A marginal structural model for multiple-outcome survival data:assessing the impact of injection drug use on several causes of death in the Canadian Co-infection Cohort.

It is often the case that interest lies in the effect of an exposure on each of several distinct event types. For example, we are motivated to investigate in the impact of recent injection drug use on deaths due to each of cancer, end-stage liver disease, and overdose in the Canadian Co-infection Cohort (CCC). We develop a marginal structural model that permits estimation of cause-specific hazards in situations where more than one cause of death is of interest. Marginal structural models allow for the causal effect of treatment on outcome to be estimated using inverse-probability weighting under the assumption of no unmeasured confounding; these models are particularly useful in the presence of time-varying confounding variables, which may also mediate the effect of exposures. An asymptotic variance estimator is derived, and a cumulative incidence function estimator is given. We compare the performance of the proposed marginal structural model for multiple-outcome data to that of conventional competing risks models in simulated data and demonstrate the use of the proposed approach in the CCC.