Marginal Structural Model (IPTW)

Marginal structural models, introduced by Robins, Hernán, and Brumback in 2000, are causal models for the mean of a counterfactual outcome under a treatment regime, estimated by inverse-probability-of-treatment weighting. They solve the same problem as the g-formula — estimating the effect of a time-varying exposure when time-varying confounders are themselves affected by prior treatment — but through a different device: instead of modeling the outcome and confounder processes, they reweight each person by the inverse of their probability of receiving the treatment history they actually received. This creates a pseudo-population in which treatment is, by construction, unconfounded by the measured covariates, so a simple weighted regression recovers the causal effect. The companion 2000 paper applying the method to zidovudine and HIV survival showed its practical payoff. In social epidemiology, MSMs with IPTW are standard for the cumulative effects of time-varying social exposures.