Marginal Structural Model

The foundational estimation technique for MSMs. Each observation is weighted by the inverse of its probability of receiving the treatment it actually received at each time point.

• Creates a pseudo-population where treatment is independent of measured confounders
• Stabilized weights reduce variance: sw = P(A|V) / P(A|L,V)
• Requires correct specification of the treatment model
• Sensitive to extreme weights; truncation is often applied at the 1st and 99th percentiles

MSMs solve a problem that standard regression cannot: when a confounder is both affected by prior treatment and predictive of future treatment.

• Example: CD4 count in HIV studies is affected by prior antiretroviral therapy and influences future treatment decisions
• Standard adjustment (conditioning on CD4) blocks the causal pathway and introduces collider-stratification bias
• MSMs handle this by modeling the marginal distribution of counterfactuals rather than conditioning on intermediate variables
• This is the defining feature that distinguishes MSMs from conventional longitudinal models

MSMs naturally extend to handle informative censoring where loss to follow-up is related to the outcome.

• Inverse probability of censoring weights (IPCW) are multiplied with treatment weights
• Assumes sequential ignorability: no unmeasured confounders for both treatment and censoring
• Final weight: sw_total = sw_treatment × sw_censoring
• Critical for supply chain disruption studies where data streams may go dark during a crisis event

A survival-analysis variant of MSMs for time-to-event outcomes with time-varying treatments.

• Estimates the causal hazard ratio in the weighted pseudo-population
• Uses robust sandwich variance estimators to account for the weighting
• Applied in supplier failure prediction: estimating the causal effect of a risk mitigation intervention on time-to-disruption
• Requires careful handling of the risk set at each event time

MSMs rely on two critical assumptions beyond no unmeasured confounding.

• Positivity: At every level of confounder history, there must be a non-zero probability of receiving each treatment level. Violations require trimming or redefining the estimand
• Correct model specification: Both the treatment model (for weights) and the structural model (for the outcome) must be correctly specified, as MSMs are doubly robust only in specific augmented forms
• Practical diagnostics include examining the distribution of weights and checking for mean weights near 1.0

MSMs and Structural Nested Models (SNMs) are the two primary g-methods for time-varying confounding.

• MSMs model the marginal mean of counterfactuals; SNMs model the conditional contrast of treatment effects within strata of confounder history
• MSMs use IPTW; SNMs typically use g-estimation
• MSMs are more intuitive to specify but more sensitive to weight instability
• SNMs handle effect modification by time-varying covariates more naturally
• Choice depends on the scientific question: population-average (MSM) vs. effect heterogeneity (SNM)

The core estimation engine behind MSMs. IPTW creates a pseudo-population where treatment assignment is independent of measured confounders by weighting each observation by the inverse of its probability of receiving the treatment it actually received.

• Stabilized weights reduce variance by multiplying by the marginal probability of treatment
• Truncation caps extreme weights to prevent a single observation from dominating the analysis
• Directly addresses time-varying confounding when weights are estimated sequentially at each time point

The central methodological challenge that MSMs are designed to solve. This occurs when a variable that affects both future treatment and the outcome is itself affected by prior treatment.

• Example: A supply chain disruption (treatment) causes inventory depletion (confounder), which in turn influences both future rerouting decisions (future treatment) and delivery delays (outcome)
• Standard regression adjustment blocks the causal pathway and introduces collider bias
• MSMs handle this by modeling the marginal structural distribution rather than conditioning on confounders

The visual language used to encode causal assumptions before fitting an MSM. A DAG represents variables as nodes and direct causal relationships as directed edges, with the critical constraint that no feedback loops exist.

• Time-ordering is explicit: nodes at time t can only affect nodes at time t+1
• DAGs identify backdoor paths that must be blocked to isolate causal effects
• The absence of an arrow is a stronger assumption than its presence—it asserts zero direct effect

The property that distinguishes a well-specified MSM from a purely predictive model. A causal relationship is invariant if it remains stable across different environments, interventions, or time periods because it captures the underlying data-generating mechanism rather than spurious correlations.

• MSMs seek to model invariant structural relationships between treatment and outcome
• Predictive models exploiting non-causal features will fail under distribution shift
• Testing invariance across supply chain regions validates the causal specification

A variance-reduction refinement of standard IPTW essential for practical MSM estimation. Instead of weighting by 1/P(treatment|confounders), stabilized weights use P(treatment)/P(treatment|confounders), centering the weights around 1.0.

• Dramatically reduces the influence of extreme weights from near-zero treatment probabilities
• Produces narrower confidence intervals and more efficient estimates
• Particularly important in supply chain applications where certain disruption responses are rare

A complementary approach to MSMs for estimating the causal effect of time-varying treatments. Unlike MSMs, which model the marginal mean of the counterfactual outcome, structural nested models model the effect of a blip of treatment at each time point.

• More robust to model misspecification of the treatment mechanism than IPTW-based MSMs
• Handles effect modification by time-varying covariates naturally
• Computationally more intensive but provides double robustness when combined with IPTW