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

Tomohiro Shinozaki,Etsuji Suzuki

doi:10.2188/jea.je20200226

Tomohiro Shinozaki, Etsuji Suzuki

Open Access

https://doi.org/10.2188/jea.je20200226

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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.

Highlights

A counterfactual approach formalizes the language of cause and effect,7–13 but has triggered the explosive development of novel analytic methods, including propensity scores14–19 and regression modelbased estimation methods,20,21 which have been evolved into doubly robust estimation
While no existent theory in the statistics literature had offered clear guidance for adjusting or not adjusting for such intermediate variables to estimate the effect of time-varying exposures, new causal methodologies emerged in the 1980s
These include Robins’ unified approach, which is comprised of the generalized computational algorithm formula and estimation methods of two classes of counterfactual, or structural, models

Summary

Introduction

ON THE TOPICWhen we try to say something meaningful about a specific exposure–outcome causal relationship, counterfactual models are among the most popular and widely accepted approaches in the epidemiologic community. A counterfactual approach formalizes the language of cause and effect, but has triggered the explosive development of novel analytic methods, including propensity scores (ie, the probability of exposure conditional on measured confounders) and regression modelbased estimation methods (ie, multivariable-adjusted outcome modeling, possibly followed by averaging predicted risks under distinct exposure statuses), which have been evolved into doubly robust estimation. More importantly, a counterfactual approach has spurred extensive discussion on the assumptions for inferring causality from data and the conditions for specific statistical methods to work using, for example, causal diagrams. Yet, the most striking illustration brought about by the counterfactual approach may be that it can offer an elegant solution to the controversy surrounding the definition and estimability of the effects of exposures that vary over time. While no existent theory (at the time) in the statistics literature had offered clear guidance for adjusting or not adjusting for such intermediate variables to estimate the effect of time-varying exposures, new causal methodologies emerged in the 1980s. These include Robins’ unified approach, which is comprised of the generalized computational algorithm formula (abbreviated as g-formula) and estimation methods (ie, inverse probability weighting and g-estimation) of two classes of counterfactual, or structural, models.

Objectives

Conclusion