Understanding Marginal Structural Models for Time-Varying Exposures: Pitfalls and Tips

Abstract

Epidemiologists are increasingly encountering complex longitudinal data, in which exposures and their confounders vary during follow-up. When a prior exposure affects the confounders of the subsequent exposures, estimating the effects of the time-varying exposures requires special statistical techniques, possibly with structural (ie, counterfactual) models for targeted effects, even if all confounders are accurately measured. Among the methods used to estimate such effects, which can be cast as a marginal structural model in a straightforward way, one popular approach is inverse probability weighting. Despite the seemingly intuitive theory and easy-to-implement software, misunderstandings (or "pitfalls") remain. For example, one may mistakenly equate marginal structural models with inverse probability weighting, failing to distinguish a marginal structural model encoding the causal parameters of interest from a nuisance model for exposure probability, and thereby failing to separate the problems of variable selection and model specification for these distinct models. Assuming the causal parameters of interest are identified given the study design and measurements, we provide a step-by-step illustration of generalized computation of standardization (called the g-formula) and inverse probability weighting, as well as the specification of marginal structural models, particularly for time-varying exposures. We use a novel hypothetical example, which allows us access to typically hidden potential outcomes. This illustration provides steppingstones (or "tips") to understand more concretely the estimation of the effects of complex time-varying exposures.

Keywords: causal inference; g-formula; inverse probability weighting; marginal structural model; time-varying exposure.

Figure 1.. Causal DAGs and SWIGs compatible with example data, where U and W are unobserved variables: (a) causal DAG without W, in which A₁–L₂, A₁–Y, and A₂–Y are (conditionally) unconfounded given observed data; (b) causal DAG with W, in which A₁–Y and A₂–Y are (conditionally) unconfounded but A₁–L₂ is confounded given observed data; (c) a “template” under intervention (a₁, a₂) of SWIG that corresponds to causal DAG (a); (d) a “template” under intervention (a₁, a₂) of SWIG that corresponds to causal DAG (b).

Appendix Figure 1.. Causal DAGs and SWIGs for dynamic regimes and without identifiability conditions: (a) causal DAG identical to Figure 1(b); (b) causal DAG with the arrow from L₂ on Y, in which L₂ is affected by A₁, and the A₁–L₂ association is confounded by unobserved W; (c) a “template” under intervention g = (g₁, g₂) = (g₁(L₁), g₂(L₁, A₁, L₂)) of SWIG that corresponds to causal DAG (a); (d) a “template” under intervention (a₁, a₂) of SWIG that corresponds to causal DAG (b).