates.
Statistical Methodology | Statistical Models | Statistical Theory | Survival Analysis
Neugebauer, Romain and van der Laan, Mark J., "Why Prefer Double Robust Estimates? Illustration with Causal Point Treatment Studies" (September 2002). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 115.
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