In observational studies with exposures or treatments that vary over time, standard approaches for adjustment of confounding are biased when there exist time-dependent confounders that are also affected by previous treatment. This paper introduces marginal structural models, a new class of causal models that allow for improved adjustment of confounding in those situations. The parameters of a marginal structural model can be consistently estimated using a new class of estimators, the inverse-probability-of-treatment weighted estimators.

Standard methods for survival analysis, such as the time-dependent Cox model, may produce biased effect estimates when there exist time-dependent confounders that are themselves affected by previous treatment or exposure. Marginal structural models are a new class of causal models the parameters of which are estimated through inverse-probability-of-treatment weighting; these models allow for appropriate adjustment for confounding. We describe the marginal structural Cox proportional hazards model and use it to estimate the causal effect of zidovudine on the survival of human immunodeficiency virus-positive men participating in the Multicenter AIDS Cohort Study. In this study, CD4 lymphocyte count is both a time-dependent confounder of the causal effect of zidovudine on survival and is affected by past zidovudine treatment. The crude mortality rate ratio (95% confidence interval) for zidovudine was 3.6 (3.0-4.3), which reflects the presence of confounding. After controlling for baseline CD4 count and other baseline covariates using standard methods, the mortality rate ratio decreased to 2.3 (1.9-2.8). Using a marginal structural Cox model to control further for time-dependent confounding due to CD4 count and other time-dependent covariates, the mortality rate ratio was 0.7 (95% conservative confidence interval = 0.6-1.0). We compare marginal structural models with previously proposed causal methods.

Even in the absence of unmeasured confounding factors or model misspeci cation, standard methods for estimating the causal effect of time-varying treatments on survival are biased when (a) there exists a time-dependent risk factor for survival that also predicts subsequent treatment, and (b) past treatment history predicts subsequent risk factor level. In contrast, methods based on marginal structural models (MSMs) can provide consistent estimates of causal effects when unmeasured confounding and model misspeci cation are absent. MSMs are a new class of causal models whose parameters are estimated using a new class of estimators-inverse-probability-of-treatment weighted estimators. We use a marginal structural Cox proportional hazards model to estimate the joint effect of zidovudine (AZT) and prophylaxis therapy for Pneumocystis carinii pneumonia on the survival of H IV-positive men in the Multicenter A IDS Cohort Study, an observational study of homosexual men. We obtained an estimated causal mortality rate (hazard) ratio of .67 (conservative 95% con dence interval .46-.98) for AZT and of 1.14 (.79, 1.64) for prophylaxis therapy. These estimates will be consistent for the true causal rate ratios when the functional forms chosen for our models are correct and data have been obtained on all time-independent and time-dependent covariates that predict both subsequent treatment and mortality.

Even in the absence of unmeasured confounding factors or model misspecification, standard methods for estimating the causal effect of a time-varying treatment on the mean of a repeated measures outcome (for example, GEE regression) may be biased when there are time-dependent variables that are simultaneously confounders of the effect of interest and are predicted by previous treatment. In contrast, the recently developed marginal structural models (MSMs) can provide consistent estimates of causal effects when unmeasured confounding and model misspecification are absent. We describe an MSM for repeated measures that parameterizes the marginal means of counterfactual outcomes corresponding to prespecified treatment regimes. The parameters of MSMs are estimated using a new class of estimators - inverse-probability of treatment weighted estimators. We used an MSM to estimate the effect of zidovudine therapy on mean CD4 count among HIV-infected men in the Multicenter AIDS Cohort Study. We estimated a potential expected increase of 5.4 (95 per cent confidence interval -1.8,12.7) CD4 lymphocytes/l per additional study visit while on zidovudine therapy. We also explain the theory and implementation of MSMs for repeated measures data and draw upon a simple example to illustrate the basic ideas.

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