Multi-period Propensity Score Weighting
Multi-period Propensity Score Weighting for Causal Inference · Also known as: longitudinal propensity score weighting, multi-wave PSW, time-varying propensity score weighting, sequential propensity score weighting
Multi-period propensity score weighting extends the standard propensity score weighting framework to settings with repeated measurements and time-varying treatments. It constructs stabilised inverse probability weights (IPW) at each time point so that the weighted sample resembles a sequence of randomised experiments, allowing unbiased estimation of causal effects under longitudinal confounding.
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When to use it
Use multi-period PSW when units are observed over three or more time points, treatment assignment is re-decided each period based on evolving covariate values, and you wish to estimate the causal effect of a time-varying treatment sequence. It is well-suited to epidemiological cohort studies, programme evaluations with rolling enrolment, and policy analyses with staggered uptake. Do not use it when treatment is fixed at baseline (standard PSW is sufficient), when there are strong unmeasured time-varying confounders (the method cannot handle them), or when the number of time periods is very large relative to sample size, which causes weight product instability.
Strengths & limitations
- Accounts for time-varying confounding — covariates that change over time and mediate the treatment-outcome path are properly handled through sequential re-weighting.
- Creates a pseudo-population analogous to a sequential randomised trial, providing a clear causal interpretation of the estimated effect.
- Stabilised weights have lower variance than raw IPW, improving finite-sample performance.
- Compatible with a wide range of outcome models (linear, logistic, Cox) and can be combined with doubly robust estimators for added robustness.
- Does not condition on post-treatment variables, avoiding the collider-stratification bias that would arise from adjusting for mediators in standard regression.
- Relies on sequential ignorability (no unmeasured time-varying confounders) at every period — a strong assumption that cannot be fully verified from the data.
- Weight products across many periods can become highly variable or extreme, especially in long follow-up studies, requiring careful trimming and diagnostics.
- Requires correctly specifying the propensity model at each period; misspecification of any period's model propagates bias into the cumulative weight.
- Can lose effective sample size substantially after weighting, reducing statistical power compared to an unweighted analysis.
- Implementation complexity increases with the number of periods and the richness of the covariate history.
Frequently asked
How is multi-period PSW different from standard propensity score weighting?
Standard PSW builds a single weight from one propensity model estimated at baseline. Multi-period PSW builds a separate propensity model at each time period and multiplies the period-specific weights together, allowing it to handle time-varying treatments and time-varying confounders that standard PSW cannot address.
What is sequential ignorability and why does it matter?
Sequential ignorability means that, at every time period, treatment assignment is independent of future potential outcomes conditional on the observed treatment and covariate history. This is the multi-period analogue of the unconfoundedness assumption. If any important time-varying confounder is unmeasured, the cumulative weights cannot remove its bias and the causal estimate is invalid.
How should I handle extreme weights?
Check the distribution of cumulative weights before fitting the outcome model. A common rule trims weights above the 99th percentile or at a fixed ceiling such as 10 or 20. After trimming, recheck covariate balance and effective sample size. If many weights remain extreme, the propensity model may be misspecified or positivity may be violated.
Can I combine multi-period PSW with doubly robust methods?
Yes. Augmented IPW (AIPW) or targeted maximum likelihood estimation (TMLE) in the multi-period setting combine the weighting step with an outcome model, so the estimate remains consistent if either the propensity model or the outcome model is correctly specified, offering added protection against misspecification.
How many time periods does multi-period PSW require?
Technically it applies from T = 2, but the method's advantage over standard PSW becomes meaningful with three or more periods in which treatment can vary. With many periods (e.g., T > 20), weight product instability becomes a serious concern, and alternative estimators such as g-estimation or TMLE may be preferable.
Sources
- Hernán, M. A., & Robins, J. M. (2020). Causal Inference: What If. Chapman & Hall/CRC. link ↗
- Cole, S. R., & Hernán, M. A. (2008). Constructing inverse probability weights for marginal structural models. American Journal of Epidemiology, 168(6), 656-664. DOI: 10.1093/aje/kwn164 ↗
How to cite this page
ScholarGate. (2026, June 3). Multi-period Propensity Score Weighting for Causal Inference. ScholarGate. https://scholargate.app/en/causal-inference/multi-period-propensity-score-weighting
Which method?
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