Marginal Structural Model (MSM)

The foundational estimation technique for MSMs. Each subject receives a weight inversely proportional to their probability of receiving the treatment they actually received, conditional on their covariate and treatment history.

• Stabilized Weights: A variant that reduces variability by multiplying the inverse probability weight by the marginal probability of treatment.
• Pseudo-Population: Weighting creates a synthetic sample where treatment is unconfounded, allowing a simple regression of the outcome on the treatment history to yield a causal estimate.
• Handles Feedback: Explicitly adjusts for scenarios where a confounder (e.g., CD4 count) is affected by prior treatment (e.g., antiretroviral therapy) and predicts future treatment.

MSMs are uniquely suited to handle time-dependent confounders affected by prior treatment, a scenario where standard regression adjustment fails.

• The Feedback Loop: In longitudinal studies, a covariate like disease severity is both a confounder (predicts future treatment) and an intermediate variable (is affected by past treatment).
• G-Computation Alternative: While g-computation also addresses this, MSMs are often preferred for their ease of implementation with standard weighted regression software.
• Censoring Weights: An additional set of weights can be applied to adjust for potentially informative loss to follow-up, assuming censoring is random conditional on observed history.

MSMs estimate a marginal (population-average) causal effect, contrasting with the conditional (subject-specific) effects from mixed models or G-estimation of structural nested models.

• Marginal Effect: Compares the expected outcome if the entire population were treated versus untreated, a parameter often most relevant for public health policy.
• Collapsibility: The odds ratio from a logistic MSM is non-collapsible, meaning the marginal effect differs from the conditional effect even without confounding.
• Link Function Choice: Using a log link for binary outcomes in an MSM directly estimates a marginal risk ratio, a collapsible measure that avoids the non-collapsibility issue of the odds ratio.

Valid causal inference with MSMs depends critically on the positivity assumption and correct specification of the treatment and censoring models.

• Positivity: Requires a non-zero probability of each treatment level for every covariate history. Violations occur if a treatment is strictly contraindicated for a subgroup.
• Weight Truncation: Extreme weights can inflate variance. Truncating weights at a percentile (e.g., 1st and 99th) trades bias for precision.
• Doubly Robust MSMs: Combine IPTW with an outcome regression model to provide two chances to correctly specify the model, yielding a consistent estimate if either the treatment model or the outcome model is correct.