Dynamic Inverse Probability Weighting

Standard IPW handles a single-time treatment: one propensity score is estimated and each observation is reweighted once. Dynamic IPW handles treatment sequences over multiple periods, estimating a propensity model at each time point and multiplying the inverse probabilities across periods. The key additional challenge is time-varying confounding — variables that are simultaneously affected by past treatment and cause future treatment — which static IPW cannot accommodate without biasing the estimate by blocking causal pathways.

Positivity requires that every individual, regardless of their covariate history, has a non-zero probability of receiving each treatment at each time point. It fails when some covariate combinations make treatment deterministic — for example, if all patients with a certain lab value always receive a specific drug. In such cases, weights become infinite and the causal effect is not identified. Checking empirical support for positivity (e.g., examining propensity score distributions) is essential before applying Dynamic IPW.

Unstabilised weights have expected values greater than one and tend to be highly variable, which increases estimator variance. Stabilised weights place the marginal (unconditional) treatment probability in the numerator, keeping the expected weight close to one and substantially reducing variance without introducing bias. In practice, stabilised weights yield narrower confidence intervals and are less sensitive to extreme observations, and they are the recommended default.

First diagnose them by examining the distribution of weights (mean, max, 99th percentile). If extreme weights are present, consider: (1) improving propensity model specification by adding interactions or using flexible machine-learning methods; (2) ensuring weights are stabilised; (3) trimming or truncating weights at a threshold such as the 99th percentile, which introduces small bias but substantially reduces variance. Always report sensitivity analyses under different trimming strategies.

Yes. A doubly robust estimator combines Dynamic IPW weights with a weighted outcome model (e.g., a marginal structural model). The resulting estimator is consistent if either the propensity models or the outcome model is correctly specified — providing a safety net against misspecification of either component. Doubly robust versions generally have better finite-sample properties than pure IPW when sample sizes are moderate.