Causal inference in longitudinal studies with history-restricted marginal structural models

A new class of Marginal Structural Models (MSMs), History-Restricted MSMs (HRMSMs), was recently introduced for longitudinal data for the purpose of defining causal parameters which may often be better suited for public health research or at least more practicable than MSMs \citejoffe,feldman. HRMSMs allow investigators to analyze the causal effect of a treatment on an outcome based on a fixed, shorter and user-specified history of exposure compared to MSMs. By default, the latter represent the treatment causal effect of interest based on a treatment history defined by the treatments assigned between the study’s start and outcome collection. We lay out in this article the formal statistical framework behind HRMSMs. Beyond allowing a more flexible causal analysis, HRMSMs improve computational tractability and mitigate statistical power concerns when designing longitudinal studies. We also develop three consistent estimators of HRMSM parameters under sufficient model assumptions: the Inverse Probability of Treatment Weighted (IPTW), G-computation and Double Robust (DR) estimators. In addition, we show that the assumptions commonly adopted for identification and consistent estimation of MSM parameters (existence of counterfactuals, consistency, time-ordering and sequential randomization assumptions) also lead to identification and consistent estimation of HRMSM parameters.

💡 Research Summary

The paper introduces History‑Restricted Marginal Structural Models (HRMSMs) as a pragmatic extension of traditional Marginal Structural Models (MSMs) for longitudinal causal inference. While MSMs define causal effects based on the entire treatment history from study start to outcome assessment, HRMSMs restrict the history to a user‑specified, fixed window of length h (e.g., the most recent 3 months or 1 year). This restriction aligns the causal estimand with many public‑health questions that focus on recent exposure, reduces dimensionality, improves computational tractability, and mitigates the loss of statistical power that often accompanies long‑lagged weighting schemes.

The authors first formalize the potential‑outcome framework for HRMSMs, retaining the standard identification assumptions used for MSMs—existence of counterfactuals, consistency, correct temporal ordering, and sequential randomization (no unmeasured time‑varying confounding). Under these assumptions, the causal parameter of interest is
θ_h(t)=E